Molecular Basis of the Phototherapy of Furocoumarins: A Theoretical Study

In: Psoriasis: Causes, Diagnosis and Treatment ISBN 978-1-61209-314-7

Editor: Julian A. Carrasco © 2011 Nova Science Publishers, Inc.

Chapter 1

MOLECULAR BASIS OF THE PHOTOTHERAPY

OF FUROCOUMARINS: A THEORETICAL STUDY

L. Serrano-Andrés and J.J. Serrano-Pérez*

Universitat de València, Instituto de Ciencia Molecular,

P. O. Box 22085, ES-46071 Valencia, Spain

Dedicated to the memory of Luis Serrano-Andrés, great scientist, teacher and friend,

who passed away recently.

ABSTRACT

Life on Earth depends, both directly and indirectly, on the influence that light has on

chemistry. The energy of the Sun´s visible and ultraviolet radiation promotes processes

that not only permit the continued existence of life on the planet such as in

photosynthesis, but which are keys for evolution by means of mutations. In molecules,

electronic excited states participate in photoinduced events as well as in thermally

activated reactions, even in many cases in which only the ground state is believed to be

involved. Studying a system in an excited state, far away from its relaxed situation, is a

challenge for chemists, both experimentalists and theoreticians.

The effect of electromagnetic radiation on biological objects extends from heating to

complex photochemistry, electronic excitation, and alteration of DNA. One of the key

points of phototherapy, which is maybe the medical area that represents better the

connection among Medicine, Physics, and Chemistry, is that a proper interaction with the

genetic material may entail beneficial effects. Furthermore, it is becoming one of the

most promising strategies against a plethora of diseases. Specifically, psoralens or

furocoumarins are used in PUVA (Psoralen + UV-A radiation) therapy to treat some skin

disorders such as psoriasis and vitiligo. Understanding the photochemical mechanism of

that type of photosensitization is crucial in order to find better drugs.

Since macroscopic properties (in this case, the photosensitizing ability) of a molecule

are determined by its electronic structure, we have to resort to Quantum Mechanics to

* E-mail address: [email protected]

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L. Serrano-Andrés and J. J. Serrano-Pérez 2

study the photosensitizing effectiveness of furocoumarins. The use of computers and

high-level programs has allowed us to analyze chemical processes theoretically, looking

for the whys and the wherefores. Indeed, a constructive interplay between theory and

experiment can provide an insight into the chemistry of the electronic state that cannot be

easily derived from the observed spectra alone.

This chapter is focused on the study of the family of furocoumarins, well-known

photosensitizers, on theoretical grounds. It is necessary to analyze the excited states of

these molecules as a first step to understand the basic mechanistic aspects of the

phototherapeutic action.

INTRODUCTION

In photomedicine the principles of photobiology, photochemistry, and photophysics are

applied to the diagnosis and therapy of diseases. Not only does therapeutic photomedicine

pursue the suppression of ongoing deterioration processes, but also tries to prevent, modulate

or abrogate the pathogenic mechanisms causing the problem [1].

Throughout the XVI century physicians realized that Physics and Chemistry were very

important in the art of healing. Modern Medicine relies on this knowledge in order to

understand how changes are made in the body and how they would be caused or prevented. It

was Paracelsus who first introduced chemical therapy in his book Labyrinthus medicorum

errantium (1553). The impact of his ideas in those days was shown by the increasing number

of followers of the new trend. Nowadays, Medicine is barely related to the classical discipline

practiced by Hippocrates or Galen.

Among the oldest but less explored procedures, the field of phototherapy is presently

undergoing a fast and sustained growing [2]. The practice consists in the employment of

electromagnetic radiation coupled with a drug, the photosensitizer. The absorption of energy

by this chromophore triggers a chain of photochemical events with therapeutic consequences.

The benefits of sunlight on human health are known from antiquity. Just to recall that

Herodotus and Hippocrates pleaded for the use of sunlight to treat several diseases [2].

However, the development of phototherapy did not reach its heyday until the 20th

century

[2,3,4]. Niels Ryberg Finsen, known as the father of phototherapy, was the first who studied

the technique scientifically, and he was awarded with the Physiology or Medicine Nobel Prize

in 1903 ―in recognition of his contribution to the treatment of diseases, especially lupus

vulgaris, with concentrated light radiation, whereby he has opened a new avenue for medical

science‖[5]. Indeed, in his book Phototherapy (Arnold, London, 1901) he pleaded for the

recognition of such a technique: ―In conclusion, the treatment which I have described seems

to have proved its value, and there is every reason to give it the place it deserves in

therapeutics, a place which it is at present still far from having obtained, doubtless owing to

its strangeness and unintelligibility. In reality, its scientific basis is much better and more

solid than that of many other methods of medical treatment‖. Since then a plethora of diseases

has been successfully treated by phototherapeutical procedures: psoriasis, vitiligo, jaundice,

rickets, and some classes of cancer. Nowadays, phototherapy is indeed considered a major

therapeutic strategy for health care in dermatology and has dramatically influenced the

treatment of many skin disorders [6].

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Molecular Basis of the Phototherapy of Furocoumarins: A Theoretical Study 3

There are different phototherapeutic techniques [2]. Sometimes the chromophore is

already present in the tissue and the phototherapy takes place naturally, e.g., the cure of

neonatal hyperbilirubinemia or the photoregeneration of vitamin D, and this area is coined as

phototherapy. Differently, in the treatment named photochemotherapy, a drug is administered

to act as a photosensitizer, a substance which is harmless in the dark but active upon

absorption of radiation, typically ultraviolet, visible, or near infrared light.

Two basic photochemical mechanisms are responsible for the phototherapeutical activity.

On the one hand, the photosensitizer can directly react with DNA bases forming stable

adducts which interfere the genetic activity [7,8,9,10]. On the other hand, the photosensitizer

can transfer its excess energy to molecular oxygen available in the cellular environment,

generating highly reactive singlet oxygen able to damage target tissues. This type of protocol

is known as photodynamic therapy (PDT) [10,11,12]. It was in 1976 that Weishaupt et al.

[13] made a breakthrough postulating that singlet oxygen is the cytotoxic agent responsible

for the photo-inactivation of tumor cells. Singlet oxygen is a strong electrophilic species that

reacts with different compounds [14], including some components of the cellular membrane

causing cell death by apoptosis [15]. Advances in PDT depend on our understanding of the

physics, chemistry, and biology of the interactions of light, tissues, and photosensitizer

[16,17,18,19]. Unlike radiation therapy, DNA is not the major target (typically

photosensitizers localize in/on cell membranes).

Figure 1. Different areas for application of phototherapy. The effect of electromagnetic radiation over

the body may excite the photosensitizer to provoke changes in DNA or to react with molecular oxygen.

When light interacts with matter or changes the medium in which it is propagated many processes may

take place: absorption, emission, diffraction, reflection, refraction, scattering, polarization…

PUVA

Phototherapy

Photochemotherapy SKIN FAT BONE

hPs Ps*

+

+

PUVA

OO PDT

Field Atenuation

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A commonly accepted classification of the photochemotherapeutic reactions comprises

three types of mechanisms. Types I and II correspond to oxygen-dependent pathways for PDT

activity, taking place when light, in the presence of a photosensitizer and molecular oxygen,

induces a chemical reaction in a substrate [10,11,20,21]. In type I reactions, the photoactive

compound in its triplet state1 promotes an electron transfer reaction to molecular oxygen,

leading to the formation of O2·, OH·, or HO2· radicals. Type II reactions correspond to energy

transfers from the triplet state of the photosensitizer to dioxygen, generating in the former the

reactive 1g excited state [11]. All these intermediate species later interact with components

of the cell membrane and may lead to cellular damage that eventually contributes to skin

photosensitization, mutation, error-prone DNA repair, and carcinogenesis [10,20,22,23]. In

contrast to the previous mechanisms, oxygen-independent type III reactions seem to lead to

direct photobinding between the photosensitizer and the DNA base monomers [24,25].

Furocoumarins (also named psoralens) are a class of heterocyclic compounds with a

known phototherapeutic activity that takes place via the three described mechanisms [26].

These systems have been found to possess mutagenic properties when applied in conjunction

with near UV-A light (320–400 nm) exposure [8,9,10,27,28,29,30,31,32]. The treatment,

coined psoralen + UV-A (PUVA) therapy, has been specifically designed to treat different

skin disorders such as psoriasis and vitiligo [33,34,35,36]. The use of plants rich in

furocoumarins constitutes a remedy known since many centuries ago that was employed in

ancient India and Egypt to treat leukoderma and vitiligo [29]. In 1834 Kalbruner isolated 5-

methoxypsoralen (5-MOP) from bergamot oil, and Abdel Monem El Mofty actually made a

breakthrough employing 8-methoxypsoralen (8-MOP), which had just been isolated by

Fahmy, to treat vitiligo in the 1940s. In 1953, Lerner, Denton and Fitzpatrick, and later

Parrish in 1974 [34], published studies of the treatment of both psoriasis and vitiligo with 8-

MOP coupled with UV-A radiation. In the 1950s, 8-MOP was made available commercially,

followed later by the synthetic compound 4,5´,8-trimethylpsoralen (TMP)[9]. Nowadays,

PUVA therapy, together with narrow-band UV-B therapy (NBUVB), is one of the most

widely used types of phototherapy [37]. Specifically, photochemotherapy with 8-MOP and

long-wavelenght UV-A light (PUVA) has been extensively used for the treatment of various

skin diseases since its approval in 1982 by the US Food and Drug Administration. For

instance, a recent retrospective study describes the results of the treatment with PUVA,

including topical and systemic treatment, over a period of 14 years on ca. 1000 patients in the

Spanish Community of Valencia region[38].

Initially, the interaction of psoralens with DNA was thought to be responsible for the

beneficial effects of PUVA therapy. The oxygen-dependent mechanism (the photodynamic

action, see Figure 2) was discovered later, and involves an energy transfer between the

furocoumarin (in its lowest triplet excited state) and molecular oxygen (in its triplet ground

state 3g

) present in the cellular environment ready to generate singlet oxygen

1O2 (

1g),

which is a strong electrophilic species that reacts with some components of the cellular

membrane causing cell death by apoptosis [15].

1 A triplet state is an allowed state (from a quantum-mechanical viewpoint, some physical quantities, like energy or

angular momentum, can be changed only by discrete amounts rather than being capable of varying continuously

or by any arbitrary amount) of the molecule in which the spin multiplicity is S = 1 (then 2S+1=3). In singlet

states, spin multiplicity is S = 0 (then 2S+1=1). In the overwhelming majority of molecules the ground state is a

singlet state, then a triplet state is often an excited state of the molecule. Spin is a purely quantum-mechanical

property, and cannot really be thought of classically.

PROOFS ONLY


Figure 2. Oxygen-dependent PUVA mechanism. In the case of molecular oxygen, the ground state (i.e.,

the most favourable state from an energetic viewpoint) is a triplet state, characterized by two electrons

with parallel spins in different highest-lying molecular orbitals.

It is generally assumed that the oxygen-independent mechanism of PUVA therapy

implies a [2+2] photocycloaddition of psoralen in its lowest triplet state and a pyrimidine

DNA base monomer [7,9,10,30,32]. The photoreactive process seems to take place in three

phases. The first step occurs in the dark: The furocoumarin is inserted between adjacent

pyrimidine base pairs in the DNA duplex, forming a complex which is stabilized by stacking

interactions. In a second step, the absorption of one photon by psoralen induces the formation

of monoadducts with the neighboring pyrimidine via interaction of the respective carbon-

carbon double bonds that both compounds have. Two different monoadducts, pyrone (PMA)

and furan (FMA) types, can then be formed by interaction of the C=C double bond of the

pyrimidine base with the C3=C4 double bond of the pyrone ring and the C4=C5 double bond

of the furan ring in psoralens, respectively (see Figure 3 and Figure 4). In this regard, thymine

has been established as the most favorable nucleoase to photoreact with furocoumarins, in

accordance with its predominance in the formation of cyclobutane dimers (T<>T) in UV-

irradiated DNA [39,40]. Indeed, they are the primary cause of melanomas in humans.

Furthermore, on irradiation of aqueous solutions containing purine and pyrimidine bases and

psoralen, modifications in the fluorescence spectra were obtained only with the pyrimidine

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bases [41]. In a third step, the monoadduct may absorb another photon, inducing the other

photoreactive C=C double bond to interact with a thymine on the opposite DNA strand.

Figure 3. Oxygen-independent PUVA mechanism.

Therefore, a diadduct that crosslinks the DNA helix is produced. It has been shown that

furocoumarins are able to form molecular complexes when added to an aqueous solution of

nucleic acids [7] and the formation of monoadducts and diadducts has been analyzed by

studying the elasticity of a psoralen-DNA mixture after irradiation. Photoadducts between

furocoumarins and thymine have also been characterized with X-ray [42] and 1H NMR

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[43,44] spectroscopies. The poly[dA-dT]·poly[dA-dT] sequence region appears to be the most

favorable site for the photocycloaddition reactions of furocoumarins [45].

The underlying mechanisms implied and the contribution of the different psoralen

derivatives are not clearly elucidated. Diadducts, for instance, are said to be formed only by

means of the furan-monoadduct, which is the only adduct capable to form cross-links at 360

nm [43,46], and although it has been described as the major component, a significant amount

of PMA is observed employing many derivatives [43,44,47]. Despite the fact that both double

bonds C4=C5 and C3=C4 are able to react with thymine, several proposals indicate that the

former is the most biologically photoreactive [32], a question that is still under debate.

Regarding TMP, addition to the C3=C4 pyrone double bond has been documented to be a

minor reaction compared to addition to the C4=C5 furan double bond. In contrast, the

reaction of 8-MOP with DNA yields a substantial amount of the pyrone-side monoadduct,

PMA [44].

It is believed that the triplet state of the photosensitizer is involved to build the DNA

cross-linked adducts given that the intersystem-crossing quantum yield2, a magnitude that

measures the probability of population of the triplet manifold, has been established 0.076 for

FMA [48]. The involvement of one or other monoadduct in the cross-link process is unclear.

Both PMA and FMA adducts are formed by irradiation at 365.5 nm (3.39 eV)3 and are non-

fluorescent and fluorescent, respectively [49,50,51]. Several studies support, on the other

hand, that FMA monoadducts, after irradiation with UV light at 253.7 nm (4.89 eV),

decompose yielding the original products [49]. Other studies have reported that adduct

distribution in DNA samples differs depending on whether 341.5 nm (3.63 eV) or 397.9 nm

(3.12 eV) light was used: In the former case the primary product is the diadduct whereas in

the latter it is a furan-side monoadduct, although a small but definite number of diadducts

were also found [52]. Monoadducts and diadducts can be split into original monomers under

irradiation with short wavelength UV light [31,53]. Furocoumarins also display effects over

cellular membrane components by means of C4-photocycloaddition between the

furocoumarin and the unsaturated fatty acids [23,26].

Regarding the clinical use of furocoumarins (see Figure 4), 8-MOP is used as an oral

photoactive chemical for the treatment of vitiligo [29] and psoriasis [34]. 5-MOP has been

introduced as an effective oral drug in the photochemotherapy of psoriasis because, in

comparison to 8-MOP, it shows less acute side effects and is slightly better tolerated by

patients. On the other hand, khellin has been found to be useful in the photochemotherapeutic

treatment of vitiligo [10]. This compound does not show long-term side effects and

phototoxic skin erythema reactions and seems to form mainly monoadducts. With respect to

TMP, it is used in the treatment of both psoriasis and vitiligo [54]. And last but not least, 3-

CPS (3-carbethoxypsoralen) has been tested in the photochemotherapy of psoriasis [55].

Apparently, it gives rise only to monoadducts with DNA, being considered as a non-

2 The quantum yield of a given process gives the efficiency of such a process as the ratio between the molecules

which undergo the process and the total number of excited molecules (that is, total number of photons absorbed).

A fully effective process would yield a ratio one. 3 There are some possibilities to express the energy of a quantum state or a given radiation. In the International

System of Units, energy is expressed in joules (J), but in atoms and molecules electron volt is preferred (given

that energy has dimensions of electric charge times electric potential: i.e., the potential energy of a particle of

charge e at a point where the potential is 1 volt), or even wavelength (due to the relation: E = Planck´s contant ×

frequency, and frequency = speed of light/wavelength; the higher the energy or frequency, the lower the

wavelength).

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carcinogenic alternative to 8-MOP. In summary: i) All the mentioned furocoumarins produce

monoadducts; ii) Only psoralen and TMP show a very strong ability to build diadducts; iii) 5-

MOP and 8-MOP do not have such a pronounced trend; and finally, iv) Diadducts are not

obtained from 3-CPS and khellin [20].

Figure 4. Structure of some relevant furocoumarins: psoralen, 8-MOP (8-methoxypsoralen), 5-MOP (5-

methoxypsoralen), TMP (4,5´,8-trimethylpsoralen), 3-CPS (3-carbethoxypsoralen), and khellin.

It is thought that illuminating the sample with UV-A (320-400 nm) or UV-B (312-320

nm) light leads to monoadducts and diadducts or just monoadducts, respectively, because the

higher-energy radiation is capable of breaking the inter-strand cross-links [53]. Formation of

cross-links was thought to be extremely relevant for the therapeutic effectiveness, although it

is also known that diadducts cause adverse side effects such as carcinogenesis, mutagenesis,

and immunosuppression. Only furocoumarins with bifunctional groups such as psoralen can

form diadducts and may produce undesired mutagenic consequences. Certain monofunctional

furocoumarins have been proved to yield as efficient phototherapy as bifunctional

OO O

OO O

OO O

OO O

OO O

OO

Psoralen 8-MOP

5-MOPTMP

3CPS Khellin

OCH3

OCH3

CH3

CH3

CH3

O

CH3

OCH3

OCH3

CO2CH2CH3

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furocoumarins, suggesting that the induction of lesions in DNA cannot be considered as the

only mechanism responsible for the phototherapeutic effects and most probably a PDT

process takes place as well.

Besides, these compounds also interact with molecular oxygen [20,22,55,56,57,58,59]. It

is known that molecular oxygen quenches the photochemical reaction between psoralens and

thymine [57,60], and that psoralen and, chiefly 3-CPS, are a priori the most effective

producers of 1O2 [20]. In addition, all the psoralen derivatives were found to generate O2

·- (or

HO2·) simultaneously along with the production of 1O2 [20]. Other researchers point out that

8-MOP is a good photodynamic sensitizer in aqueous solution [22,57]. Furocoumarins may

also produce 1O2 even when complexed with or covalently bound to DNA [61]. Since

1O2 and

O2·- generated by psoralens can induce photooxidation of lipids, it is conceivable that these

reactive oxygen moieties cause the membrane-damaging effects. A good similarity exists

between 1O2 production of a furocoumarin and both the appearance of erythema and the

pigmentation activity in the human skin [22].

The determination of the relative contribution of one (adduct formation) or other (singlet

oxygen generation) process to the effectiveness of the PUVA therapy is still obscure. It has

been observed that molecular oxygen quenches the photochemical reaction between psoralens

and thymine [57,60], whereas there are evidences indicating that the binding of 8-

methoxypsoralen (8-MOP) to double stranded poly-(dA-dT) inhibits the furocoumarin ability

to sensitize via singlet oxygen generation [57]. In principle both mechanisms can be expected

to be competitive, not synergic, although higher values of singlet oxygen production have

been reported for complexed furocoumarins than for the free compounds for psoralen, 8-

MOP, and 5-MOP [62,63]. The yield of formation and activity of singlet oxygen from the

different furocoumarins has been estimated by several research groups, but no agreement has

been reached due to the problems in evaluating the generation of the species in different

conditions and the simultaneous production of other oxygen radicals [20].

Hence, we can see how important furocoumarins are in modern Medicine. The state-of-

the-art in synthesis of psoralen and analogs was reviewed in the early 1990s [64]. An intense

experimental research is emerging in recent years. Understanding the photophysical

properties of furocoumarins represents a crucial step in order to rationalize the corresponding

phototherapeutic mechanisms.

Spectroscopic techniques give important information about the absorption and emission

processes in furocoumarins. The low-lying region of the absorption spectrum of psoralen, the

reference compound, has two main bands: A weak and structured band is observed ranging

from 360 to 270 nm (3.44–4.77 eV) and a sharp feature appears at 240 nm (5.16 eV) in

aqueous solution and ethanol [65,66]. Both fluorescence and phosphorescence emissions have

been detected for psoralen in ethanol (77 K) at 409 nm (3.03 eV) and 456 nm (2.72 eV, band

origin), respectively. The phosphorescence/fluorescence quantum yield ratio, 7.1, indicates

the effectiveness of an intersystem crossing (ISC) mechanism [67], i.e., the transfer of energy

between states of different spin multiplicity (for instance from a singlet to a triplet state), a

process that is typically orders of magnitude slower than that between states of the same

multiplicity, named internal conversion (for instance singlet to singlet). It has been proposed

that photoreactivity of furocoumarins proceeds through the lowest-lying triplet state (T1) in all

types of photosensitization, that is, PDT and PUVA therapies [10]. It can be therefore

expected that by increasing the quantum yield of the triplet formation, the phototherapeutic

action will be enhanced.

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Unfortunately, the experimental data are scarce. The basic trends of the absorption

spectra are in all cases similar. The intensity pattern varies for the series of furocoumarin

compounds and the position of the band maximum is strongly solvent dependent: 340 nm

(3.60 eV) for 8-MOP in different environments [45,68]; 335 nm (3.66 eV) in ethanol, 334-

305 nm (3.71-4.02 eV) in dioxane, and 313 nm (3.91 eV) in water for 5-MOP [67,69]; 338-

320 nm (3.62-3.83 eV) for khellin in various solvents [70,71]; 335 nm (3.66 eV) for TMP in

several media [54,67], and 318 nm (3.85 eV) in both water and ethanol-water mixture for 3-

CPS [72]. Independently of the location of the maxima, this electronic transition is

undoubtedly responsible for the UV-A absorption, source of the phototherapeutic action.

Both fluorescence (F) and phosphorescence (P) emissions have been detected for the

different compounds in a similar energy range: for 8-MOP in different solvents and

temperatures at 482-440 nm (F, 2.54-2.78 eV) and 456.5 nm (P, 2.68 eV, band origin)

[54,67,69,70,73,74]; for 5-MOP at 510-425 nm (F, 2.40-2.88 eV) and 472 nm (P, 2.60 eV,

band origin) in various media [54,67,68,69]; for khellin emission ranges from 553 to 422 nm

(2.22-2.90 eV) [70,71]; for TMP in ethanol fluorescence has been detected from 450 to 416

nm (2.72-2.94 eV), and the phosphorescence band origin is located at 446.5 nm (2.74 eV)

[67,74], and finally for 3-CPS the emission band maxima takes place at 448-395 nm (F, 2.50-

2.77 eV) and 490 nm (P, 2.53 eV), depending on the temperature [72,75]. The measured

fluorescence quantum yield is similar (0.02) in psoralen, 5-MOP, and 3-CPS, somewhat

higher for TMP, and lower for 8-MOP and khellin [54,67,70,71]. Together with this

parameter, that indicates that 8-MOP and khellin fluorescence is better quenched, we can use

the phosphorescence/fluorescence quantum yield ratio (P/F) as a good measure of how

favorable is the global intersystem crossing process. Comparing data in the same environment

(ethanol at 77 K), the P/F ratio ranges from 7.1 in psoralen to 13.1 in 8-MOP, 11.9 in 5-

MOP, and 6.0 in TMP [67], indicating that the relative population of the triplet state is the

highest in 8-MOP. Khellin and 3-CPS, on the other hand, seem to give rise to higher triplet

quantum yield formation than the other compounds in several solvents [55,70,71,75]. Such

experimental evidence points out toward 8-MOP and khellin, and perhaps 3-CPS, as the most

promising photosensitizers, considering that the efficient population of the T1 state is a sine

qua non condition to display an effective action via PDT and PUVA therapies [10].

The strong dependence of the data on the solvent and thermal effects and the lack of

systematic and modern photochemical studies on the molecules make the rationalization of

their properties quite difficult, because in many cases they cannot be compared. Apart from

that, there is not a straightforward relationship between the photophysical and

phototherapeutic properties, because the latter strongly relies on the ability for subsequent

formation for mono- and diadducts with DNA nucleobases.

From the photochemical standpoint, an effective photosensitizer should possess, in

principle, certain desirable key features: it must be harmless in the dark; in order to treat deep

tissues, it should be activated by long-wavelength light, because the longer wavelength

radiation the photosensitizer absorbs, the deeper the energy penetrates in the tissue; its triplet

state must be efficiently populated from the excited singlet state and effective in transferring

the energy to molecular oxygen in the PDT mechanism, and finally, it should form

monoadducts and perhaps not diadducts with DNA to avoid mutagenic side effects.

Additionally, a good photosensitizer should be amphiphilic to favor the injected

administration of the drug, easily synthesized or isolated from natural sources, be deactivated

soon after the treatment, and quickly eliminated from the body [2].

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In this chapter we are going to study the electronic structure and properties underlying in

the photochemical behavior of furocoumarins. After a necessary theoretical background, we

shall move on to the results: firstly, the photophysics of psoralen, the parent molecule, will be

studied. Afterwards how the lowest triplet excited state is populated will be analyzed, since

this state is the responsible for the photosensitizing action. The next step is studying the

photocycloaddition between psoralen and thymine that culminates in the formation of

monoadducts and diadducts in DNA, which is the key point in the photosensitizing ability of

these compounds. A parallel study of other furocoumarins (8-MOP, 5-MOP, TMP, khellin

and 3-CPS) will be carried out in order to rationalize which is the best drug from a quantum-

chemical viewpoint. Finally, we will consider the other side of PUVA therapy as well: the

interaction of furocoumarins with molecular oxygen through energy transfer to yield singlet

oxygen, which is a strong electrophilic species that reacts with some components of the

cellular membrane causing cell death by apoptosis.

Since macroscopic properties (in this case the photosensitizing ability) of a molecule are

determined by its electronic structure, we have to resort to Quantum Mechanics, a theory

whereby the state of a system is represented by a wave function, in order to study the

photosensitizing effectiveness of furocoumarins. Quantum Mechanics and Relativity have

been two of the most important scientific revolutions in History and most amazing

humankind´s achievements. Furthermore, both theories are the source of the overwhelming

majority of the advances which we currently enjoy. The use of computers and high-level

programs has allowed us to analyze chemical processes theoretically, looking for the whys

and the wherefores. Basically, a theoretical model for any complex process is an approximate

but well-defined mathematical procedure of simulation. When applied to Chemistry, the task

is to use input information about the number and character of component particles (nuclei and

electrons) to derive information and understand the resultant molecular behaviour.

The development of Quantum Mechanics was spread over by Erwin Schrödinger and

Werner Heisenberg in the mid-1920s. The wave and particle aspects of matter (the wave-

particle duality of light and matter is one of the most important premises in quantum theory)

are reconciled by the Schrödinger equation, H = E. The Hamiltonian operator, H, is the

operator associated to the total energy of a physical system and is the sum of the kinetic

energy and the potential energy operators associated with electrons and nuclei. This is an

eigenvalue problem, in which wave functions are the eigenfunctions of H and E stands for

the corresponding eigenvalues (energies). The square of the modulus of the wave function is

everywhere positive, and when normalized is interpreted as being the probability of finding

the particle in a volume dV. The probability interpretation emphasizes one of the most

important features of Quantum Mechanics: it is not always possible to predict with certainty

the result of a measurement. Often a distribution of probabilities is the best that we can

obtain. Another feature emerges when we solve the Schrödinger equation: physical quantities

such as energy or momentum are restricted to certain discrete values instead of having a large

continuous range, as we assume in Classical Mechanics.

Quantum Mechanics provides the framework to understand natural phenomena, from

Theoretical Physics (particles, strings) and Theoretical Chemistry (chemical reactions,

intermolecular forces) to the most complex Theoretical Biology. Complexity increases as the

simplicity of models decreases owing to the progressively larger number of variables that we

should deal with and the difficulty in simulating the environment. The challenge lies in the

ascertainment that life takes place into hierarchically-structured matter (macromolecules,

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cells, tissues, organs, and entities) and it requires the action of several physical properties of

its constituent elements on the whole: the interactions among them and with the environment.

Undoubtedly, the development and refinement of quantum-chemical methods (the software)

and computers (the hardware) has made easier such a task, still unfinished and with

fascinating challenges in the foreseeable future.

Besides this, the accuracy of quantum-chemical methods decreases as the complexity of

the system under study increases. To study a system in gas phase, without the interaction with

other molecules (the solvent molecules, for instance), provides in general more accurate

results. Likewise it is easier to study a molecule in the ground state than in excited state (as in

our case, the triplet state of the furocoumarin is an excited state of the molecule). In other

words, there is no point in trying to study a problem with a very powerful method if this

method is not suitable and, as a result, the calculation is extremely awkward and time-

consuming (calculations which last months and need 20-30 GB of RAM memory and over 1

TB of storage space are not unusual in Quantum Chemistry). We must sacrifice accuracy if

we want to deal with more complex systems and situations. In this case, benchmarking is

essential in order to make sure that our results have physical meaning.

Specifically, in this chapter several studies are going to be explained in the light of the

multiconfigurational CASPT2//CASSCF methodology, which in the field of excited states has

proved to have an excellent ratio between quality of the results and computational cost. These

studies are made in gas phase (in spite of being analyzing a process which takes place within

the body) and within a static picture. Contrary to dynamics (i.e., where does the system

evolve to and how does it get there solving the time-dependent Schrödinger equation) our aim

is to ascertain if there is a favorable path to populate the states protagonist of the

photosensitizing action. We will not know whether this path is more or less probable than

others (in other words, how many molecules will follow one path or another), but we will

know if it exists with high accuracy and we will also predict how the inclusion of solvent may

change the panorama. Summarizing, the present results, studied on quantum-chemical

grounds and at molecular level, are directly comparable with the gas-phase context. Aspects

such as solvent effects, synthesis, pharmacokinetics, pharmacodynamics, tolerance by

patients, etc, are out of the scope of this research.

2. THEORETICAL BACKGROUND

The understanding of the spectroscopic phenomena in the light of molecular orbital4

theory has opened new avenues in the comprehension of the photoinduced events.

Traditionally, the two most important orbitals involved in the changes that a molecule may

experience are the HOMO (highest occupied molecular orbital) and the LUMO (lowest

unoccupied molecular orbital). In the simplest orbital model, if a molecule captures an

electron, this electron may well be placed in the LUMO (energetically is the most favorable

4 At the end of the 19

th century scientists supposed that the electrons in an atom or molecule were describing orbits

as planets, with the nucleus as a star. Soon, this planetary model was seen insufficient (as light, electrons display

dual nature as waves and particles, and this dual character eliminates the concept of trajectory). Conversely, we

talk about regions in which there is a certain probability of finding an electron (orbitals). The only thing we can

estimate is the probability that the electron will be found at each point of space, not, as in classical physics, the

precise location of the electron at any instant.

PROOFS ONLY


situation), and if a molecule loses an electron, it would be more favorable if this electron was

placed in the HOMO.

Molecules, consisting of electrically charged nuclei and electrons, may interact with the

oscillating electric and magnetic fields of light. Spectroscopic experiments demonstrate that

energy can be absorbed or emitted by molecules (and atoms) in discrete amounts (energy is

quantized), corresponding to precise changes in energy of the molecule (or atom) concerned.

As matter, light is a form of energy that exhibits both wave- and particle-like properties

[76,77,78]. Absorption of the relevant frequencies from incident radiation raises molecules

from lower to higher levels, in particular, from the ground state (the most favorable situation)

to excited states. Electrons in molecules occupy molecular orbitals (MOs) with precise energy

levels. Transitions from lower, usually filled orbitals (, or n5, depending on their symmetry

[79,80,81]) to upper (higher energy) usually empty orbitals (*,*

), typically involve

absorption of radiation in the UV and visible range of the spectrum, giving rise to different

types of excited states (*,*

, n*, etc). Much smaller quantities of energy are linked to

changes in the vibrational and rotational energy of the molecule. We should take into account

that, since energy is quantized, we can distinguish between different states of a molecule

characterized by a specific value of energy. In matter each electronic state spans different

vibrational states (changes of vibration of a molecule, considering the bonds as springs),

much closer in energy; and each vibrational state spans different rotational states (changes in

the way the molecule rotates), even much closer in energy. When light interacts with matter,

energy quanta are distributed among the different degrees of freedom of the molecule,

characterized by different movements. A transition in the range of electronic energies is

related to ultraviolet or visible spectroscopy, whereas transitions in the range of vibrational

and rotational energies are related to infrared and microwave spectroscopy, respectively. A

molecule in an excited state is metastable, and it tends to dissipate the excess energy in

different ways: a radiative transition (i.e., emission of light), a non-radiative transition (energy

is dissipated as heat in a transition between different allowed states of the molecule), an

energy transfer to another molecule or a photochemical reaction.

In the semiclassical treatment of the interaction radiation-matter, the electric and

magnetic fields of the radiation will interact with the atomic or molecular electrons giving a

time-dependent perturbation. At first approximation, absorption and emission of radiation are

due to the effect of a potential which depends on the interaction between the molecule (with

its electric dipole moment vector, which stems from the partial charges on the atoms in the

molecule that arise from differences in electronegativity or other features of bonding, giving

rise to two charges +q and q separated by a distance r) and the radiation (with its electric

field vector)6. Higher-order multipole may interact with the electric and/or the magnetic field

5 These labels are related to the symmetry (the topology) of the molecular orbital. The superscript * is related to the

nature of antibonding orbital: when a molecule is formed, the atomic orbitals of the atoms belonging to the same

symmetry are combined; when two orbitals are overlapped, the electronic density of the combination areas may

be summed (bonding) or subtracted (antibonding). 6 If both magnitudes, electric field and dipole moment, have the same frequency, then the energy transfer between

them is maximum (resonance). The same effect takes place when two pendulums share a slightly flexible support

and one is set in motion: the other is forced into oscillation by the motion of the common axle. As a result,

energy flows between the two pendulums. The energy transfer occurs most efficiently when the frequencies of

the two pendulums are identical. The coupling between the electric field of the radiation with higher multipoles

(quadrupoles, octupoles), if they exist, or between the magnetic field and any of them, is usually less intense.

PROOFS ONLY


of the radiation, despite the interaction may be less intense. Such interaction is treated

quantum-mechanically like a perturbation (perturbation theory).

The molecule in excited state is often prone to react more easily than in the ground state.

The excess energy of an excited species can alter its reactivity, and this is particularly

significant in the case of electronic excitation because of the energies involved are of similar

order of magnitude as bond energies. Electronic excitations can then have a considerable

effect on the structure of a species. Accordingly, the energies correspond roughly with typical

activation energies for many reactions, which are too high to be reached from the ground but

not from the excited state. The new electronic rearrangement may be also the key of the

reactivity since the molecule in an excited state may exhibit nucleophilic (tendency to donate

or share electrons; i.e. zones with negative partial charge) or electrophilic (tendency to gain

electrons, i.e. zones with positive partial charge) properties different than those of its ground

state.

Three modern developments have been produced in the last years that are the key for the

comprehension of the photophysics and photochemistry of many chemical and biochemical

phenomena: (i) rapid advances in quantum-chemical methods allow to study the excited states

with high accuracy; (ii) improved molecular beams techniques permit studies of isolated

molecules, despite their sometimes low vapor pressure and propensity for thermal

decomposition, and (iii) the revolutionary impact that femtosecond (1 fs = 1015

s) laser and

multiphoton techniques have had on the study of the electronic energy relaxation processes.

Indeed, now it is possible to get information about reaction intermediates at very short times

from femtochemical techniques, and, more than ever, the participation of quantum chemistry

to interpret such findings has become crucial. A constructive interplay between theory and

experiment can provide an insight into the chemistry of the electronic state that cannot be

easily derived from the experiment alone.

From the theoretical viewpoint the calculation of excited states is still a very complex

task. Considering the many different electronic structure situations occurring in the potential

energy hypersurfaces (PEHs) of the excited molecular systems the only methods generally

applicably to all of them are the multiconfigurational approaches (more than one

configuration is important in the description of one specific state). The application of these

procedures requires a lot of skill and experience, and the limitations on the size of the

problem are noticeable. More popular single-reference (black-box) methods only work in

certain regions of the PEHs. In general, the excited state problem can be considered largely

multiconfigurational. New tools and strategies are required for excited states at the highest

levels of calculation: optimization of minima, transition states, hypersurface crossings

(conical intersections), and reaction paths, whereas states couplings (nonadiabatic, electronic,

spin-orbit) need to be computed. This solves only the first part of the problem, that is, the

solution of the time-independent Schrödinger equation. Once the potential represented by the

PEHs is obtained, time-dependent equations have to be solved to finally determine reaction

rates, states lifetimes or populations. Coupling at the proper level those two types of

calculations, static and dynamic approaches representing the electronic structure and reaction

dynamics problems, respectively, is still a task under development.

In the following pages a sketch of the main concepts in Quantum Chemistry and

Theoretical Spectroscopy will be found. However, the interested reader in the mathematics

and physics behind abbreviations such as HF, CC, DFT, CASPT, etc, is encouraged to read

other reviews [82,83,84,85] or the references mentioned in the following section. Certainly,

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the intimate details of the quantum-chemical methods might not be required for non-expert

readers to understand the chemical problem itself.

2.1. Quantum Chemistry

The Schrödinger equation [86,87,88,89] for stationary states, H = E, is the quantum

analog of the classical Newtonian, Lagrangian, and Hamiltonian equations of motion, since it

describes the quantum state of a system which can be described by a wave function. The

Hamiltonian operator, H, is associated to the total energy of a physical system and is the sum

of the kinetic energy and the potential energy operators associated with electrons and nuclei

(H = Te + TN + VNN + VNe + Vee). This is an eigenvalue problem, in which wave functions

are the eigenfunctions of H and E stands for the corresponding eigenvalues (energies). The

main challenge in Quantum Chemistry is that we cannot solve exactly the Schrödinger

equation, except for one-electron systems, due to the electron repulsion term present in the

Hamiltonian. The physics of electron correlation is hidden in the Hamiltonian itself. The

Coulomb repulsion given by the term r1

present in the Vee energy, the inverse distance

between two electrons, increases enormously in the regions close to rij = 0, preventing that

two electrons may occupy the same space. Therefore, the motion of any two electrons is not

independent but it is correlated. The phenomenon is known as electron correlation.

Moreover, the statement that two electrons are correlated is equivalent to express that the

probability of finding two electrons at the same point in space is zero. The instantaneous

position of electron i forms the centre of a region that electron j will avoid. For this reason, it

is stated that each electron, as described by the exact wave function , is surrounded by a

Coulomb hole. However, electron correlation is not taken into account properly by many

approximate methods. The effect of neglecting electron correlation partly in approximate

quantum-chemical approaches has great impact in the computed molecular spectroscopic

properties of interest.

The molecular orbital is the most fundamental quantity in contemporary Quantum

Chemistry and most computational methods used today start by a calculation of the molecular

orbitals of the system. It is in the simplest model occupied by zero, one or two electrons. In

the case of two electrons occupying the same orbital, the Pauli principle demands that they

have opposite spin. Such an approach leads to a total wave function for the system, which is

an antisymmetrized product of molecular spin orbitals, that is, the product of a spatial

molecular orbital times a spin function.

Quantum-chemical methods [82,83,84,85,90,91,92,93,94,95,96] look for approximate

solutions of the Schrödinger equation, employing computational numerical methods based in

general on the variational principle or/and on perturbation theory. A point worth bearing in

mind is that none of these models is applicable under all circumstances. Actually, we should

get the best method in order to find what it has been wisely defined as ―the right answer for

the right reason‖. Actually, giving the right answer for the wrong reason is also common in

daily life. Who has not interpreted a natural phenomenon wrongly? One assumes that a fact is

produced by some cause, but maybe this cause is not actually the one which provokes the

phenomenon. For instance, if we release a hammer and a feather from the same height, the

hammer arrives first to the floor. We can assume that the velocity is proportional to the

PROOFS ONLY


weight. This is an example of the right answer (obviously, the hammer arrives sooner to the

ground) for the wrong reason (because, actually, both objects experience the same

acceleration due to gravity, independent of its mass, and hit the ground at the same time in a

free fall; but drag is important within the Earth and it depends on the shape and the mass of

the object). On quantum-chemical grounds, it is necessary to make sure that a specific method

provides the proper result owing to its mathematical formulation, and not by error

compensation (then we can think that one specific methodology is suitable for analyzing a

specific property in a molecule, but the calculations fails with other molecules). For instance,

the Koopmans´ theorem provides the theoretical justification for interpreting Hartree-Fock

(one of the simplest quantum-chemical methods) orbital energies as ionization potentials: the

first ionization energy of a molecular system is equal to the negative of the orbital energy of

the highest occupied molecular orbital. However, this is only an approximation and there are

two sources of error: the electron correlation and the orbital relaxation (which refers to the

changes in the Hartree-Fock orbitals when changing the number of electrons in the system).

However, in H2 there is an excellent agreement between the Koopmans´ value and the

experimental result owing to fortuitous cancellation of errors: correlation has no effect on the

final one-electron H2+ but lowers the energy of the initial H2 state. Relaxation, on the other

hand, lowers the energy of the final H2+ state. These two effects very nearly cancel in this

example. However, we cannot say that Koopmans´ theorem is an extremely accurate way to

compute ionization potentials in general.

The variational principle states that given a normalized wave function that satisfies the

appropriate boundary conditions, then the expectation value of the Hamiltonian is an upper

bound to the exact ground state energy. In the linear variational problem, the trial function is a

linear combination of basis functions, in general using the Linear Combination of Atomic

Orbitals (LCAO) approach. On the other hand, in perturbation theory the total Hamiltonian of

the system is divided into two terms: a zeroth-order part, which has known eigenfunctions

and eigenvalues, and a perturbation part. The exact energy and wave function are then

expressed as an infinite sum of contributions of increasing complexity. If we have chosen the

zeroth-order Hamiltonian wisely, then the perturbation is small and the expansion (i.e., the

sum of the 1st, 2

nd, …, nth-order energies) converges quickly.

We can group computational-chemical methods in three basic categories: (i) ab initio

methods, in which the complete Hamiltonian is used, all the integrals are solved numerically,

and no essential parametrization is employed; (ii) semiempirical methods, in which a simpler

Hamiltonian is used or integrals are adjusted to experimental values or ab initio results; (iii)

molecular mechanics, in which Newton´s equation of motion are solved, only valid for

situations where no bonds are broken or formed, i.e., conformational changes. Obviously, the

larger is the system under study the less accurate is the available method. Despite their

inherent drawbacks, classical semiempirical methods are still employed in large systems,

whereas modern semiempirical methods, based in the Density Functional Theory, have a

widespread use. A combined approach, QM/MM (Quantum Mechanics/Molecular

Mechanics) treats an internal part of the problem with QM methods (for instance, the active

site of an enzyme), whereas the surroundings or a large part of a macromolecule (the rest of

the macromolecule) is introduced using classical mechanics.

According to the number of configurations used to build the reference wave function, the

ab initio methods can be classified into the following two categories:

PROOFS ONLY


Single-configuration methods. They are typically based in the single Hartree-Fock (HF)

reference, which determines the optimal ground-state energy and MOs (molecular orbitals).

Post-HF methods introduce the electron correlation usually at the Configuration Interaction

(CI), Coupled-Cluster (CC) or perturbative (PT) Møller-Plesset (MP, or PT in general) levels.

The coupled-cluster methods with singly and doubly excited configurations including the

effect of triple excitations by perturbation theory CCSD(T), as well as related approaches,

yield accurate results in well-defined ground-state situations and are considered as benchmark

results for small to medium molecules. In general, the applicability of the methods in this

group is restricted to situations where a single reference wave function is adequate for the

description of a chemical process, something not generally true for bond breaking cases,

degeneracies, and excited states.

Multiconfigurational methods. Part of the electronic correlation is already included in the

reference wave function, normally by using a Multiconfigurational Self-Consistent-Field

(MCSCF) wave function, which determines a set of MOs. The remaining electron correlation

effects are accounted for by MRCI, MRCC or MRPT techniques, where MR stands for

multireference. They have a more ample range of applicability (ground state, excited states,

transition states…) than single-reference methods.

Figure 5. Single-configurational and multi-configurational quantum-chemical methods: since the

macroscopic properties of a molecule are determined by its electronic structure, we have to resort to

quantum mechanics to analyze the spectroscopic properties of the molecule. A plethora of mathematical

methods is available, but we have to choose the most appropriate one for our aims. In this regard,

multiconfigurational approaches give the most general and unbiased description of all types of

excitations and situations. In addition, there are other methods not included in this graph: DFT, TD-

DFT, CIS, DFT/MRCI, CC, MR-CC…

In general, we can find the highest degree of accuracy within the ab initio methods. Once

more, the suitability of a specific method to one specific problem must be highlighted. There

is no possibility in applying high-level ab initio methods in the study of a system with

thousands of atoms. There are other methods, less accurate but capable of dealing with such

gigantic systems, that provide reliable results, at least qualitatively although not

quantitatively.

We represent the exact wave function as a linear combination of N-electron trial

functions and use the linear variational method (see Figure 6). Therefore, when we face a

Quantum methods

Single-configurationals Multi-configurationals

VariationalsVariationals Perturbationals

H-F

(SCF)

CI

MBPT

Perturbationals Mixed

MCSCF

(CASSCF)

MRCI

QDPTMCPT

(CASPT2)

MS-CASPT2

PROOFS ONLY


chemical problem, two things must be defined previously: the method we are going to employ

and the basis set. Both choices must be made carefully attending to the nature of the problem.

The choice of the one-particle space is a most important decision when setting up any

calculation, and there is no point in trying to improve the result if the selection of the one-

electron basis set is not adequate. This is especially true for the calculation of excited states,

in which states of very different nature (for instance, compact and diffuse) have particular

requirements that must be fulfilled simultaneously when selecting the basis set. This is the

essence of the LCAO formulation: to define a set of functions to expand the spatial part of

spin orbitals7. The most widespread basis sets used for ground-state calculations are the Pople

basis sets (6-31g type), whereas for excited states the correlation-consistent (cc) basis sets and

ANOs (atomic natural orbitals) are more suitable, since correlation effects are usually more

important in this case.

Figure 6. Many-electron expansion (CI) and one-electron expansion (basis set). The total wave

function, , is a linear combination of N-electron wave functions 0, ar, etc… Each one of these

functions is an antisymmetrized and normalized product of spin orbitals, i. Each of them is constituted

by a one-electron wave function, i, and a spin function, . Each one-electron wave function is defined

as a linear combination of a set of basis functions, , which are used to be contracted gaussian

functions, CGTFs (linear combinations of a set of primitive functions, gK).

If the basis were complete, we would obtain the exact energies of all the electronic states

of the system. In spite of providing the exact solution of a many-electron problem, we can

handle only a finite set of N-electron trial functions. As a result, the CI method provides only

upper bounds to the exact energies. Specifically, the lowest eigenvalue, 0, will be an upper

bound to the ground state energy of the system. When all the N-electron wave functions are

taken into account, the calculation is named full configuration interaction (FCI) and the

corresponding eigenvalues and eigenvectors computed are exact within the space spanned by

7 In fact, any mathematical function can be exactly represented as a linear combination of basis functions, if the set

is complete.

rs

ab

ra srba

rs

ab

r

a

r

a CCC;

00

K

K

K

K

ii

iiNjii

gdrrCr

1

,/

N-electron basis set

1-electron basis set

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the finite basis set. Despite the great advances in FCI technology in the last few years, the size

of the eigenvalue problem becomes rapidly too large to be handled by modern computers. As

a result, FCI solutions are only available for very small molecular systems. The truncation of

both N-electron basis and one-electron basis is the main source of inaccuracies in quantum-

chemical calculations.

Quantum-chemical methods provide information for excited states directly applicable to

explain and predict the spectroscopy, photophysics, and photochemistry of molecular

systems. A balanced description of the different electronic states is required in order to obtain

the initial, basic data, that is, energy differences and transition probabilities, in an accurate

way. This goal is a much more difficult task for excited states as compared to the ground

state. First, one has to deal with many classes of excited states, each one showing different

sensitivity to the amount of electronic correlation energy and also flexible one-electron basis

functions able to describe all effects simultaneously are required, in general larger than that

used in ground-state quantum chemistry. Then, it is necessary to compute extremely

complicated potential energy hypersurfaces where the number of minima, transition states,

and surface crossings like conical intersections, is multiplied. Because of the inherent

complexity of the problems, the methods and algorithms to compute excited states are not as

widespread as for ground states or are still under development.

In particular, the CASSCF (complete active space self-consistent field) level (a particular

case of MCSCF) both the many-electron-function coefficients of the MCSCF expansion and

the coefficients included in the expansion of each molecular orbital are optimized

simultaneously. Their variations are considered as rotations in an orthonormalized vector

space. In few words, the user chooses a defined number of orbitals and electrons which are

important in the chemical process8 in study (by benchmarking or by chemical intuition) and

the CASSCF wave function is formed by a linear combination of all the possible

configurations that can be built by distributing the active electrons among the active orbitals

and are consistent with a given spatial and spin symmetry. With this method the so-called

static correlation (due to states which are very close in energy) is taken into account. Next, the

CASPT2 (complete active space perturbation theory to second order) method, which can be

seen as as a conventional non-degenerate perturbation theory, that is, a single state is

independently considered, with the particularity that this zeroth-order wavefunction is

multiconfigurational (CASSCF), includes the remaining dynamic correlation due to short-

range electronic interactions.

On the other hand, adding the effects of the environment for excited states accurately is,

if possible, even more complex than for the ground state. Usual procedures use cavity models

such as Onsager‘s or the Polarized Continuum Model (PCM), with the additional

consideration of the non-equilibration of the electronic response for the excited states that

leads to divide the reaction field in slow, inertial, and fast, optical, parts [91,97]. Results

obtained with cavity models cannot be expected to be as accurate as those for the isolated

system when compared with gas-phase results, among other things because using large basis

sets as those required for excited states will force the charge to leave the cavity and provide

non-physical results. Solvation is a very dynamical phenomenon which requires also the

8 For instance, if we are studying the breaking and formation of a single bond in a chemical reaction, the σ and σ

*

orbitals of this bond must be included in the active space; if we want to analyze the spectrum of the molecule (the

lowest-lying excited states), π and π* orbitals must be included since ππ

* are often the lowest-lying ones.

PROOFS ONLY


inclusion of statistical effects. More sophisticated studies require the employment of

dynamical approaches making use of statistical mechanics, such as Monte Carlo type of

calculations. Solvent molecules can be then simulated by point charges (like in QM/MM

approaches as it will be discussed later) and dynamical time shots with their positions taken

for a subsequent quantum chemical calculation. In addition, in certain small systems and

situations, is possible to carry out direct dynamics methods (trajectory surface hopping

[TSH], ab initio multiple spawning [AIMS], variational multiconfiguration Gaussian

wavepackets [vMCG]...) solving the time-dependent Schrödinger equation [98].

2.2. Molecular Spectroscopy

Quantum Mechanics provides the machinery to describe the states of the molecules, and

the study of the transitions from one state to another falls in the realm of Spectroscopy

[99,100,101,102,103], which is the study of the interaction between matter and light. As

mentioned earlier, we consider that matter has to be described by quantum mechanics,

whereas light has to be described by classical mechanics. In other words, light is a transverse

electromagnetic wave. By transverse we mean that the vibrating electric-field and magnetic-

field vector are at right angles to the direction of propagation of the wave. The magnetic

vector B (which acts on moving charged particles) is always perpendicular to the electric

vector E (which acts on charged particles, whether stationary or moving) at any point in the

wave.

Light is a wave, but has actually particle-like nature as well. Further evidence for this

comes from the measurement of the energies of electrons produced in the photoelectric effect.

As explained by Einstein at the beginning of the 20th

century, light should be a beam of

photons of energy h· (Planck´s constant time frequency) or h·c/ (being c the speed of light

and the wavelength). Electromagnetic radiation of frequency can possess only the

energies 0, h, 2 h ... Since the energy of atoms and molecules is also confined to discrete

values, for then the energy can only be absorbed or emitted in discrete amounts. We say that a

molecule undergoes a spectroscopic transition, a change of state, when the Bohr frequency

condition, E = h, is fulfilled. The observation of discrete spectra from atoms and molecules

can be pictured as the atom or molecule generating a photon of energy h when it discards an

energy of magnitude E = h.

Modern theoretical photophysics and photochemistry are based on the study of the

potential energy hypersurfaces (PEHs) of the electronic states given that they are the

playground in which physical and chemical phenomena take place. Indeed, every

photophysical and photochemical process is produced owing to the relations between the

hypersurfaces of the electronic states which contribute to that process. When radiated energy

is absorbed an electronic excited state is populated and the energy becomes potential energy

with the molecular system ready to evolve along the PEH of the excited state toward more

stable conformations.

PROOFS O

NLY


Figure 7. Electromagnetic wave and the electromagnetic spectrum.

The concept of PEHs comes from the Born-Oppenheimer approximation, based on the

separation of electronic and nuclear motion due to the large difference in mass between these

particles (that is, nucleus move more slowly): to a good approximation, one can consider the

fast electrons in a molecule to be moving in the field of fixed nuclei (therefore the kinetic

energy of the stationary nuclei is zero and we talk about potential energy curves). Therefore

an electronic and a nuclear Hamiltonian can be defined. Solving the electronic Schrödinger

equation provides a description of the movement of electrons, whereas the rotation, vibration,

and translation of the molecule is considered solving the nuclear counterpart. The solution of

the electronic Schrödinger equation is the energy of a particular nuclear configuration. The

total energy for fixed nuclei must also include the constant (within this approximation)

nuclear repulsion potential. The value of this total potential energy for every possible nuclear

configuration is specifically the potential energy hypersurface. Thus the nuclei in the Born-

Oppenheimer approximation move on a potential energy surface obtained by solving the

electronic problem.

Photophysical and photochemical processes take place through interactions between

PEHs. In other words, what makes that a specific state is populated (like the state protagonist

of the photosensitizing action in furocoumarins) or that an energy transfer process between

two molecules takes places (for instance, the energy transfer between furocoumarins and

molecular oxygen to yield reactive and toxic singlet oxygen) is actually the relations among

different PEHs which represent different electronic states. In the case of a single molecule,

different regions of the PEHs, which may represent different states (i.e., different energy) or

different nuclear arrangements (i.e., different geometry because distances, angles and/or

dihedrals change) may be protagonist of a specific chemical process. Topologically, along the

PEHs extreme points (maxima and minima) appear. Minima represent stable situations (like

the reactants and products of a chemical reaction) and the systems cannot escape from them

without an external supply of energy. Another interesting structure is a saddle-point, which is

a stationary point but not a local extreme structure. It has the form of a hyperbolic paraboloid

and can be related to a transition state.

Co

smic

rays

R

ays

X

Rays

Vacu

um

Ultravio

let

Ultravio

let

Visib

le

Near

Infrared

FarIn

frared

Micro

-waves

Rad

io

waves

yB

xE

z

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Figure 8. Minimum (left) and saddle-point (right) on a PEH.

A proper nomenclature for excited states is not easy to establish. The less ambiguous

(and less informative too) form is purely enumerative: S0, S1, T1, T2, where S represents a

singlet state and T stands for the triplet states, and the states are ordered by increasing energy.

The absorption of photons by a molecule is hardly a static problem. After the absorption

(ABS) of one photon a state of the same multiplicity as the ground state is mainly populated.

Direct absorption to states of different multiplicity is only possible if the states heavily

interact, for instance, by spin-coupling9 effects. Actually, in the general case, the energy goes

to a vibrational excited state of an electronic excited state of the molecule. Straight afterwards

a non-radiative decay occurs, with emission of heat (IVR, intramolecular vibrational

relaxation), toward more stable structures of the state PEH, in many cases the state minimum.

It might frequently happen that along the decay other states cross and, if appropriately

coupling, the system can evolve towards other electronic states of the same multiplicity via a

non-radiative internal conversion (IC). Finally, the molecule arrives to the lowest-lying

singlet excited state, S1, from which the molecule may emit (F, fluorescence) and return to the

ground state. Alternatively, a non-radiative transition between two states of different

multiplicity is also possible (ISC, intersystem-crossing). After, and by successive internal

conversions the system reaches the lowest-lying triplet excited state, T1, from which the

molecule may also emit (P, phosphorescence).

Figure 9 contains a simplified Jablonski diagram summarizing the main photophysical

and photochemical effects undergone by a molecular system. It is common to reserve the

word photophysics to processes not involving the generation of new photospecies, that is, just

to decays leading to emission or returns to the ground state. However, non-radiative internal

conversions or intersystem crossing are also considered photochemical processes, therefore

the use of both terms is somewhat loose.

9 In principle, a transition between states of different multiplicity is forbidden, since light does not affect the spin

directly. However, an electron has a magnetic moment that arises from its spin. Similarly, an electron with orbital

angular momentum acts as a circulating current, and possesses a magnetic moment that arises from its orbital

momentum. The interaction of the spin magnetic moment with the magnetic field arising from the orbital angular

momentum is called spin-orbit coupling (SOC). A transition between a singlet and a triplet state may be

produced if both the SOC is high and the energy gap is low.

PROOFS ONLY


Figure 9. Jablonski´s diagram, lifetimes of the basic photophysical processes and deexcitation pathways

from the lowest-lying excited states of a molecule.

The resonance condition provided by the energy differences between the different PEHs

of the corresponding states relates to the absorbed or emitted energy quanta. Regarding the

transfer probability, it is related with the strength of the interaction between the time-

dependent field and the multipolar (the dipole, d, approach is usually enough) charge

distribution of the molecular system. Such strength is proportional to the transition dipole

moment (TDM). The basic issues required to rationalize a photoinduced phenomenon are the

energy levels of the excited solutions and the probability of energy (population) transfer from

one state to the other. In the semiclassical treatment of the interaction radiation-matter,

whereas we treat the molecule quantum-mechanically, the radiation field is seen as a classical

wave obeying Maxwell´s equations10

. The electric and magnetic fields of the radiation will

interact with the atomic or molecular electrons giving a time-dependent perturbation. Solving

the time-dependent Schrödinger equation provides us the comprehension of absorption and

stimulated emission, whereas to explain spontaneous emission we need the machinery of

quantum electrodynamics.

10

Maxwell´s equations are a set of four differential equations that relate the electric and magnetic field vectors to

their sources, which are electric charges, currents, and changing fields.

ABS: 10−15 s

IVR: 10−14-10−11 s

IC: 10−12-10−6 s

ISC: 10−8-10−2 s

F: 10−9-10−6 s

P: 10−3-102 s

S1

Fluorescence

Internal conversion to S0

Intersystem-crossing to T1

Energy transfer

or photochemical reaction

T1

Phosphorescence

ABS

IVR

IC ISC

IC

F

P

S0

S1

S2

S3

T1

T2

IVR

IC

ISC

Energy transfer

or photochemical reaction

Intersystem-crossing to S0

PROOFS ONLY


Figure 10. Vertical energies and band origins: EVA = ES1[geom. S0] ES0 [geom. S0]; EVE = ES1[geom.

S1] ES0 [geom. S1]; TeF = ES1[geom. S1] ES0 [geom. S0]; Te

P = ET1[geom. T1] ES0 [geom. S0]. Notice

that the PES associated with T1 is not displayed in this figure. Vibrational states are labeled

with the greek character .

As an initial feature, the population of the electronic states produce a superposition of

bands which characterize the absorption spectrum. The range of absorbed energies fluctuates

between the vertical absorption energy, EVA (difference between the minimum of the ground

state and the excited state at the same geometry, that is, the Franck-Condon transition), and

the adiabatic transition or band origin, Te (difference between the excited state and the ground

state at their respective optimized equilibrium geometries): it is the minimal energy difference

allowed in absorption if the assumption that all excitations begin from the relaxed ground

state is considered, as well as the largest energy emitted from the relaxed excited state. Then,

a vertical transition is one in which the final state has the same nuclear geometry as the initial

state, rather than its own equilibrium nuclear geometry (adiabatic transition). In many cases,

the determination of Te provides enough information to assign band origins, however, the

zero-point vibrational energy (ZVE) has to be included in both initial and final states to get

the vibrational band origin, T0, which can be directly compared to the experimental value, at

least that obtained in the gas phase or in molecular beams. In addition, there is another

magnitude named vertical emission energy, EVE, which is the difference between the excited

state and the ground state at the relaxed geometry of the former. The Franck-Condon

principle stipulates that the vertical absorption can be related with the experimental band

maximum. In fact this is hardly the case, except when the ground and excited states have very

similar geometries, and in this case the T0 transition (S0 ˝=0 S1 '=0) yields the most

intense peak. The vertical excitation has, however, no experimental counterpart, whereas to

get a true band maximum the band vibrational profile must be computed. The only direct

comparison relates the theoretical and experimental band origins, T0 actually. Trying to assess

the quality of a theoretical approach by comparing theoretical vertical excitations and

experimental band maxima is one of the most frequent mistakes seen in the literature.

Regarding the transfer probability, far from the conical intersection regions the Fermi‘s

Golden Rule is employed, in which the one-photon (optical) transition probability between

two states |n |m is proportional to the square of the TDM (transition dipole moment)

PROOFS ONLY


between such states: TDM=m|d|n∫m*dn

*d. Two- and higher-order multipole

probabilities can be also obtained. Based on symmetry considerations selection rules for

electronic transitions have been developed, because only the totally symmetric matrix

elements yield allowed non-zero probabilities (at first order). Using the so-computed

electronic TDM it is useful to estimate the electronic oscillator strength as f = (2/3) EVA

TDM2, with EVA being the vertical energy difference. The oscillator strength is a classically-

derived magnitude that represents the relative area of the electronic transition band and that it

can be compared with the experimental estimation based in shapes and bandwidths. On the

other hand, the vibrational contributions to the band intensity (or, in general, the strength of

the transfer) can be obtained by computing the TDM between vibrational states. If belonging

to the same electronic states, infrared or Raman intensities can be produced, otherwise

electronic band vibrational profiles can be obtained. The vibrational TDM is proportional to

the vibrational overlap term between the electronic states, m|n, which are called the

Franck-Condon factors (the probability of transition is proportional to its square). The

vibrational profiles are basically related to the differences in geometry existing from the

initial to the final electronic state and, therefore, the most intense progressions proceed

through the normal modes which trigger the aforesaid changes. Within the harmonic and

Born-Oppenheimer approaches, the complete TDM with respect the nuclear coordinates Qi is

defined by the Herzberg-Teller expansion:

(3.1)

Equation 1

Each one of the terms has an electronic and a vibrational component. The neglect of all

terms except the first one is known as the Condon approximation, a usual way to proceed but

only applicable for the one-photon dipole-allowed transitions. Otherwise, TDM (Q0) is zero

by symmetry and the first term vanishes. Nonetheless, this approximation is valid only when

the Born-Oppenheimer approximation is also valid. Otherwise, the phenomenon of vibronic

coupling arises [104], which leads to other approximations.

To study photophysical and photochemical processes on theoretical grounds we need to

determine the topography of the potential surfaces of the implied states (see Figure 11).

According to the different reaction paths through what a system might evolve, one can

normally make the following classification that defines the photochemical panorama:

adiabatic and non-adiabatic photochemistry. In an adiabatic reaction path, once vertical

absorption takes place, the system proceeds along the hypersurface of the excited state to

reach a local (or absolute) minimum leading in some cases to an emitting feature. On the

contrary, in a nonadiabatic photochemical reaction, one part of the reaction takes place on the

higher state hypersurface and after a nonradiative jump at the surface crossing (or funnel)

continues on the lower state hypersurface. In a typical closed-shell ground state molecule the

reaction usually begins on the potential energy surface of the excited state (S1 or higher) at the

Franck-Condon geometry (i.e., at the ground-state equilibrium geometry) and evolves either

to the S1 state minimum, from which it might emit, or to a crossing region with the ground

state. Depending on the properties of such a crossing the process will end up on the reactant

minimum or a new photoproduct minimum on the ground-state surface (S0). In other words,

from an initially populated singlet excited state, the energy decays to other regions of the

QQQ

Q

QTDMQQQTDMTDM nKm

Qk K

nm

0

0

PROOFS ONLY


PEH, like water moving down by gravitational force within a pipe net, being the pipes

interconnected at some specific locations, which allows that water pass from one to another.

The crossings between the excited state relevant from the photochemical view and the

ground state are frequent and they represent the basis of the photochemical phenomena

[105,106,107,108,109]. Therefore, a molecule evolving through the PEH of an excited state

may well enter in a crossing region between two hypersurfaces during the lifetime11

of such

an excited state. Hence, the lifetime of excited states is determined by the barriers that

separate the excited states at the Franck-Condon geometry from the low-lying crossings.

Many chemical processes can be rationalized in terms of the dynamics of the atomic nuclei on

a single potential energy surface (Born-Oppenheimer adiabatic approximation).

Figure 11. Scheme of the main photophysical and photochemical molecular events. Notice that the

order of the states changes along the nuclear coordinate, Q, which represents changes in the molecular

geometry. Notice also the crossings which are the cornerstone of the spectroscopic phenomena as well

as the barriers the system may surmount (like a train in a roller-coaster) to go to different places of the

PEH (which means different photoproducts and phenomena).

Nonadiabatic processes, that is, chemical processes which involve nuclear dynamics on at

least two coupled potential energy surfaces and thus cannot be rationalized within the Born-

Oppenheimer approximation, are nevertheless ubiquitous in photochemistry and

photobiology. Typical phenomena associated with a violation of the Born-Oppenheimer

approximation are the radiationless relaxation of excited electronic states, photoinduced

unimolecular decay and isomerization processes of polyatomic molecules. For the specific

case of close degeneracies between the surfaces, where ultrafast energy transfers take place,

11

The average time the molecule stays in its excited state.

E

Q

0S

0S

1S

1S

2T

Ab

so

rptio

n

Ph

osp

ho

resce

nce

2S2S

1S

1T2T

1T

Flu

ore

sce

nce IC

ICIC

ISCF

luo

resce

nce

Adiabatic

Process

Photoproduct (P)

Photoproduct (P)

Reactive (R)

R*

R*

P*

crossing

crossing

crossing

barrier

barrier crossing

PROOFS ONLY


the Born-Oppenheimer approximation breaks down and we need special methods in order to

localize, optimize and study the crossing structures. Since our aim is to explore the

photochemical panorama of furocoumarins, a deep comprehension of the hypersurfaces of the

low-lying electronic states is necessary to ascertain the pathway that follows the energy once

absorbed by the chromophore. This knowledge is the key to understand the phototherapeutic

mechanism of these drugs.

There are two types of crossings: conical intersections (CI) [83,84,85,110,111,112,113],

when the two interacting hypersurfaces have the same multiplicity, and (within the

nonrelativistic approximation) singlet-triplet crossings (STC) or any other crossing between

states that have different multiplicity. Therefore, internal conversions take place through CIs,

and intersystem crossings through STCs. The name of conical intersection reflects the fact

that a cone-shaped crossing is obtained when the energy of the states is plotted against the

two privileged coordinates, the gradient differential vector, x1, and the nonadiabatic coupling

vector, x2. Thus the total coordinate space F-dimensional is divided in two: the intersecting

space (of dimension F2), in which both states are degenerated, and the branching space (of 2

dimensions). Actually, the intersection space is an hyperline that consists of an infinite

number of CI points. Locating a CI point is equivalent to minimizing the energy in the

intersection space. In the case of STCs (if the nonrelativistic Hamiltonian is considered), we

have only one privileged coordinate since the nonadiabatic coupling vector vanishes.

Therefore we should refer this feature as an hyperplane, since we are moving along a F1-

dimension space.

Figure 12. Description of a conical intersection. When the energy of the two states is plotted against the

two privileged vectors (they are combinations of bond distances, angles, etc.) the corresponding energy

surfaces have the shape of a double cone.

The nonadiabatic transfer in regions close to the seam of CIs and undergoing a large

coupling between states is much faster than the radiative relaxation. In essence, the strength

of the coupling is based on the structure of the vibronic states mixing both states. Apart from

that, the smaller is the gap between the states, the larger is usually the transfer probability. In

addition, the degeneracy at a crossing point can also be lifted at second order. As a

consequence, we can choose a coordinate system in which to mix the branching and

intersection space coordinates to remove this splitting and preserve the degeneracy to second

order. These new coordinates give the curvature of the conical intersection hyperline and

Ground state

Excited state

CI

x1

x2

EF−2-dimensional

intersection space

2-dimensional

branching space

x3, x4, …, xF

CI

x1

x2

PROOFS ONLY


determine whether one has a minimum or a saddle point on it. These studies may also provide

the vibrational modes that must be stimulated in order to enhance nonradiative decay, because

they decrease the energy gap and can lead to a CI [114,115,116].

A computational strategy can be designed, namely the Photochemical Reaction Path

approach, in which the mechanism of the photoinduced process is accounted for by

determining the fate of the energy on the populated state by computing the reaction profile.

The whole process can be described by computing Minimum Energy Paths (MEPs),

describing the lowest-energy, and therefore most favorable, although not unique, path for

energy decay. The MEP [83,84,85] is often built as steepest descent paths, guaranteeing the

absence or presence of barriers along the path. Each step requires the minimization of the

PEH on a hyperspherical cross section of the hypersurface centered on the initial geometry

and characterized by a predefined radius. The optimized structure is taken as the center of a

new hypersphere of the same radius, and the procedure is iterated until the bottom of the

energy surface is reached. Mass-weighted coordinates are used, therefore the MEP coordinate

corresponds to the so-called Intrinsic Reaction Coordinate (IRC), measured in atomic units,

that is, bohr∙(amu)1/2

. The end of the path and the states crossed along the computed profile

will inform about the fate of the energy, and, in particular, of the location of possible radiative

minima and surface crossings, CIs and STCs. More crucial than the presence of a crossing is

its accessibility. The path of available energy should reach the crossing region to take place.

Otherwise, if a too high energy barrier hinders the access to the crossing, the feature could be

totally ineffective.

A step further may be done if dynamics is included in the calculation. In direct dynamics,

the potential energy surface over which the nuclei move is calculated ―on-the-fly‖ as it is

required during the dynamics calculation by solving the electronic Schrödinger equation at

relevant nuclear geometries [98,117,118], given that most of the space is never visited by the

system owing to its high energy. We are only interested in those structures which can be

formed (i.e., regions of the PEH panorama which can be reached) during a photochemical

process. In particular, non-adiabatic phenomena are inherently dynamic as the evolution of

the system depends on the initial conditions and kinetic energy needs to be accounted for. In

addition, coupled PEHs mean that quantum effects play an important role in the nuclear

dynamics, especially if a conical intersection is present. In this case, the classical limit of the

Schrödinger equation is not reasonable, and then the evolving wave packet may not be

represented by a swarm of trajectories moving over the surface under classical equations of

motion. We have to resort to quantum dynamics, currently available for small systems and/or

lower levels of theory with respect to the methodology employed in the studies described in

this chapter.

3. COMPUTATIONAL DETAILS

In this section the computational details of the calculations carried out will be detailed.

The quantum-chemical programs employed were mainly MOLCAS [119,120,121] and

GAUSSIAN [122] depending on the type of calculation.

The excitation energies were computed at CASPT2//CASSCF level of theory. This

implies that energies are computed at the CASPT2 level, whereas the wave function is

PROOFS ONLY


computed at the CASSCF level, which is usually enough for our purposes. Since we are

interested in several electronic states, we employed the so-called SA (state-average)-

CASSCF, which means that the molecular orbitals obtained are not the most suitable for any

of the states, but are on average acceptable for all of them. This is a price to be paid in order

to avoid the problem of root flipping (the interchange of roots along the CASSCF

optimization procedure) and to assure that the panorama of excited states is realistic. On the

other hand, to compute excitation energies we employ specifically the LS (level-shift)-

CASPT2 approximation, since this method is often recommendable to get reliable results

avoiding ill-behaved situations due to near-degeneracy effects, which can invalidate the

perturbative treatment.

The geometries of the most relevant electronic states were often optimized at the

RASSCF (restricted active space self-consistent field) level of theory, since this method

allows to compute analytical gradients (i.e., the objective is minimize a function of several

variables, that is, bond distances, angles and dihedrals). It is a more general extension of the

CASSCF method. Now, there are three subspaces within the active orbitals: RAS1 (orbitals

that are doubly occupied except for a maximum number of holes allowed in this orbital

subspace), RAS2 (in these orbitals all possible occupations are allowed), and RAS3 (orbitals

that are unoccupied except for a maximum number of electrons allowed in this subspace).

CASSCF calculations can be performed by allowing orbitals only in the RAS2 space. With

the RASSCF method a larger amount of correlation energy is usually recovered in

comparison with CASSCF, since the number of active orbitals and active electrons is usually

larger. The CASSCF method was employed to map the MEP and to look for crossings

between hypersurfaces (conical intersections and singlet-triplet crossings). Actually, what we

get is not a conical intersection, but a minimum-energy crossing point (MECP), since

MOLCAS implementation does not compute the non-adiabatic coupling terms. Finally, the

CASSI (CAS State Interaction) method was employed to compute the transition properties

(oscillator strengths, transition dipole moments, spin-orbit coupling parameters…).

The suitable active space for the CASPT2//CASSCF calculations was chosen according

to previous RASSCF analysis. We shall use a short notation to the CAS defined: CAS (n, m),

where n is the number of electrons and m is the number of orbitals. In π-conjugated molecules

like furocoumarins, the ππ* excited states are usually the lowest-lying ones, and often nπ

*

excited states are also important (since they possess a different nature the SOC term between

them is usually high according to El-Sayed rules [123,124]). Then we can label the different

active spaces as: (14,13) for psoralen, (12,12) for 8-MOP and 5-MOP, (14,11) for TMP and

(12,10) for khellin and 3-CPS. Such large active spaces mean time-consuming calculations.

Nevertheless, the results obtained are highly reliable and accurate.

In the majority of the systems, the ANO-L basis set with the contraction scheme C,O

[4s3p1d]/H[2s1p] was employed.

4. RESULTS

The following section is organized as follows: first the parent molecule, psoralen, is

analyzed. This is the smallest molecule, and then the calculations are faster and easier in this

case. The objective is finding a favorable path to populate the lowest-lying triplet excited

PROOFS ONLY


state, the protagonist of the photosensitizing action. We must follow the trail of the energy

since the precise moment of the absorption of light. The question is: may the energy reach the

T1 state or not? In other words, the first question which arises is how the lowest-lying triplet

excited state, the protagonist of the photosensitizing action, is populated.

The energy absorbed by a molecule can be released radiatively, that is, slowly emitted via

fluorescence or phosphorescence, or nonradiatively. In that case it can give rise to productive

photochemistry, yielding photoproducts different from the initial species, or it can become

unproductive, meaning that it is dissipated to the environment through the vibrational degrees

of freedom, ending in some cases in the initial ground state of the system. Photophysics and

photochemistry are typically combinations of all such processes. From the theoretical

viewpoint the best initial strategy to understand the photochemical processes is trying to

follow closely the path of the energy from the initially populated states at the Franck-Condon

region (the ground state stable geometry) toward favorable regions of the PEHs. That means

to trace the lowest-energy pathway until reaching an energy barrier, that is, a minimum, or a

transition state, or a hypersurface crossing, in particular conical intersections (CIs)

[125,126,127], the protagonists of the ultrafast radiationless nonadiabatic energy transfers

between PEHs.

Once the parent molecule has been studied, the rest of the family will be analyzed as

well, in order to see which of them displays the most favorable path to populate the T1 state.

Next, the photochemical properties of the monoadducts psoralen-thymine will be studied (that

is, its formation, the fact that only FMA yields diadducts, etc). Finally, we will study the other

face of PUVA therapy: the interaction with singlet oxygen through triplet-triplet energy

transfer.

4.1 The psoralen molecule

Our final goal is to understand the photophysical properties of psoralen in order to relate

the obtained information to its biological activity [128]. At the Franck-Condon (FC) geometry

the lowest singlet excited states 21A' (*), 1

1A'' (n*), and 3

1A' (*) lie at 3.98, 5.01, and

5.03 eV, respectively. Whereas the transition to the n* state is predicted with negligible

intensity (i.e., low oscillator strength), the * states have related oscillator strengths of 0.027

and 0.107. Unlike other states, the 31A' state has a high dipole moment, 8.70 D, differing by

more than 2.5 D from that of the ground state. This information may well be very useful to

infer what happens if solvent effects are included, at least for qualitative purposes. States with

dipole moments larger than that of the ground state were expected to undergo a relative

stabilization in polar solvents (a spectral red-shift takes place, since red is placed at larger

wavelengths, i.e. shorter frequencies in the visible spectrum) than those with smaller dipole

moments (blue-shift, since blue is located at shorter wavelengths, i.e. larger frequencies in the

visible spectrum), typical case of the n* states, which additionally, tend to directly interact

with protic solvents forming hydrogen bonds and pushing the excitation energy up in energy,

sometimes even 0.5 eV. In our case, the observed * transition is expected to undergo a red-

shift (bathocromic effect) in polar environments. Regarding the vertical excitations to the

triplet states, the 13A' * (T1) state lies at 3.27 eV, near 0.7 eV below the 2

1A' (S1) state.

Three other 3A' * states are next in energy at 3.55, 4.08, and 4.66 eV. The lowest triplet

PROOFS ONLY


state of n* character 3A'', has been located vertically (i.e., at the optimized geometry of the

ground state) at 4.85 eV, slightly below with respect to its corresponding singlet state.

The nature of the low-lying transitions of each symmetry, which are those basically

responsible for the photophysical properties of psoralen, can be graphically described by

computing the differential electron density plots as displayed in Figure 13. These pictures

allow us to rationalize which changes experiment the molecule after absorption of light and

how it affects to its reactivity (for instance, enhancing its nucleophilic –Lewis bases- or

electrophilic – Lewis acids- character). Transition to the S1 * state is mainly benzene-like,

with the charge migration concentrated in the central benzenoid ring. On the contrary, that

related to the T1 * state has its major contributions in the pyrone ring, with high

participation of the carbonyl oxygen and a shift in the density away from the pyrone ring C3-

C4 bond: a priori this fact makes the bond more reactive, which is what we are looking for.

This is in agreement with the obtained optimized geometries of such states, which shows that

the furan ring (C4´-C5´) does not vary a lot in the S1 or T1 state in comparison with the bond

distance in the ground state, whereas the pyrone double bond experiments a significant

enlargement in the T1 state. Also in Figure 13, we find the expected differential density plots

of the n* states centered on the carbonyl group.

Figure 13. Differential electron density for the main valence transitions in psoralen computed at the

ground state optimized geometry. The electron density is shifted upon light-induced excitation from

darker to lighter regions.

Regarding emission properties, psoralens are characterized by weak fluorescence

emission and strong phosphorescence bands. In particular, in psoralen the fluorescence

quantum yield was measured in ethanol as F = 0.019-0.02 [129], whereas the

phosphorescence quantum yield was reported to be P =0.13 [67]. The ratio P/F is

approximately 7.1, meaning that the phosphorescence (from the T1 state) is much more

important than the fluorescence (from the S1 state). Therefore, there should be a very efficient

PROOFS ONLY


way to populate the T1 state, from which the molecule may emit or photoreact with thymine

or molecular oxygen to exert its phototherapeutic action. The total phosphorescence decay

time (P) has been reported 1.1 s in glycerol-water and 0.66 s in ethanol [67]. With those data,

the phosphorescence radiative lifetime rad (=P·P) can be therefore expected between 8 and

5 s.

The low-lying singlet excited state 21A' (*) is responsible for the lowest-energy

absorption and emission fluorescence bands (see Table I). Vertically, at the ground-state

geometry, the transition energy is computed to be 3.98 eV and, upon relaxation of the

geometry, the band origin (Te) decreases to 3.59 eV (i.e. adiabatically: comparison between

the energies of two states in different state surfaces at their respective optimized geometries).

This means that the range of absorption goes from 3.59 to 3.98 eV, well within the scope of

the PUVA action.

The structural changes of the computed equilibrium geometries for the ground (S0) and

the 21A' (*) (S1) states affect the bond alternation of the system, mainly in the central ring

(cf. Figure 13 and Figure 14), as expected from the differential charge density plots. By using

the Strickler-Berg relationship [103,130,131] a fluorescence radiative lifetime of 74 ns is

calculated for the S1 state. The low-lying 11A'' (n*) state (vertically S2) becomes relaxed by

more than 1 eV upon geometry optimization. The main variations are obtained in the pyrone

ring (up to 0.13 Å) and in the C=O bond length (0.16 Å). Although the 11A'' (n*) minimum

belongs to the S1 hypersurface, the final Te value is about 0.3 eV higher in energy than the

computed and measured band origin for 21A'' (*). Therefore the n* state is not a plausible

candidate for the fluorescence, which is better attributed to the * state. In principle, no

experimental lifetimes have been reported, but from our computed radiative lifetimes, 74 ns

for 21A' (*) and 3 s for 1

1A'' (n*), and the experimental fluorescence quantum yield

(0.016) [67], they can be deduced as 1.2 and 72 ns, respectively. Taking into account that the

reported measurements were performed at time resolutions not lower than 2 ns [67], the lack

of measured lifetimes points out to a preferred assignment to the 21A' S1 state, with a faster

fluorescence decay.

Table I. Computed and experimental excitation energies (eV) and emission radiative

lifetimes (rad) relevant for the photophysics of psoralen. EVA: vertical absorption, Te:

adiabatic electronic band origin, EVE: vertical emission, Absmax: experimental

absorption maximum, T0: experimental band origin, and Emax: emission maximum

Theoretical (CASPT2) Experimentala

State EVA Te EVE Absmax T0 Emmax

21A' (*)

3.98 3.59 3.45 74 ns 3.7-4.3 3.54 3.03 -

11A'' (n*)

5.01 3.91 2.78 3 s - - - -

13A' (*)

3.27 2.76 2.29 28 s - 2.7 2.7 5-8 s

13 A'' (n*)

4.85 3.84 2.79 9 ms - - - -

aData in ethanol [65,66,67,129,132]. See other solvents [68].

rad rad

PROOFS ONLY


The 13A' (*) state is clearly protagonist of the phosphorescence. The computed band

origin at 2.76 eV perfectly relates to the observed value in solution at 2.72 eV [67]. The

change in geometry calculated from the ground state minimum is here more pronounced, in

particular, at the pyrone ring, whereas the relaxation energy is about 0.5 eV. The largest

structural change is obtained for the C3-C4 bond of the pyrone ring, which enlarges by near

0.13 Å. The computed spin population, displayed in Figure 12, is mainly placed on each of

the carbon atoms forming the bond. In that way, psoralen becomes highly reactive in its

lowest triplet state through its pyrone C3-C4 bond. This finding is the cornerstone of the

photophysics of psoralen, which has been repeatedly proposed to take place through a

reactive triplet state. The computed phosphorescence radiative lifetime is 28 s, somewhat

higher than those estimated experimentally from the quantum yield and the total relaxation

time, 5 and 8 s [67,132]. For the 23A' (*) state the spin population is placed mainly on the

carbon atoms forming both C=C bonds, that is, C3-C4 (pyrone) and C4´-C5´ (furan).

Figure 14. Spin density for the low-lying triplet states in psoralen computed at the ground state

geometry.

Now, we know that the triplet state of psoralen is reactive as well as long-lived (28 s) to

exert its photosensitizing action. Nevertheless, is it efficiently populated? [133]. PUVA

therapy initiates by irradiation with light of wavelengths of 320–400 nm (3.87–3.10 eV). In

psoralen the only state which will be significantly populated by direct absorption is the bright

spectroscopic 21A' (*) S1 singlet state (hereafter S), which will evolve towards the

minimum of S1, from which fluorescence will take place. As we have already mentioned,

according to experimental data, an efficient population of the lowest-lying triplet state 13A'

(*) T1 (hereafter T) may take place, either by direct absorption (unlikely if the ground state

is a singlet, as in this case; in any case, this mechanism may not justify the high

phosphorescence of the molecule) or by an effective intersystem crossing mechanism (more

probable). The T1 (T) state lies much lower in energy than the S1 (S state, both vertically

(≈0.6 eV) and adiabatically (≈1.2 eV). Direct interaction between the singlet and triplet

vertical excited states is unlikely (because neither the gap nor the SOC is suitable), and

therefore another mechanism has to be found, involving most probably population of higher-

energy triplet states and subsequently internal conversion towards T1. There are two

PROOFS ONLY


conditions to be fulfilled if an ISC process has to be efficient: low energy gap between a

singlet and a triplet state and high SOC terms between them. In this regard, the spin-orbit

coupling is large between states of * and n* types and small between states of the same

character. Thus, the nonradiative decay to a triplet state should occur along the relaxation

pathway of S, the only state significantly populated in the energy range employed in PUVA

therapy, starting from the Franck-Condon region, and in close vicinities of a singlet-triplet

crossing. The vertical energy gaps S-triplet states are quite large, and the spin-orbit coupling

(SOC) elements are small. For instance, the largest SOC, 3 cm−1

, occurs between 21A' (*)

(S), that is, S1, and 13A'' (n*) (Tn), vertically T7, which are separated by 0.87 eV, which is a

gap too large. A promising possibility that should be explored is that the nonradiative decay

to a triplet state could occur along the S relaxation pathway between S and Tn. A minimum

energy path (MEP) on the S state hypersurface was built from the Franck-Condon geometry.

Along the initial steps of such a costly calculation the Tn (n*) state, while it remains with the

largest SOC terms with S, increases its energy with respect to the latter state almost 0.2 eV.

It was therefore concluded that no efficient ISC could be expected along the main relaxation

path, and that the S state quickly reaches its own minimum, (S)MIN, without crossing T or

Tn. Nevertheless, it is known that the T1 state may be populated according to experimental

data. Therefore, another alternative may well be found. This is why we carried out a linear

interpolation in internal coordinates (LIIC) from the S to the Sn minima (the lowest-lying

singlet excited state of n* character), being the latter a geometry in which the Sstate is

higher in energy and share the same basic structure (both of them are n* excited states) and

energetic as Tn.

Figure 15. LIIC path between Sπ and Sn minima. Between the second and the third point the crossing

between Sπ and Tn is verified (notice the black square).

As we can see in Figure 15, the gap (S- Tn) decreases as the SOC increases until

reaching the crossing point between the second and the third geometry. Since these

geometries were not obtained by means of a MEP calculation, these results can be considered

-0.81

-0.80

-0.79

-0.78

-0.77

-0.76

-0.75

-0.74

-0.73

-0.72

-0.71

0 1 2 3 4

En

erg

y +

64

6/a

u

LIIC

1-cm 46.5

eV 24.1

SOC

E

1-cm 18.6

eV 79.0

SOC

E

1-cm 22.9

eV 15.0

SOC

E

1-cm 97.12

eV 26.0

SOC

E

1-cm 06.24

eV 51.0

SOC

E

S

T

nS

nT

2T

3T

4T

min S min nSPROOFS ONLY


as upper limits to the actual values. However, it is enough since the crossing is verified. The

geometry closer to the crossing point was used as initial geometry to initiate a search at the

CASSCF level for a singlet–triplet crossing (STC) between S and Tn, that is, (S/Tn)X. As

expected, the main change in geometry from the minimum of S to the optimized structures of

Sn or Tn is related to the length of the C=O bond, much larger (≈0.15 Å) for the n* states.

The SOC term in STC is computed as 6.4 cm1

. As displayed in Figure 16, the barrier from

(S)MIN to (S/Tn)X was computed 0.36 eV at the CASPT2 level, and represents the excess

energy required for the ISC process to take place. Once the Tn state is efficiently populated

through a favorable ISC mechanism, it will quickly evolve towards the nearby energy

minimum, (Tn)MIN, placed 0.11 eV below (S/Tn)X. At those geometries Tn is the second-

energy excited triplet state (at Franck-Condon is the 7th

), and can be expected that the energy

follows a pathway for favorable internal conversion (IC) toward the low-lying T state.

Actually, we have found, at CASSCF level of theory, a conical intersection (Tn/T)CI placed

isoenergetic with (Tn)MIN. An efficient IC (internal conversion) will therefore take place

transferring the population to T, which will subsequently evolve to its own minimum,

(T)MIN. Then, the state protagonist of the photosensitizing action is finally populated. The

C=O bond length undergoes the most important change, enlarging from 1.346 Å at (Tn)MIN to

1.372 Å at the conical intersection (Tn/T)CI, and becoming much shorter, 1.198 Å , at

(T)MIN, in accordance with the * or n* nature of the excited states.

Figure 16. Scheme of the gas-phase photochemistry of psoralen based on quantum-chemical CASPT2

calculations. Energies are referred to (S)MIN (zero energy).

Consequences of breaking the planarity of the molecule were explored here at different

levels, but geometry optimizations always led to planar minima for the different states. The

relevance of out-of-plane displacements for the relaxation of the S state has been emphasized

recently [134,135,136], together with the enhancement of the SOC terms between low-lying

PROOFS ONLY


S and T states by vibronic coupling effects involving out-of-plane modes, as an alternative

mechanism for efficient ISC. With information at hand, both mechanisms have to be viewed

as competitive. Taking into account that nπ* states tend to destabilize in polar solvents, the

(Tn)-mediated mechanism here proposed will surely decrease its importance in polar media,

remaining a plausible candidate for the efficient population of the low-lying T triplet state in

the gas phase.

4.2 The family of furocoumarins

Regarding the rest of the family (8-MOP, 5-MOP, TMP, khellin and 3-CPS), the

photophysical properties are suitable for the phototherapeutic process, as in the case of the

parent molecule and, in principle, the same mechanism (S Tn T) to populate the state

protagonist of the photosensitizing action may be appropriate for all the molecules [137]. Our

aim is to validate this general mechanism for all the furocoumarins.

The initially promoted S1 * (S) state is clearly higher in energy for psoralen, 8-MOP,

and 5-MOP, whereas the associated transitions have not large oscillator strengths. Khellin and

TMP, on the other hand, have transitions in the low near-UV range which are predicted

relatively more intense, representing undoubtedly an advantage from the photochemical

viewpoint. 3-CPS represents an intermediate situation. In addition, all the lowest-lying triplet

excited states are sufficiently long-lived to exert its photosensitizing action. The computed

radiative lifetimes (Strickler-Berg approach: [1/rad] = 2.1420051010

Te3 TDM

2) tend to be

close or one order of magnitude larger than the experimental values (1-100 ns), reflecting in

that manner the presence of actual non-radiative decay channels.

Table II. Main spectroscopic parameters of furocoumarins: Abs (absorption energies in

eV; EVA vertical absorption energy, Te band origin); f (oscillator strength); rad

(radiative lifetime)

Compound Sπ Sn Tπ Tn

Abs f Abs Abs rad Abs

Psoralen 3.98 (EVA);3.59

(Te) 0.027 5.01 (EVA);3.91 (Te)

3.27 (EVA);2.76

(Te) 28 s 4.85 (EVA);3.84 (Te)

8-MOP 3.90 (EVA);3.50

(Te) 0.006 5.01 (EVA);3.91 (Te)

3.16 (EVA);2.72

(Te) 60 s 4.85 (EVA);3.84 (Te)

5-MOP 3.96 (EVA);3.60

(Te) 0.002 5.05 (EVA);3.95 (Te)

3.14 (EVA);2.66

(Te) 95 s 4.89 (EVA);3.88 (Te)

Khellin 3.52 (EVA);3.26

(Te) 0.012 4.00 (EVA);3.26 (Te)

3.05 (EVA);2.83

(Te) 3.4 h 3.61 (EVA);3.03 (Te)

TMP 3.57 (EVA);3.25

(Te) 0.06 4.92 (EVA);3.91 (Te)

3.04 (EVA);2.63

(Te) 180 s 4.78 (EVA);3.73 (Te)

3-CPS 3.73 (EVA);3.05

(Te) 0.03 4.84 (EVA);3.59 (Te)

2.88 (EVA);2.40

(Te) 81 s 4.72 (EVA);3.58 (Te)

The most important geometric parameters for the lowest-lying electronic states of these

molecules are given in Table III. All of the molecules, except khellin, are prone to react

PROOFS ONLY


through the pyrone double bond in its T1 excited state to form PMAs. Khellin, with a different

structure (see Figure 4), will form FMA through the furan double bond in its T1 excited state.

In order to map the pathway of the population of T1 we carried out the same LIIC path as

in psoralen between Sand Sn minima. The profiles are very similar among furocoumarins.

At the ground state Franck-Condon region, a direct ISC between S and Tn is unlikely in all

the case, because neither the gap nor the SOC is suitable (Pso: 0.87 eV and 3 cm1

; 8-MOP:

0.95 eV and 3 cm1

; 5-MOP: 0.93 eV and 3 cm1

; Khellin: 0.09 eV and 3 cm1

; TMP: 1.21

eV and 6 cm1

; 3-CPS: 0.98 eV and 4 cm1

). Only khellin displays a very low gap at the

Franck-Condon region, and thus the population of the triplet manifold may take place just

vertically.

Table III. Selected bond lengths (P:pyrone; F: furan) at the excited states optimized

geometries of furocoumarins

Compound d (C=C)F /Å a d (C=C)P /Å b

S0 S T S0 S T

Psoralen 1.348 1.365 1.344

(0.05,0.00)c 1.342 1.373 1.469

(0.31,0.73)

8-MOP 1.346 1.362 1.342

(0.05,0.00) 1.341 1.382

1.469

(0.32,0.76)

5-MOP 1.345 1.365 1.343

(0.00,0.04) 1.342 1.377

1.467

(0.29,0.78)

Khellin 1.337 1.352 1.444

(0.81,0.19) 1.332 1.328

1.333

(0.00,0.08)

TMP 1.348 1.365 1.345

(0.06,0.14) 1.345 1.374

1.475

(0.34,0.66)

3-CPS 1.343 1.363 1.342

(0.00,0.02) 1.344 1.418

1.472

(0.40,0.71) a Bond C4Ć5´

b Bond C3C4 except for khellin, which is C2C3 c Spin population at the carbons located in the reactive double bonds of each moiety.

According to the LIIC path for each molecule, we found that the barrier to reach the

triplet manifold is similar in all of the furocoumarins: Pso: 0.42 eV12

; 8-MOP: 0.39 eV; 5-

MOP: 0.26 eV; Khellin: 0.11 eV; TMP: 0.41 eV; and 3-CPS: 0.44 eV). Notice that khellin

displays again the lowest barrier along the LIIC path (however, the population of the triplet

manifold may well be produced just at the Franck-Condon region, as we stated previously). A

dynamics calculation may be interesting to evaluate which percentage of molecules populates

the triplet manifold at the Franck-Condon region or along the Sπ relaxation pathway.

However, this is not strictly necessary: we only need to know that such possibilities exist.

Then we can conclude that there is a common mechanism to populate the triplet manifold

in furocoumarins: If the Franck-Condon gap between the initially populated Sπ state and the

Tn state (E1 in Figure 17) is small enough, like in khellin, a very efficient ISC process will

12

0.42 eV is the upper limit of the actual value (0.36 eV). The difference is that in the former value we are not

taking into account the actual STC structure, but the values of the energies at the closest point to the crossing.

However, in the rest of the molecules we did not look for the STC or CI structures, since the similarity in the

LIIC paths reflects that there is a likelihood that such structures exist and it is not necessary to localize them.

PROOFS ONLY


take place already near the initial Franck-Condon geometry, provided that the SOC terms are

large enough. In the other furocoumarins, reaching a region of favorable Sπ /Tn ISC means to

surmount a barrier (E2 in Figure 17) toward the singlet-triplet crossing point. The barrier has

been computed much larger in psoralen, 8-MOP, TMP, and 3-CPS than in 5-MOP, in which

the ISC process can be therefore considered slightly more efficient. In all cases, but especially

in khellin, once the Tn state is populated the energy transfer to the Tπ state will be extremely

favorable.

Figure 17. Scheme of the suggested mechanism of the triplet state population of furocoumarins.

4.3 Formation of monoadducts

We shall move on now to the formation of monoadducts between psoralen and thymine

[138], the main target in DNA. This photochemical reaction may be considered as the

cornerstone of the PUVA therapy. The overall framework of the reaction is complex

[139,140].

Despite the extended use of the PUVA technique and the characterization of the

furocoumarin-thymine complexes, the underlying formation mechanism of the mono- and

diadducts is far from being known. According to the Woodward-Hoffmann rules

[141,142,143], [2+2] cycloadditions are pericyclic thermally forbidden reactions, that, upon

conservation of the orbital symmetry, are allowed photochemically. For instance, in the

simplest model reaction of two ethene molecules, their lowest singlet excited state correlates

directly with that of cyclobutane. Consequently, there is no symmetry-imposed barrier to this

transformation and the reaction is named as symmetry-allowed. On quantum-chemical

grounds, this reaction, that involves 4 electrons, is excited-state allowed because the surface

topology of S1 possesses a minimum that corresponds to a diradicaloid character as the anti-

aromatic transition state on S0 [105,109,144,145]. Therefore, the key point in the mechanism

(S /T ) n X

(T /T )n CI

E2

(T )MIN

(S )MIN T

S

(T )n MIN

Tn

T

ISCh

F

P

S0

IC

E1

Tn

+ Reactivity

crossing

min

barrier

crossingcrossing

crossing2

EEE

EEE

S

TS n

PROOFS ONLY


of such type of pericyclic reaction is the existence of a suitable surface crossing, a conical

intersection (CI), (S1/S0)CI, that behaves as a funnel allowing the occurrence of a radiationless

jump, that is, an internal conversion (IC), from S1 to S0. Within the same framework, the

formation of furocoumarin-thymine adducts would in principle involve population of the S1

state of the supermolecule, either localized in the furocoumarin or in the thymine moiety and

subsequent evolution toward the corresponding CI, (S1/S0)CI. This is not, however, the only

posibility. It is believed that the triplet state of the furocoumarin is involved in the formation

of the DNA cross-linked adducts. Relatively high intersystem-crossing quantum yields

(0.076) have been also established in the production of FMA [48]. If the T1 state of the

supermolecule participates in the photoreaction, this will proceed from the populated T1 state

toward a singlet-triplet crossing (STC) with the ground state, (T1/S0)STC, finally leading to the

formation of the adduct in S0.

With respect to the behavior of the different furocoumarins, it can be concluded that only

psoralen and TMP show a very strong ability to build diadducts, that 5-MOP and 8-MOP do

not have such a pronounced trend, and that diadducts are not obtained from 3-CPS and khellin

[20,146]. Since the formation of diadducts are linked to undesirable side effects, these two

compounds are, in principle, promising substitutes to the widespread employed 8-MOP

[6,38]. Indeed, according to the previous section of this chapter, khellin has been suggested as

the most efficient furocoumarin to populate the triplet manifold, another point worth bearing

in mind when searching for the most promising drug.

Figure 18. Psoralen-thymine pyrone (PMA) and furan (FMA) monoadducts and diadducts.

From the theoretical standpoint, studies have been only focused on the intercalation of the

photosensitizer between the -stacked nucleobases, using classical mechanics approaches

[147] and in the determination of the ground state structures of the adducts, at the

semiempirical [148,149,150,151,152] or ab initio single-reference RHF, DFT, MP2 and

CCSD(T) levels [153]. The complexes have been determined much more stable in the non-

coplanar trans than in the stacked cis arrangements.

O O O

NH

HN

H3C

O O

O O O

NH

HN

H3CO

O

NH

HN

H3C

O O

O O O

NH

HN

H3CO

O

PMA FMA

Diadduct

PROOFS ONLY


Initially, the ground state of reactives, psoralen and thymine, and products, monoadducts

PMA and FMA, were optimized at the DFT/B3LYP/6-31G(d) level of theory13

. At the

optimized geometries of the species several singlet and triplet excited states were computed

using CASSCF multiconfigurational wave functions as reference and second-order

perturbation theory, the CASPT2 method, to obtain electronic energies, always employing the

6-31G(d) basis sets. An active space of eight electrons in eight active orbitals (8/8) was

employed in the CASSCF procedure, both to compute vertical excited states of the

monoadducts and to optimize CIs and STCs in the different hypersurfaces. In order to make a

straightforward comparison, the corresponding singlet and triplet excited states of the

reactives, isolated psoralen and thymine, were optimized at the CASSCF level with the spaces

(6/6) and (2/2), respectively, which constitute approximately equivalent active spaces that

those each moiety possesses in the supermolecule (FMA or PMA). Energies, displayed

relative to the ground states of the separated reactives, include in all cases the Basis Set

Superposition Error (BSSE) corrected through the counterpoise procedure [154], as described

elsewhere [155]. It is always present when computing moleculer dimers or aggregates as long

as we compare energies at different geometries (for instance, if we compute binding energies,

i.e., when energies at large internuclear distances are compared to those at short distances: the

BSSE error varies from one specific monomer-monomer distance to another). The source of

the BSSE is the use of finite basis sets (for practical reasons, obviously). The majority of the

contribution to the energy of a system comes from the internal electrons (core). If the basis set

of an atom is deficient in the core region, a molecular method recovers a large amount of

energy correcting this deficient area with the basis set of the other atoms. The BSSE is

therefore related with the improper inclusion of the correlation energy in a quantum-chemical

calculation. In general the result of ignoring BSSE is both a shortening of bond lengths and an

increasing of bond energies, because the net effect is an increase of the energy in absolute

value. This error is a purely mathematical artifact owing to the fact that the supermolecule

possesses a larger basis set than the isolated monomers and as a result the potential energy

surface is altered.

In principle, there are four possibilities regarding the formation of PMA and FMA in its

ground electronic state:

1) Pso (T1) + Thy (S0) (ISC)14

(S0/T1)STC PMA (S0)

2) Pso (S0) + Thy (T1) (ISC) (S0/T1)STC FMA (S0)

3) Pso (S1) + Thy (S0) (IC) (S0/S1)CI PMA (S0)

4) Pso (S1) + Thy (S0) (IC) (S0/S1)CI FMA (S0)

All of them has been analyzed, since we found the structures (S0/T1)STC and (S0/S1)CI in

each supermolecule, that is, the singlet-triplet crossing and the conical intersection that allow

the photochemical process, at the CASSCF level of theory.

13

DFT (Density Functional Theory) is one of the most popular methods employed in Quantum Chemistry. In spite

of its limitations, it gives accurate results in some specific situation at low computational cost. B3LYP is the

functional employed in the calculation, and 6-31G(d) is the basis set, specifically a Pople basis set. These

numbers mean: one function of 6 gaussians for the core shell and two functions, of 3 gaussians and 1 gaussian

respectively, to describe the valence shell. In addition, polarization functions (d) are included to describe the

changes of the electronic density of an atom in the molecule 14

ISC stands for ―inter-system crossing‖ and IC for ―internal conversion". See Figure 9.

PROOFS ONLY


Mechanisms (1) and (2) are triplet-mediated since the initial step is the population of the

triplet state of psoralen (1) or thymine (2). The former is more likely to be populated, since in

a previous section of this chapter we proved that there is an efficient way to populate the

lowest-lying triplet excited state in psoralen (see Figure 16). As reactants we have the two

isolated molecules, psoralen (Pso) and thymine (Thy), optimized in the corresponding state.

Therefore, excitation energies from the ground state, Pso(S0) +Thy(S0), are displayed as

adiabatic transitions. As mentioned above, direct UV-A radiation basically populates the

psoralen S1(*) state, adiabatically placed at 3.57 eV, and, by means of an efficient ISC

(intersystem crossing) process, the system can transfer its population to the molecule lowest

triplet T1(*) state, adiabatically at 2.58 eV from the ground state minimum. The

enlargement of the psoralen pyrone C3=C4 bond and the localized spin population in C3 and

C4 inform about the reactive character of such bond and strengthens the hypothesis of an

efficient reactivity at the pyrone side of psoralen with the thymine C5=C6 bond to form

PMAs. The mechanism is displayed in Figure 19, and comprises the evolution of the system

from the isolated systems Pso(T1) +Thy(S0), constituting an overall triplet state in the

supermolecule, toward a singlet-triplet crossing (S0/T1)STC connecting with the ground state of

PMA. At the STC there is a reaction intermediate in which a covalent bond has been formed

between two of the carbon atoms of the reactive bonds, C3 from psoralen and C6 from

thymine.

The path toward the STC intermediate from the initial products, located energetically

almost 0.9 eV below, will be probably barrierless15

in most cases, as proved in the

photocycloaddition of nucleobases [156,157], although it would ultimately depend on the

favorable insertion of the drug between the strand of nucleobases, on the diffusion of the two

species, and on the inherent flexibility of the DNA structure to provide reactive orientations.

From the STC intermediate, and after a subsequent ISC process, the system will evolve to the

ground state of PMA, which is placed 0.19 eV above the initial reference. As regards the

formation of FMA monoadducts via a triplet manifold, it is unlikely that it can take place by

the absorption of a photon from psoralen and further population of the molecule T1 state. The

furan fragment of psoralen is barely involved in the lowest triplet state, and therefore the

corresponding C4´ =C5´ cannot be considered reactive, having a bond length of 1.344 Å and

no spin population (see Table III). Still, a probably minor mechanism may participate

depending on the external conditions. The thymine S1 state is too high in energy [158] to be

populated at the phototherapeutic wavelengths, but, as it has been observed, thymine T1 state

can be directly activated by an energy transfer process from an endogenous, e.g., other

nucleobases, or exogenous, different photogenotoxic substances or psoralen itself, which is

known to be an efficient triplet photosensitizer [156]. However, the mechanism (2) may not

be as favorable as the mechanism (1) to the formation of a specific monoadduct.

15

Imagine a roller-coaster. The train will surmount a hill as long as it possesses enough kinetic energy (i.e.,

velocity) at the bottom of the hill. Otherwise, the train will be stopped halfway through and come back. In other

words, we need enough kinetic energy to convert it in potential energy to surmount the hill. In this example, the

hill is a potential energy barrier. Once the train has arrived at the top of the hill (or if there is no hill), the next

path is obviously barrierless and the kinetic energy is not invested in potential energy (and we do not notice any

decrease in velocity as long as friction is negligible).

PROOFS ONLY


Figure 19. Photochemical mechanism proposed for the formation of psoralen (Pso) – Thymine (Thy)

pyrone monoadducts (PMA) in the triplet manifold via a singlet-triplet hypersurface crossing (STC).

The photoreaction starts upon population of the T1 state of psoralen after an ISC process from the

initially activated S1 state of the molecule.

Mechanisms (3) and (4) have not been discussed up to now. These correspond to the

singlet manifold, that is, singlet-mediated processes. FMA may well be formed along the

singlet manifold (mechanism 4). PMA can also be formed in the same way (mechanism 3).

However, since the population of Pso (T1) from Pso (S1; the initially populated in the range of

energy employed in PUVA therapy) is so favorable, the mechanism (1), triplet-mediated, is

more likely to happen. Despite that in psoralen the ISC process toward T1, after one-photon

absorption in S1, is quite efficient, part of the population of the singlet state can evolve toward

an intermediate structure representing a conical intersection with the ground state, (S0/S1)CI,

that will behave as a funnel for IC (internal conversion) toward the formation of the

monoadduct in its ground state. This type of photoreaction does not require a reactive double

C=C bond elongated as in the triplet case. In addition, since an internal conversion exists (and

not a spin-forbidden singlet-triplet crossing), this kind of mechanism may well be even more

favorable than the production of PMAs, which are formed via spin-forbidden processes. The

energy difference with respect to the initial channel, Pso(S1) + Thy(S0), is smaller than in the

case of the triplet manifold, but still the CI is clearly below the asymptotic limit.

Considering the four proposed mechanisms, we suggest that PMA formation takes place

mainly via the triplet manifold, whereas FMA, which is also expected to give rise to

diadducts in major proportion [48], is probably more efficiently formed in the singlet

manifold with the participation of a CI structure and the corresponding internal conversion

process.

PMA (S0) Pso (S0) + Thy (S0)0.00

0.19

PMA (S1)4.32

1.65ISC process

(S0/T1)STC

PMA (T1)

PMA (S1)

Pso (S0) + Thy (T1)

Pso (S1) + Thy (S0)

Pso (T1) + Thy (S0)2.58

2.97

3.573.67

4.64

ISC

h

Reaction

E/eV

PROOFS ONLY


Figure 20. Photochemical mechanism proposed for the formation of psoralen (Pso) – Thymine (Thy)

furan monoadducts (FMA) in the singlet manifold via a conical intersection hypersurface crossing (CI).

The photoreaction starts upon direct population of the S1 state of psoralen by UVA light.

Finally, the electronic structure of both monoadducts will be analyzed in order to explain

why only FMAs give rise to diadducts. Whereas FMA has vertical excitation energies for its

lowest excited triplet and singlet states at 3.06 and 4.25 eV, respectively, the corresponding

energies in PMA rise to 3.48 and 4.45 eV, respectively. Both excitations involve the psoralen

fragment. The first conclusion we obtain is that it is the S1(ππ*) state of FMA and not of

PMA, located too high in energy, which is more favored to absorb the second photon that

triggers the formation of diadducts with a new thymine molecule (see

Figure 2). The hypothesis is further supported by the analysis of the T1 state properties. By

optimizing the lowest triplet state of both monoadducts at the CASSCF level we identified

that the spin population in this state is basically localized in the C3=C4 bond of the pyrone

moiety in FMA and somewhat delocalized on the psoralen ring in PMA (see Figure 21).

Therefore, the formation of diadducts with a thymine in the opposite DNA strand is favored

in FMA, whose T1 state has an elongated and reactive C3=C4 pyrone double bond. This

conclusion is supported by experimental estimations, which determined that PMA, unlike

FMA, could not give rise to diadducts [43,46]. The production of FMA diadducts may be

diminished by some photoreversibility from FMA toward the separated subsystems. In fact,

several experiments support this hypothesis. FMA species have been shown to decompose

yielding the original products after irradiation with middle UV light, at 4.89 eV [49]. Also,

both mono- and diadducts can be split into the original monomers under irradiation with short

wavelength UV light [31,53]. Among other factors, the distribution of adducts in DNA

samples seems to depend also on the wavelength of the irradiation. Increasing the absorbed

energy favors the diadduct vs monoadduct formation [47], which can be understood by the

higher energy of the initially populated singlet excited state in the monoadduct rather than in

psoralen, as computed here.

Reaction

E/eV

FMA (S0) Pso (S0) + Thy (S0)0.000.03

FMA (T1)3.41

3.24IC process

(S0/S1)CIFMA (T1)

FMA (S1)

Pso (S0) + Thy (T1)

Pso (S1) + Thy (S0)

Pso (T1) + Thy (S0)2.58

2.97

3.57

3.09

4.28

h

PROOFS ONLY


Figure 21. Spin population in the optimized T1 excited state of FMA (left) and PMA (right). FMA has

density on both carbon atoms of the elongated C3=C4 pyrone double bond.

4.4 Interaction with singlet oxygen

Finally, we are going to study the other face of PUVA therapy: the interaction with

molecular oxygen [159]. Indeed, photodynamic action refers to the damage or destruction of

living tissue by visible light in the presence of a photosensitizer and oxygen. The effect was

discovered in 1897-1898 [2] at the Ludwig-Maximillian University in Munich. Oscar Raab, a

medical student, spent time in the pharmacology laboratory of Prof. H. von Tappeiner. He

realized that using low concentrations of acridine as photosensitizer, paramecia were killed in

the presence of daylight, but in the darkness they survived. In 1903, von Tappeiner and

Jesionek proposed various dermatological applications for photosensitizers (such as eosin). In

1904, von Tappeiner and Jodlbauer used the term ―photodynamische wirkung‖ for the first

time.

The yield of formation and activity of singlet oxygen from the different furocoumarins

has been estimated by several research groups, but no agreement has been reached due to the

problems in evaluating the generation of the species in different conditions and the

simultaneous production of other oxygen radicals [20]. In the family of the most common

furocoumarins (see Figure 1), psoralen and, mainly, 3-CPS are typically considered the most

effective producers of 1O2 in aqueous solution [20,22,57,160,161]. The situation is less clear

for khellin, 8-MOP, 5-MOP, and TMP [20,22,62,63,160,161,162,163].

The interaction of molecular oxygen and organic molecules is believed to be produced

through the so-called excitation energy transfer (ET) mechanism between the furocoumarin in

its lowest triplet long-lifetime excited state, behaving as a photosensitizer, and the molecular

oxygen, initially in its triplet ground state, 3g

−. Oxygen is present in the cellular environment

ready to transform into singlet oxygen 1O2 (

1g)

16, which is a strong electrophilic species that

reacts with different compounds [2,14], including some components of the cellular membrane

causing cell death by apoptosis [15]. The ET process is triggered by electronic coupling

between a molecule in an excited state, the donor (D*), and a molecule, the acceptor (A) or

quencher within a collision complex [164,165,166,167,168,169,170,171,172], a mechanism

that strongly depends on the inter-fragment distance. At large separation between the moieties

(20-30 Å or even larger) the electronic coupling arises from the Coulomb interaction between

electronic transitions that, under the dipole approximation, reduces to the known Förster‘s

dipole-dipole coupling [173]. The process is actually a non-radiative transfer of excitation

16

These representations of the nature of the state inform us about the spatial and spin symmetry of the electronic

state.

PROOFS ONLY


occurring whenever the emission spectrum of D overlaps with the absorption spectrum of A

(although no intermediate photon takes part on it). It is the electric field around D*, behaving

like a field generated by a classical oscillating dipole, that causes the excitation of A

[105,174,175,176,177].

At larger separations than Förster‘s, fluorescence resonance ET (with photon emission by

D* and subsequent absorption by A) becomes more efficient than excitation ET [178]. At

shorter inter-fragment distances, however, the so-called Dexter exchange coupling

predominates, arising from the exchange integrals that account for the indistinguishability of

the electrons in polyelectronic wave functions. This factor decreases steeply with separation

[179]. If the interaction is assumed weak and a large overlap between D* and A wave

functions is produced, Fermi‘s Golden Rule for coupled transitions can be applied. Such

processes have been studied theoretically in depth in recent years, in particular for singlet-

singlet ET processes [180,181,182,183,184], which implies an exchange of electrons of the

same spin but different energies, that is, the spin state of each fragment is conserved. In PDT

the actual mechanism is, on the other hand, an intermolecular triplet-triplet energy transfer

(TET), that is, a process of exchanging both spin and energy between a pair or molecules or

molecular fragments. This type of reactions are commonly used to efficiently populate the

triplet states of many organic molecules [105,185,186].

Figure 22. Examples of TET, which can be understood as two simultaneous electron transfers between

the donor (D) and the acceptor (A) with exchange of spin and energy in each fragment.

TET processes can be therefore understood as two simultaneous ETs with spin exchange

between the interacting fragments (see Figure 22) [187] and it is similar to the Dexter

coupling for singlet-singlet ET, in particular because, as it depends on an electron exchange

mechanism, it only takes place at short donor-acceptor distances (<10 Å) [173,178]. In TET

the Förster‘s mechanism will not contribute, because at short distances the dipole

approximation breaks down and because the transitions are dipole-forbidden [187].

The electronic coupling is not the only key factor that determines the efficiency of the ET

process, but also the resonance condition, that is, the energy available in the donor must be at

least equal or higher than that required to populate the excited state of the acceptor. If this is

the case, the process is usually controlled by diffusion and described as exothermic. In the

opposite situation, that is, if the energy of the acceptor is lower than that of the donor, the

process becomes thermally activated and lies in the endothermic region. That means that there

PROOFS ONLY


is an energy barrier whose height will depend on the nature of the acceptor, either classical

(for rigid systems) or non-classical (flexible systems which might find conformations for

efficient, non-vertical TET), with a corresponding larger or smaller, respectively, decay in the

process rate [188].

Figure 23. Scheme of the oxygen-dependent PUVA mechanism.

In particular, the TET process taking place between psoralen and molecular oxygen is:

)(OSPso)(O)T(Pso1*

2

1

0

13

2

3

1

*3

gg

Equation 2

where activated psoralen behaves as a donor in its lowest triplet state, and triplet ground state

oxygen is the acceptor. The lowest excited singlet state of molecular oxygen (1g) is located

at 0.97 eV [2,189,190,191]. Furocoumarins have their lowest-lying triplet T1(Tπ) state energy

at least 1.4 eV higher than the oxygen singlet state (the values of the T1 state at this optimized

geometry for each fucoumarin were computed: Pso, 2.29 eV; 8-MOP, 2.33 eV; 5-MOP, 2.28

eV; TMP, 2.24 eV; Khellin, 2.42 eV; 3-CPS, 2.14 eV), what makes the TET exothermic and

diffusion-controlled, with molecular oxygen behaving as a rigid, classical acceptor [188].

Figure 23 displays a scheme of the TET process for singlet oxygen generation from a triplet

photosensitized psoralen molecule.

In order to analyze reaction rates for electron transfer in the organic molecule-molecular

oxygen (M-O2) photosystem the electronic coupling at some specific arrangement of the

moieties has at least to be estimated. Looking for an appropriate arrangement yielding the

most effective TET process is nontrivial and, in general, not even relevant, in particular in

diffusion-controlled systems which may form a collision complex at short distances. It is

important, however, to estimate reaction rates and lifetimes at different intermolecular

distances. Furthermore, M-O2 interaction potentials are very weak, and the potential surfaces

are generally characterized by multiple shallow minima. Hence it is necessary to consider

different orientations when approaching M and O2 through a basic inter-fragment coordinate,

here the distance R [192]. To find which orientation becomes the most favorable for an

effective TET we have performed an initial exploration taken three molecular systems as

models, studying how the relative orientation of both fragments (donor and acceptor) affects

PROOFS ONLY


the ET process. In particular, we have studied the systems formed by two ethylene molecules

(Et-Et), by the methaniminium cation and ethylene (MetN+-Et), and by ethylene and

molecular oxygen (Et-O2). In the light of this previous study, the most favourable

rearrangement for the photosensitizing process is the face-to-face (FF) conformation.

Figure 24. Face-to-face molecular arrangement between psoralen and molecular oxygen.

Using the information obtained from the model calculations, the supermolecule

furocoumarin-O2 was built placing the molecular oxygen at different distances with respect to

the furocoumarin in a parallel FF orientation with respect to the reactive double bond, which

is the pyrone double bond in psoralen, 8-MOP, 5-MOP, TMP and 3-CPS, and the furan

double bond in khellin. The geometries of both furocoumarin and molecular oxygen were

kept fixed at the CASSCF optimized triplet excited (T1) state structure and the triplet ground

(3g

−) state experimental geometry [100], respectively. The active space employed in all cases

(furocoumarin + O2) was 14 electrons/11 orbitals (8/7 located in the furocoumarin and 6/4

located in O2). The active space was validated after comparing the results with previous

findings in the isolated furocoumarins and control calculations on the oxygen molecule with

larger active spaces and basis sets. The four lowest singlet states and the three lowest triplet

states of the supermolecule were computed. No symmetry restrictions were imposed and the

ANO-L basis set with the contraction scheme C,O [4s3p1d]/H[2s1p] was employed as in our

previous studies in isolated furocoumarins.

In the weak coupling regime in which the electronic interaction is smaller than the

vibrational reorganization energy, the rate for triplet-triplet energy transfer (kTET), and the

corresponding lifetime (kTET), between the donor and the acceptor can be estimated using the

Fermi‘s Golden Rule [178,187]:

EEji

TET

TET Hh

Hh

k

22

22

4ˆ41

Equation 3

where the matrix element of the Hamiltonian, H’, is the electronic part of the energy transfer

(i.e., the electronic coupling) and E is the density of vibrational states in the initial and final

states and their spectral overlap. The inverse of the rate is the lifetime of energy transfer. To

obtain the TET rates for the systems Et-Et, MetN+-Et, Et-O2, and furocoumarin-O2 we have

taken values of E = 0.1 eV1

and (42/h) = 9.5510

15 eV

1 s1

. This order of magnitude for

the value of the density of states was used previously as a good estimation in systems of this

size [187].

PROOFS ONLY


The calculation of the electronic coupling matrix element H’ is the crucial part in the

determination of ET rates and lifetimes. The extent of the coupling controls the energy

transfer process, specifically the passage from one state to another and it can be taken as a

measure of the efficiency of the ET process. Different procedures to estimate the ET coupling

have been developed [193,194,195] based on diabatic localized dimer calculations, monomer

transition densities or transition dipole moments, and a supermolecule ansatz of the dimer

[178], whereas generalization of such approaches to determine TET couplings are also

available [187]. From all procedures, an energy-gap based method such as supermolecule

dimer approach, in which the value of the coupling is obtained as half of the splitting or

perturbation between the interacting states, has been shown to be convenient and accurate

[178,187]. It is clear that its accuracy strongly relies on the quality of the quantum-chemical

method used to perform the electronic structure calculations, something guaranteed in the

present study by using the highly reliable and accurate CASPT2 method.

As already stated, the furocoumarin behaves as a donor in its triplet state and it is capable

of transferring its energy to the molecular oxygen in its triplet ground state to generate the

singlet ground state furocoumarin and excited singlet oxygen (1g). In all cases the energy of

the triplet state of the furocoumarin is much higher (from 2.42 eV in khellin to 2.14 eV in 3-

CPS, vide supra) than the energy of the oxygen 1g state (computed 1.09 eV at this level,

experimental 0.97 eV [2]) and the process falls clearly into the exothermic regime, expected

to be controlled by diffusion. Figure 25 displays the potential energy curves of the lowest-

lying singlet and triplet states of the supermolecule psoralen-O2 in a FF arrangement with

respect to the C3=C4 bond of the pyrone ring at different intermolecular distances.

Figure 25. Potential energy curves of the low-lying excited states of the supermolecule psoralen-

molecular oxygen along the inter-fragment distance (R). The energy coupling H' is obtained as half of

the energy difference |∞ - i| between the initial 41A (T1 of psoralen and

3g

− of O2) and final 1

1A (S0 of

psoralen and 1g of O2) states of the supermolecule at infinite (here 10 Å: we suppose that at 10 Å there

is no coupling between psoralen and molecular oxygen) distance (∞, zero coupling situation) and at

each of the distances (i).

-796.98

-796.96

-796.94

-796.92

-796.90

-796.88

-796.86

-796.84

-796.82

-796.80

2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00

E / a

u

R /Å

A3

1

A3

2

A3

3

A1

1

A1

2

A1

3

A1

4

i

2

iH

2

1

0

1

2

3

1

1 14 OPsoSAOPsoTA gg

PROOFS ONLY


The states of the supermolecule protagonist of the TET are 41A (T1 of psoralen and

3g

−

of O2) as initial energy level and 11A (S0 of psoralen and

1g of O2) as the final outcome of

the process in which both moieties have changed spin and energy. We know that these states

of the supermolecule (41A and 1

1A) correspond to the states involved in the TET process

analyzing the CASSCF wavefunction. Within the present approach the electronic coupling

(H') is obtained (see Figure 25) as half the difference |−i|, where and i are the energy

gaps between the states 41A and 1

1A at infinite distance (at 10 Å in the current computation)

and at the different inter-fragment distances, respectively. In this way, the coupling represents

the perturbation introduced in each state due to the interaction within the dimer. Similar

potential energy curves have been obtained for the rest of the family. The comparison of the

electronic couplings in each furocoumarin at each inter-fragment distance is displayed in

Figure 26.

Figure 26. Comparison between the electronic couplings (H´) triggering the TET process between a

furocoumarin and molecular oxygen at the different inter-fragment distances (R). The coupling

increases as the distance decreases, but the values among furocoumarins are very similar at each

distance.

The computed values of the electronic coupling are very similar among furocoumarins at

each separation. However, it is known experimentally that their efficiency in generating

singlet oxygen is different, so this magnitude may not be the key point in modulating the

efficiency of the ET process in furocoumarins; consequently, the efficiency in populating the

lowest-lying triplet excited state may be again the cornerstone of the problem.

The whole process of generation of singlet oxygen from a photosensitized furocoumarin

does not only depend on the efficiency of the TET from the triplet state of the furocoumarin,

but also on the rate of formation of the triplet state itself. As shown previously in this

chapter, in furocoumarins the crucial step to populate the triplet manifold in the gas phase is

the intersystem crossing (ISC) process between the initially populated singlet Sπ(ππ*) state

and the lowest-lying triplet Tn(n*) state. The latter state evolves subsequently toward the

lowest triplet T1(ππ*) state via a corresponding (and essentially barrierless and ultrafast)

PROOFS ONLY


internal conversion (IC). In a similar manner as for Equation 3, the estimation of the rate

constant, here for nonradiative ISC (kISC), can be obtained as

ESOISC Hh

k 2

24

Equation 4

where HSO stands for the spin-orbit coupling terms for the nonradiative transition Sπ (ππ *)

Tn(n*), which is actually the initial step in the population of the lowest-lying triplet excited

state, the protagonist of the photosensitizing action (see Figure 17). An estimated value of 200

eV1

will be employed for E as used for psoralen in studies explicitly computing vibronic

factors [136].

Additionally to the HSO strength, the presence of energy barriers in the potential energy

hypersurfaces may strongly affect the value of the rate constants, which can be corrected

using the Arrhenius exponential term in the framework of the transition state theory

[196,197,198,199,200]. As a qualitative estimation of these effects, a corrected ISC rate

(k′ISC) can be obtained from:

RTE

ISCISC ekk

'

Equation 5

where kISC is that computed from Equation 4, E is the energy of the barrier from the initial

electronic singlet to the triplet state, R is the ideal gas constant, and T the temperature (298

K).

Figure 27. New scheme of the population of the triplet manifold in furocoumarins. The minimum of S1

is no longer the reference, but we take into account the vibrational excess energy at the Franck-Condon

region. Once the energy has reached the S1 state vertically, the process to its minimum is barrierless and

very fast. However, another possibility is to employ this energy to surmount the barrier and reach the

triplet manifold. Both processes are likely to happen. We will need dynamics calculations in order to

establish which one is the most probable.

OO O

(S /T ) n X

(T /T )n CI

0.26 eV0.36 eV

0.00

–0.83 eV

0.39 eV

(T )MIN

(S )MIN T

S

0.25 eV

(T )n MIN

Tn

1.26 eVTn

T–0.32 eV

ISCSOC~10 cm

-1

h

F P

S0

~3.6 eV74 ns

~2.8 eV28 s

–3.59 eV

E

PROOFS ONLY


In this particular context, E will be estimated as the energy difference between the

singlet S(*) state, populated at the Franck-Condon geometry, and the triplet Tn(n*) state

in the computed crossing point with the singlet state (S/Tn)X. We consider now the

vibrational excess energy at the Franck-Condon region to surmount the barrier and reach the

triplet manifold. In other words (see Figure 17), the S is no longer the reference of energy

(notice that 0.00 is crossed out in Figure 27). In case of excess energy, that is, negative

barriers, we will consider the energy difference as zero. Spin-orbit coupling (HSO) terms and

energy barriers (E) were determined previously for the family of furocoumarins at the

CASPT2 level.

Table IV. Rate constants (k) and decay times () of the radiationless intersystem

crossing (ISC) process S π Tn in the family of the furocoumarins

Furocoumarin E / eV a HSO / cm-1 b kISC / s-1 c k'ISC / s

-1 d 'ISC / ns e

psoralen 0.03 9.2 3.58109 1.11109 0.90

8-MOP −0.01 4.9 1.02109 1.02109 0.98

5-MOP −0.10 3.5 5.18108 5.18108 1.93

khellin −0.19 2.9 3.56108 3.56108 2.81

TMP 0.09 32.2 4.391010 1.32109 0.76

3-CPS −0.24 9.2 3.58109 3.58109 0.28

a Computed energy barriers from Sπ (at the Franck-Condon region) to Tn (at the Sπ-Tn crossing region). See

Table II. b Spin-orbit coupling terms at the Sπ-Tn crossing region along the LIIC path (see Figure 15) computed for

every furocoumarin. c ISC rate constants obtained using Eq. 4. d ISC rate constants obtained using Eq. 5. Negative barriers are taken as zero. e ISC decay times. Inverse of the rate constant as obtained using Eq. 5.

Most of the studied furocoumarins have their initially populated Sπ state well above the

crossing point energy, what leads to negative barriers. In such cases, as we consider that the

system has sufficient energy to reach the ISC region and such process is in the exothermic

regime, the energy barrier on Equation 5 has been made zero. Once all factors considered, the

ISC rates and lifetimes (all in the nanosecond range), although similar for the different

compounds, allows to establish an approximate order of efficiency of the furocoumarins:

khellin < 5-MOP < 8-MOP < psoralen < TMP < 3-CPS, an order which slightly differs from

that proposed in the previous section (remember that khellin was considered the most

efficient photosensitizer) because of the different type of energy barrier considered earlier. To

choose one reference of energy or another is arbitrary, but taking into account the vibrational

excess energy seems to be more relevant in this context, where the interest focuses on rate

constants. The present results can be compared, at least qualitatively, with those reported in

the literature, which are summarized in Table V for the sake of simplicity.

The basic order of efficiency holds true in most cases. In particular, 3-CPS is confirmed

as the best singlet oxygen generator because of its ability to populate the triplet state, in

contrast to the smallest value obtained for the coupling term in this molecule in a previous

section of this chapter. Comparison with experiment seems to support the approach based on

PROOFS ONLY


spin-orbit couplings and energy barriers. Psoralen is also confirmed as good photosensitizer,

whereas TMP and 8-MOP have intermediate efficiency. As most of the experiments show and

our calculations predict, 5-MOP would be a much poorer oxygen generator. For khellin we

also predict a less favorable situation, which more exhaustive experiments will have to

confirm.

Table V. Summary of computed and experimental estimated efficiency orders of the

singlet oxygen generation process by photosensitized furocoumarins

a The theoretical results are based on the estimated efficiency of the ISC

process S (*) → Tn (n*), the crucial step to populate the lowest triplet state of the

furocoumarin, T (*), and initiate the TET process.

CONCLUSIONS

Getting a deep understanding of photochemotherapeutic effects requires having profound

knowledge of the molecular mechanisms involved. Quantum mechanics are one of the most

powerful tools available to analyze the intrinsic mechanisms involved in chemical processes.

The present review has summarized a complete set of studies performed in the family of

furocoumarin molecules, a set of systems which display many of the processes involved in

the phototherapeutic action, from interaction and formation of adducts with DNA nucleobases

to generation of toxic singlet oxygen.

Here we will first outline the key points of our studies and then summarize the results.

The employed quantum-chemical methods (particularly the multiconfigurational

CASPT2 approach) are among the most complex and accurate in theoretical chemistry,

because of the specificity of the treatment of the excited state. Indeed, the results displayed in

this chapter give answers both quantitatively and qualitatively. We should take into account

the employed approximations (systems with more than one electron, truncation of the many-

and one-electronic basis sets) when one judges critically the values obtained. However,

according to previous studies with the method, we can consider CASPT2 results as very

accurate. The calculations were made in the isolated systems, expecting to represent the

Efficiency of the process Ref.

Theorya

khellin < 5-MOP < 8-MOP < psoralen < TMP < 3-CPS Present

Experiment

khellin<8-MOP<psoralen<5-MOP 163

TMP≈5-MOP≈8-MOP<<psoralen<3-CPS 161

5-MOP<8-MOP<psoralen<TMP 20

8-MOP<5-MOP<TMP<khellin<3-CPS 62

5-MOP<8-MOP<psoralen<3-CPS 63

5-MOP<TMP<8-MOP<psoralen 160

PROOFS ONLY


intrinsic chemical phenomena, but we infer qualitatively the effects of the solvent, leaving for

the future simulations of the embedded molecular system.

We have analyzed the two mechanisms of photosensitization in furocoumarins, the

interaction with DNA and with O2 by using high-level quantum-chemical methods. The order

of efficiency of furocoumarins is different depending on the vibrational excess energy after

the absorption process is taken into account or not. This ―extra-energy‖ is usually available in

all system after absorption of electromagnetic radiation. From a static point of view, both

possibilities are likely to happen. To take into account kinetic rate constants is more

reasonable to consider this excess energy. In addition, we have proved that the key point in

both photosensitization mechanisms (interaction with DNA, on the one hand, and energy

transfer to molecular oxygen, on the other hand) is the population of the lowest-lying triplet

excited state (T1 or T). In all the furocoumarins there is a favourable pathway to populate

such a state from the initially-populated S1 state, via hypersurface crossings.

Regarding the properties of the molecules, in the light of our results all of the

furocoumarins, except khellin, may well form pyrone-nucleobase monoadducts (PMAs).

Conversely, khellin may form furane-nucleobase monoadducts (FMAs). Analyzing the

specific case of the monoadduct psoralen-thymine, we have inferred why FMAs are more

abundant than PMAs (because the former is a singlet-mediated mechanism, and the latter is a

triplet-mediated mechanism, which suffer from some spin forbidden processes according to

quantum mechanics). According to the spin population in both monoadducts, we know why

only FMAs may yield diadducts. Spin and charge population are two of the most important

data to explain the reactivity of molecules. In other words, identifying in which zones a

positive or negative charge density is placed, or the spin population is located, gives us a clue

to predict in which specific position the molecule will be attacked by other molecule (and also

the nature of such a molecule), or from which location the molecule is prone to react (and

which kind of reaction is likely to be produced). In this case, FMA (when the

photocycloaddition thymine-furan double bond has already taken place) is likely to react

specifically at the pyrone C=C double bond, then forming diadducts.

To sum up, we can consider 3-CPS as the molecule with the best properties, on quantum-

chemical grounds, to be the best phototherapeutic furocumarine drug. However, we have to

be cautious: the present results, studied at molecular level and focused on the photochemical

properties of the system, are directly comparable only with the gas-phase context. Aspects

such as solvent effects, synthesis, pharmacokinetics, pharmacodynamics, tolerance by

patients, etc, are out of the scope of this research.

Now we are going to analyze the afore-mentioned conclusions in depth: Our findings

show that all of the studied furocoumarins (psoralen, 8-MOP, 5-MOP, khellin, TMP, and 3-

CPS) display similar photophysical properties. The lowest-lying valence singlet state (of *

character, S) absorbs, with more or less intensity, in the energy range employed in

phototherapy, and the lifetime for the lowest triplet * excited state, T, is large enough to

exert its photosensitizing action, in agreement with the literature. This is basically the reactive

state in all compounds, which enlarges one of the two reactive C=C double bonds in the

triplet state increasing then its activity.

Taking into account the qualitative El-Sayed rules, a direct intersystem crossing (energy

transfer) between S and T states is unlikely to happen at the Franck-Condon region because

PROOFS ONLY


neither energy gaps (too large) nor spin-orbit coupling elements (too small) are suitable.

Hence the process may well take place along the relaxation path of S.

The calculations point out that the population mechanism of the T state can be

summarized as follows: πnπ TTS CISTC

, where STC and CI stand for singlet-triplet

crossing and conical intersections, respectively; that is, degeneracy points in the potential

energy hypersurface describing the energetics of the reaction path. The location of those

crossings and the barriers to reach them (in essence their accessibility), together with the

coupling of the intervening states, are the key features which determine the efficiency of the

energy transfer process, and then the outcome of the reaction. Among all furocoumarins,

khellin and 5-MOP show the lowest barrier to reach the STC region. Such a barrier was

computed as the energy difference between the minimum of Sand the singlet-triplet

crossing, (S/Tn)X. Only khellin shows clearly a crossing between S and Tn, on the one hand,

and Tn and T, on the other hand, reflecting the high photosensitizing effectiveness of this

compound. However, the choice of the barrier is not unique. If we take into account the

excess vibrational energy at the Franck-Condon region, the order of photosensitizing ability is

different. In addition, the triplet state of all the furocoumarins, except khellin, is localized in

the pyrone moiety, which is in agreement with both the enlargement of the corresponding

double bond and the Mulliken spin population. Khellin, with a different chemical structure,

shows the spin density localized in the furan reactive double bond. Since there are two

possible monoadducts to be formed due to the existence of two (in principle) reactive double

bonds in each furocoumarin, all of the compounds form PMA (pyrone-monoadduct) through

the T state of the furocoumarin, whereas khellin forms FMA (furan-monoadduct).

The triplet state properties suggest then that FMA would be expected to be formed with

khellin and PMA preferently with the other furocoumarins. The [2+2] photocycloaddition can

be rationalized through different paths. Whereas PMA would be better formed in the triplet

manifold, FMA will be formed in the singlet manifold. As regards PMA, the process begins

with the direct activation of S1(*) state of psoralen, followed by a fast ISC process to the

triplet states of this molecule. As a result, the T1(*) state of the furocoumarin is finally

populated. Next, the system evolves to an intermediate species with a covalent simple bond

between psoralen and thymine, whose lowest triplet state and the singlet manifold are

connected via STC, (S0/T1)STC. The ISC process that takes place through this crossing between

hypersurfaces yields the monoadduct in its ground state. Since the furan double bond is not

reactive in the T1(*) state of psoralen, an alternative way to form FMA along the triplet

manifold is to populate the T1 of thymine due to the action of another photosensitizer.

Nevertheless, this process may be less favorable than the formation of PMA. Considering the

singlet manifold, both monoadducts may well be formed favorably following a barrierless

mechanism that begins with the population of the lowest singlet excited state of psoralen and

finishes in the ground state of the monoadduct by means of a conical intersection, (S0/S1)CI.

Therefore FMA minimum is probably reached through this way. In connection with these

findings, it is probable that the diadduct is formed from the monoadduct in its lowest singlet

state, after the absorption of one photon by the latter and subsequent ISC to T1 state. In FMA,

the spin density is concentrated in the reactive double bond of the pyrone moiety, whereas in

PMA is delocalized. Furthermore, the S1 state of FMA is lower in energy than that of the

PMA, in agreement with experimental findings. Accordingly, FMA may be more prone to

form diadducts than PMA. Additionally, it is understandable that systems with important

PROOFS ONLY


steric repulsions, such as 3-CPS, or with a different structure in the ring, like khellin, yield

FMA preferentially and do not react with a thymine placed in the opposite strand of DNA to

form diadducts, so the undesired side effects connected to crosslinks between the two strands

of DNA are avoided.

The other side of PUVA therapy is the photosensitization via generation of singlet

oxygen. We have analyzed this phenomenon in the light of TET (triplet-triplet energy

transfer) theory. Employing Fermi´s Golden Rule, we have estimated TET rate constants and

lifetimes. To this end, we have considered the system [furocoumarin-O2] as a supermolecule,

and the strength of the electronic coupling between the protagonist states (the lowest triplet

excited state of the former, acting as a donor, and the triplet ground state of the latter, acting

as an acceptor) has been evaluated within the energy-gap approximation. Additionally, the

estimated values for the electronic coupling, TET rate constants and lifetimes are similar for

all the systems (FC-O2; FC = psoralen, 8-MOP, 5-MOP, khellin, TMP and 3-CPS) and the

determined rates do not follow the reported tendencies (obtained experimentally).

Consequently, the electronic coupling factor does not permit rationalizing the differential

efficiency in the generation of singlet oxygen by the furocoumarins, because it is similar for

donors with closely-related structures. Therefore, the key point in this process is probably the

population of the lowest-lying triplet excited state of the donor, that is, the furocoumarin

molecule. In other words, we have to resort to the same feature as in the case of the formation

of furocoumarin-thymine adducts. In this case, we have not only taken into account the

strength of the spin-orbit coupling related to the intersystem crossing (ISC) process between

the initially excited singlet state and the triplet manifold, but we have also analyzed the effect

on the ISC rates of the energy barrier required to access the triplet state. The main difference

with respect to our previous study is that we have considered now the excess (vibrational)

energy available in the system from the initially populated electronic state S(at the Franck-

Condon geometry) to the singlet-triplet crossing structure, (S/Tn)X. The qualitative estimation

of the efficiency of the ISC process leads us to suggest an order for the efficiency of the

singlet oxygen generation in the different furocoumarins for PUVA therapy: khellin < 5-MOP

< 8-MOP < psoralen < TMP < 3-CPS. In this respect, from all compounds studied here, 3-

CPS can be predicted as the best photosensitizer, followed by TMP and psoralen. 5-MOP and

khellin would not be, on the other hand, so efficient. The determined tendencies seem to agree

with most of the experimental determinations in aqueous solution based on the production of

reactive singlet oxygen.

REFERENCES

[1] M. Weichenthal, T. Schwarz. Photodermatol. Photoimmunol. Photomed. 21 (2005)

260.

[2] R. Bonnett. Chemical Aspects of Photodynamic Therapy. Gordon and Breach Science,

Amsterdam, 2000.

[3] O.Arad, A.Gavaldá, Ó.Rey, N.Rubio, D.Sánchez-García, J.I.Borrell, J.Teixidó,

S.Nonell, M.Cañete, A.Juarranz, A.Villanueva, J.C.Stockert, P.J.Díaz. Afinidad 59

(343) 2002.

[4] S.K.Pushpan, S.Venkatraman, V.G.Anand, J.Sankar, D.Parmeswaran, S.Ganesan,

T.K.Chandrashekar. Curr. Med. Chem. − Anti-Cancer Agents 2 (2002) 187.

PROOFS ONLY


[5] The Nobel Foundation: http://www.nobel.org.

[6] J.M. Carrascosa. Actas Dermosifiliogr. 95 (2004) 259.

[7] B.R. Scott, M.A. Pathak, G.R. Mohn. Mutat. Res. 39 (1976) 29.

[8] P.S. Song, K.J. Tapley, Jr. Photochem. Photobiol. 29 (1979) 1176.

[9] E. Ben-Hur, P.S. Song. Adv. Radiat. Biol. 11 (1984) 131.

[10] D. Averbeck. Photochem. Photobiol. 50 (1989) 859.

[11] R. Bonnett. Chem. Soc. Rev. 24 (1995) 19.

[12] A.M. Rouhi. Chem. Eng. News 76 (1998) 22.

[13] K.R.Weishaupt, C.J.Gomer, T.J.Dougherty. Cancer Res. 36 (1976) 2326.

[14] M. Hotokka, B.O. Roos, P. Siegbahn. J. Am. Chem. Soc. 105 (1983) 5263.

[15] W.H. Elliott, D.C. Elliott. Biochemistry and Molecular Biology. Oxford University

Press, 2005.

[16] B.C. Wilson, M.S. Patterson. Phys. Med. Biol. 31 (1986) 327.

[17] W-F. Cheong, S.A. Prahl, A.J. Welch. IEEE J. Quantum Elect. 26 (1990) 2166.

[18] B.C. Wilson, M.S. Patterson. Phys. Med. Biol. 53 (2008) R61.

[19] M. Ochsner. J. Photochem. Photobiol. B: Biol. 39 (1997) 1.

[20] P.C. Joshi, M.A. Pathak. Biochem. Biphys. Res. Comm. 112 (1983) 638.

[21] Y.N. Donan, R. Gurny, E. Alléman. J. Photochem. Photobiol. B: Biol. 66 (2001) 89.

[22] N. J. De Mol, M.J. Beijensbergen van Henegouwen. Photochem. Photobiol. 33 (1981)

815.

[23] H. Meffert, F. Böhm, E. Bauer. Stud. Biophys. 94 (1983) 41.

[24] J. Llano, J. Raber, L.A. Eriksson. J. Photochem. Photobiol. A: Chem. 154 (2003) 235.

[25] J. Cadet, P. Vigny in: H. Morrison (Ed.). Bioorganic Photochemistry 1, John Wiley &

Sons, New Jersey, 1990.

[26] F. DallÁcqua, P. Martelli. J. Photochem. Photobiol. B: Biol. 8 (1991) 235.

[27] W.L. Fowlks. J. Invest. Dermatol. 32 (1959) 249.

[28] M.A. Pathak, J.H. Fellman. Nature (London) 185 (1960) 382

[29] M.A. Pathak, T.B. Fitzpatrick. J. Photochem. Photobiol. B: Biol. 14 (1992) 3.

[30] J.E. Hearst. Chem. Res. Toxic. 2 (1989) 69.

[31] N. Kitamura, S. Kohtani, R. Nagakaki. J. Photochem. Photobiol. C: Photochem. Rev. 6

(2005) 168.

[32] B.J. Parsons. Photochem. Photobiol. 32 (1980) 813.

[33] A.B. Lerner, C.R. Denton, T.B. Fitzpatrick. J. Invest. Dermatol. 20 (1953) 299.

[34] J.A. Parrish, T.B. Fitzpatrick, L. Tannembaum, M.A. Pathak. N. Eng. J. Med. 291

(1974) 1207.

[35] H. Van Weelden, E. Young, J.C. Van der Leun. Br. J. Dermatol. 103 (1980) 1.

[36] W.L. Morison. Photodermatol. Photoimmunol. Photomed. 20 (2004) 315.

[37] J.M. Carrascosa, J. Gardeazábal, A. Pérez-Ferriols, A. Alomar, P. Manrique, M. Jones-

Caballero, M. Lecha, J. Aguilera, J. de la Cuadra. Actas Dermosifiliogr. 96 (2005) 635.

[38] C. Grau-Salvat, J.J. Vilata-Corell, A. Azón-Massoliver, A. Pérez-Ferriols. Actas

Dermosifiliogr. 98 (2007) 611.

[39] M. Aida, M. Kaneko, M. Dupuis in Computational Molecular Biology, edited by J.

Leszczynsky (Elsevier, Ámsterdam, 1999), Vol. 8.

[40] B. Durbeej, L.A. Eriksson. Photochem. Photobiol. 78 (2003) 159.

[41] L. Musajo, G. Rodighiero, F. DallÁcqua. Experiencia XXI (1964) 24.

[42] E.J. Land, F.A.P. Rushton, R.L. Beddoes, J.M. Bruce, R.J. Cernik, S.C. Dawson, O.S.

Mills. J. Chem. Soc., Chem. Commun. (1982) 22.

[43] D. Kanne, K. Straub, J.E. Hearst, H. Rapoport. J. Am. Chem. Soc. 104 (1982) 6754.

[44] D. Kanne, K. Straub, H. Rapoport, J.E. Hearst. Biochem. 21 (1982) 861.

PROOFS ONLY


[45] D.J. Yoo, H.D. Park, A.R. Kim, Y.S. Rho, S.C. Shim. Bull. Korean Chem. Soc. 23

(2002) 1315.

[46] T. Sa e Melo, P. Morliere, R. Santus, L. Dubertret. Photochem. Photobiophys. 7 (1984)

121.

[47] D. Kanne, H. Rapoport, J.E. Hearst. J. Med. Chem. 27 (1984) 531.

[48] R.V. Bensasson, C. Salet, E.J. Land, F.A.P. Rushton. Photochem. Photobiol. 31 (1980)

129.

[49] L. Musajo, F. Bordin, R. Bevilacqua. Photochem. Photobiol. 6 (1967) 927.

[50] M. Sasaki, F. Meguro, E. Kumazawa, H. Fujita, H. Kakishima, T. Sakata. Mut. Res.

197 (1988) 51.

[51] L. Musajo, F. Bordin, G. Caporale, S. Marciani, G. Rigatti. Photochem. Photobiol. 6

(1967) 711.

[52] D. Kanne, H. Rapoport, J.E. Hearst. J. Med. Chem. 27 (1984) 531.

[53] M.S. Rocha, N.B. Viana, O.N. Mesquita. J. Chem. Phys. 121 (2004) 9679.

[54] H. Matsumoto, A. Isobe. Chem.& Pharm. Bull. 29 (1981) 603.

[55] J.C. Ronfard-Haret, D. Averbeck, R.V. Bensasson, E. Bisagni, E.J. Land. Photochem.

Photobiol. 35 (1982) 479.

[56] C.N. Knox, E.J. Land, T.G. Truscott. Photochem. Photobiol. 43 (1986) 359.

[57] W. Poppe, L.I. Grossweiner. Photochem. Photobiol. 22 (1975) 217.

[58] D. Averbeck, L. Dubertret, M. Craw, T.G. Trusscott, F. DallÁcqua, P. Rodighiero, D.

Vedaldi, E.J. Land. Il Farmaco 39 (1983) 57.

[59] N.J. de Mol. Pharmaceutisch Weekblad 3 (1981) 599.

[60] R. Bevilacqua, F. Bordin. Photochem. Photobiol. 17 (1973) 191.

[61] N.J. de Mol, G.M.J. Beijersbergen van Henegouwen, B. van Beele. Photochem.

Photobiol. 34 (1981) 661.

[62] S.G. Jones, A.R. Young, T.G. Truscott. J. Photochem. Photobiol. B: Biol. 21 (1993)

223.

[63] D. Vedaldi, F. DallÁcqua, A. Gennaro, G. Rodighiero. Z. Naturforsch, 38 (1983) 866.

[64] E. Bisagni. J. Photochem. Photobiol. B: Biol. 14 (1992) 23.

[65] P.S. Song, S.C. Shim, W. W. Mantulin. Bull. Chem. Soc. Jpn. 54 (1981) 315.

[66] M. Collet, M. Hoebeke, J. Piette, A. Jakobs, L. Lindqvist, A. Van de Vorst. J.

Photochem. Photobiol. B: Biol. 35 (1996) 221.

[67] W.W. Mantulin, P.S. Song. J. Am. Chem. Soc. 95 (1973) 5122.

[68] H. Matsumoto, Y. Ohkura. Chem. Pharm. Bull. 11 (1978) 3433.

[69] T.S.E. Melo, A. Maçanita, M. Prieto, M. Bazin, J.C. Ronfard-Haret, R. Santus.

Photochem. Photobiol. 48 (1988) 429.

[70] H.K. Kang, E.J. Shin, S.C. Shim. Bull. Korean Chem. Soc. 12 (1991) 554.

[71] M.L. Borges, L. Latterini, F. Elisei, P.F. Silva, R. Borges, R.S. Becker, A.L. Maçanita.


[72] P. Vigny, F. Gaboriau, M. Duquesne, E. Bisagni, D. Averbeck. Photochem. Photobiol.

30 (1979) 557.

[73] J.H. Kim, S.W. Oh, Y.S. Lee, S.C. Shim, Bull. Korean Chem. Soc. 8 (1987) 298.

[74] T. Lai, B.T. Lim, E.C. Lim. J. Am. Chem. Soc. 104 (1982) 7631.

[75] M. Craw, R. V. Bensasson, J. C. Ronfard-Haret, M. T. S. E. Melo, T. G. Truscott.


[76] P.A. Tipler, G. Mosca. Physics for scientists and engineers. 5th edition. W.H. Freeman

and Company. 2003.

[77] P.W. Atkins, J. De Paula. Atkins´s Physical Chemistry. 8th edition. Oxford University

Press. 2006.

PROOFS ONLY


[78] P. Atkins. Galileo´s Finger: The Ten Great Ideas of Science. Oxford University Press.

2003.

[79] F.A. Cotton. Chemical Applications of Group Theory. 3rd edition. John Wiley & Sons.

1990.

[80] M. Hamermesh. Group Theory and its application to physical problems. Addison-

Wesley Publishing Company. 1962.

[81] D.M. Bishop. Group Theory and Chemistry. Dover Publications, Inc. 1993.

[82] M. Merchán, L. Serrano-Andrés. Ab initio methods for Excited States in: M. Olivucci

(Ed.) Computational Photochemistry. Elsevier, Amsterdam. 2005.

[83] L. Serrano-Andrés, M. Merchán. J. Mol. Struct. (THEOCHEM) 729 (2005) 99.

[84] L. Serrano-Andrés, M. Merchán. Spectroscopy: Applications in: Shleyer, PvR. Et al.

(Eds.) Encyclopedia of Computational Chemistry. Wiley, Chichester. 2004.

[85] L. Serrano-Andrés, J.J. Serrano-Pérez. Calculation of Excited States: Molecular

Photophysics and Photochemistry on Display in: A.J. Sadlej, A. Kaczmarek (Eds.)

Vademecum of Computational Chemistry. World Scientific, Singapore. Chapter 3.

2010.

[86] P.W. Atkins, R.S. Friedman. Molecular Quantum Mechanics. Oxford University Press.

3rd edition. 1997.

[87] F. Pilar. Elementary Quantum Chemistry. Dover Publications, Inc. 2001.

[88] G.B. Arfken, H.J. Weber. Mathematical Methods for Physicists. Elsevier Academic

Press. 6th edition. 2005.

[89] L. Pauling, E.B. Wilson, Jr. Introduction to Quantum Mechanics with Applications to

Chemistry. Dover Publications, Inc. 1985.

[90] Szabo, N.S. Ostlund. Modern Quantum Chemistry: Introduction to Advanced

Electronic Structure Theory. Dover Publications, Inc. 1996.

[91] P.-O. Widmark, B.O. Roos (Eds.). European Summerschool in Quantum Chemistry

2005. Books I, II and III. Lund University. 2005.

[92] T. Helgaker, P. Jørgensen, J. Olsen. Molecular Electronic-Structure Theory. John

Wiley & Sons. 2004.

[93] J.M. Mercero, J.M. Matxain, X. López, D.M. Cork, A. Largo, L.A. Eriksson, J.M.

Ugalde. Int. J. Mass Spectrom. 240 (2005) 37.

[94] Dreuw, M. Head-Gordon. Chem. Rev. 105 (2005) 4009.

[95] F. Jensen. Introduction to Computational Chemistry. John Wiley & Sons. 2001.

[96] J. Andrés, J. Bertrán (Eds.). Theoretical and Computational Chemistry: Foundations,

Methods and Techniques. Publicacions de la Universitat Jaume I. Castelló de la Plana.

2007.

[97] O. Tapia. J. Mathem. Chem. 10 (1992) 139.

[98] G.A. Worth, M.A. Robb, B. Lasorne. Mol. Phys. 106 (2008) 2077.

[99] I.N. Levine. Molecular Spectroscopy. John Wiley & Sons. 1975.

[100] D.C. Harris, M.D. Bertolucci. Symmetry and Spectroscopy: An Introduction to

Vibrational and Electronic Spectroscopy. Dover Publications, Inc. 1989.

[101] R.S. Mulliken. Chem. Rev. 6 (1930) 503.

[102] K. Wittel, S.P. McGlynn. Chem. Rev. 77 (1977) 745.

[103] J.L. McHale. Molecular Spectroscopy. Prentice-Hall, Upper Saddle River. 1999.

[104] T. Azumi, K. Matsuzaki. Photochem. Photobiol. 25 (1977) 315.

[105] M. Klessinger, J. Michl. Excited States and Photochemistry of Organic Molecules.

VCH Publishers. 1995.

[106] E. Teller. J. Phys. Chem. 41 (1937) 109.

[107] G. Herzberg, H.C. Longuet-Higgins. Discuss. Faraday Soc. 35 (1963) 77.

[108] M. Klessinger. Angew. Chem. Int. Ed. Engl. 34 (1995) 549.

PROOFS ONLY


[109] F. Bernardi, M. Olivucci, M.A. Robb. Chem. Soc. Rev. 25 (1996) 321.

[110] W. Domcke, D.R. Yarkoni, H. Köppel (Eds.). Conical Intersections: Electronic

Structure, Dynamics & Spectroscopy. Advanced Series in Physical Chemistry. World

Scientific. 2004.

[111] D.R. Yarkoni. J. Phys. Chem. A 105 (2001) 6277.

[112] G.J. Atchity, S.S. Xantheas, K. Ruedenberg. J. Chem. Phys. 95 (1991) 1862.

[113] M. Ben-Nun, T.J. Martínez. Chem. Phys. 259 (2000) 237.

[114] M.J. Paterson, M.J. Bearpark, M.A. Robb, L. Blancafort. J. Chem. Phys. 121 (2004)

11562.

[115] F. Sicilia, L. Blancafort, M.J. Bearpark, M.A. Robb. J. Phys. Chem. A 111 (2007)

2182.

[116] F. Sicilia, M.J. Bearpark, L. Blancafort, M.A. Robb. Theor. Chem. Acc. 118 (2007)

241.

[117] B. Lasorne, F. Sicilia, M.J. Bearpark, M.A. Robb, G.A. Worth, L. Blancafort. J. Chem.

Phys. 128 (2008) 124307.

[118] B. Lasorne, M.J. Bearpark, M.A. Robb, G.A. Worth. J. Phys. Chem. A 112 (2008)

13017.

[119] K. Andersson, M. Barysz, A. Bernhardsson, M.R.A. Blomberg, P. Boussard, D. L.

Cooper, T. Fleig, M. P. Fülscher, B. Hess, G. Karlström, R. Lindh, P.-Å. Malmqvist, P.

Neogrady, J. Olsen, B. O. Roos, A. J. Sadlej, B. Schimmelpfennig, M. Schütz, L. Seijo,

L. Serrano-Andrés, P. E. Siegbahn, J. Stålring, T. Thorsteinsson, V. Veryazov, U.

Wahlgren, and P.-O. Widmark. MOLCAS, Version 6.0. Department of Theoretical

Chemistry, Chemical Center, University of Lund, P.O.B. 124, S-221 00 Lund, Sweden

2002.

[120] G. Karlström, R. Lindh, P.-Å. Malmqvist, B.O. Roos, U. Ryde, V. Veryazov, P.-O.

Widmark, M. Cossi, B. Schimmelpfennig, P. Neogrady, L. Seijo. Comp. Mat. Sci. 28

(2003) 222.

[121] V. Veryazov, P.O. Widmark, L. Serrano-Andrés, R. Lindh, B.O. Roos. Int. J. Quantum

Chem. 100 (2004) 626.

[122] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman,

V.G. Zakrzewski, J.A. Montgomery, Jr., R.E. Stratmann, J.C. Burant, S. Dapprich, J.M.

Millam, A.D. Daniels, K.N. Kudin, M.C. Strain, O. Farkas, J. Tomasi, V. Barone, M.

Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G.A.

Petersson, P.Y. Ayala, Q. Cui, K. Morokuma, D.K. Malick, A.D. Rabuck, K.

Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz, B.B. Stefanov, G. Liu, A.

Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R.L. Martin, D.J. Fox, T. Keith,

M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, C. González, M. Challacombe, P.M.W.

Gill, B. Johnson, W. Chen, M.W. Wong, J.L. Andrés, M. Head-Gordon, E.S. Replogle,

J.A. Pople. Gaussian 98, revision A.6. Gaussian, Inc.: Pittsburgh, PA, 1998..

[123] M.A. El-Sayed. J. Chem. Phys. 38 (1963) 2834.

[124] P. Avouris, W.M. Gelbart, M.A. El-Sayed. Chem. Rev. (Washington D.C.) 77 (1977)

793.

[125] M. Merchán, L. Serrano-Andrés. J. Am. Chem. Soc. 125 (2003) 8108.

[126] M. Merchán, R. González-Luque, T. Climent, L. Serrano-Andrés, E. Rodríguez, M.

Reguero, D. Peláez. J. Phys. Chem. B 110 (2006) 26471.

[127] J.J. Serrano-Pérez, I. González-Ramírez, P.B. Coto, L. Serrano-Andrés, M. Merchán. J.

Phys. Chem. B 112 (2008) 14096.

[128] J.J. Serrano-Pérez, L. Serrano-Andrés, M. Merchán. J. Chem. Phys. 124 (2006)

124502.

[129] T.A. Moore, M.L. Harter, P.S. Song, J. Mol. Spectrosc. 40 (1971) 144.

PROOFS ONLY


[130] S.J. Strickler, R.A. Berg. Relationship J. Chem. Phys. 37 (1962) 814.

[131] Ò. Rubio-Pons, L. Serrano-Andrés, M. Merchán, J. Phys. Chem. A 105 (2001) 9664.

[132] E. Yeargers, L. Augenstein, J. Invest. Dermatol. 44 (1965) 181.

[133] J.J. Serrano-Pérez, M. Merchán, L. Serrano-Andrés. Chem. Phys. Lett. 434 (2007) 107.

[134] J. Tatchen, M. Kleinschmidt, C.M. Marian. J. Photochem. Photobiol. A: Chem. 167

(2004) 201.

[135] J. Tatchen, C.M. Marian. Phys. Chem. Chem. Phys. 8 (2006) 2133.

[136] J. Tatchen, N. Gilka, C.M. Marian. Phys. Chem. Chem. Phys. 9 (2007) 5209.

[137] J.J. Serrano-Pérez, R. González-Luque, M. Merchán, L. Serrano-Andrés. J. Photochem.

Photobiol. A: Chem. 199 (2008) 34.

[138] J.J. Serrano-Pérez, M. Merchán, L. Serrano-Andrés. J. Phys. Chem. B 112 (2008)

14002.

[139] B.H. Johnston, M.A. Johnson, C.B. Moore, J.E. Hearst. Science 197 (1977) 906.

[140] R.V. Bensasson, E.J. Land, C. Salet. Photochem. Photobiol. 27 (1978) 273.

[141] R.B. Woodward, R. Hoffmann. Angew. Chem. Int. Ed. 8 (1969) 781.

[142] J. Clayden, N. Greeves, S. Warren, P. Wothers. Organic Chemistry. Oxford University

Press. 2001.

[143] W.Th.A.M. Van der Lugt, L.J. Oosterhoff. J.Am.Chem.Soc. 91 (1969) 6042.

[144] F. Bernardi, A. Bottoni, M.A. Robb, H.B. Schlegel, G. Tonachini. J. Am. Chem. Soc.

107 (1985) 2260.

[145] F. Bernardi, S. De, M. Olivucci, M.A. Robb. J. Am. Chem. Soc. 112 (1990) 1737.

[146] P.C. Joshi, M.A. Pathak. Ind. J. Biochem. Biophys. 32 (1995) 63.

[147] P. Saenz-Méndez, R.C. Guedes, D.J.V.A. Dos Santos, L.A. Eriksson. Res. Lett. Phys.

Chem. 2007 (2007) 60623.

[148] J.H. Kim, S.W. Oh, Y.S. Lee, S.C. Shim. Bull. Korean Chem. Soc. 8 (1987) 298.

[149] J.H. Kim, S.H. Shon. Bull. Korean Chem. Soc. 13 (1992) 173.

[150] J.H. Kim, S.H. Shon, G.S. Lee, S.K. Yang, S.W. Hong. Bull. Korean Chem. Soc. 14

(1993) 487.

[151] J.H. Kim, S.H. Shon, S.K. Yang. Bull. Korean Chem. Soc. 15 (1994) 597.

[152] J.H. Kim, S.H. Shon, S.K. Yang, I.H. Cho, S.W. Hong. Bull. Korean Chem. Soc. 18

(1997) 123.

[153] T.M. El-Gogary, G.J. Koehler. Mol. Struct.: Theochem. 808 (2007) 97.

[154] S.F. Boys, F. Bernardi. Mol. Phys. 100 (2002) 65.

[155] G. Olaso-González, D. Roca-Sanjuán, L. Serrano-Andrés, M. Merchán. J. Chem. Phys.

125 (2006) 231102.

[156] F. Bosca, V. Lhiaubet-Vallet, M.C. Cuquerella, J.V. Castell, M.A. Miranda. J. Am.

Chem. Soc. 128 (2006) 6318.

[157] D. Roca-Sanjuán, G. Olaso-González, I. González-Ramírez, L. Serrano-Andrés, M.

Merchán. J. Am. Chem. Soc. 130 (2008) 10768.

[158] J.J. Serrano-Pérez, R. González-Luque, M. Merchán, L. Serrano-Andrés. J. Phys.

Chem. B 111 (2007) 11880.

[159] J.J. Serrano-Pérez, G. Olaso-González, M. Merchán, L. Serrano-Andrés. Chem. Phys.

360 (2009) 85.

[160] Q.A. Blan, L.I. Grossweiner. Photochem. Photobiol. 45 (1987) 177.

[161] M.A. Pathak, P.C. Joshi, Biochimica et Biophysica Acta 798 (1984) 115.

[162] P. Martelli, L. Bovalini, S. Ferri, G.G. Franchi. M. Bari. Febs Letters 189 (1985) 255.

[163] H.Y. Aboul-Enein, A. Kladna, I. Kruk, K. Lichszteld, T. Michalska. Biopolimers

(Biospectroscopy) 72 (2003) 59.

[164] F. Wilkinson. J. Phys. Chem. 66 (1962) 2569.

[165] G.W. Robinson, R.P. Frosch. J. Chem. Phys. 38 (1963) 1187.

PROOFS ONLY


[166] A.A. Gorman, I. Hamblett, C. Lambert, B. Spencer, M.C. Standen. J. Am. Chem. Soc.

110 (1988) 8053.

[167] O.L.J. Gijzeman, F. Kaufman, G. Porter. J. Chem. Soc. Faraday Trans. 2 69 (1973)

708.


721.


1143.

[170] F. Wilkinson, D.J. McGarvey, A.F. Olea. J. Phys. Chem. 98 (1994) 3762.

[171] A.F. Olea, F. Wilkinson. J. Phys. Chem. 99 (1995) 4518.

[172] S. Wang, R. Gao, F. Zhou, M. Selke. J. Mater. Chem. 14 (2004) 487.

[173] Th. Förster. Ann. Phys. 2 (1948) 55.

[174] J. Barber. Rep. Prog. Phys. 41 (1978) 1159.

[175] H. Singh, B. Bagchi. Current Science 89 (2005) 1710.

[176] L. Stryer, R.P. Haugland. Biochem. 58 (1967) 719.

[177] J.R. Lakowicz. Principles of Fluorescence Spectroscopy. 2nd edition, Kluwer

Academic/Plenum Publishers, 1999.

[178] R.F. Fink, J. Pfister, A. Schneider, H. Zhao, B. Engels. Chem. Phys. 343 (2008) 353.

[179] D.L. Dexter. J.Chem.Phys. 21 (1953) 836.

[180] D.W. Liao, W.D. Cheng, J. Bigman, Y. Karni, S. Speiser, S.H. Lin. J. Chin. Chem.

Soc. 42 (1995) 177.

[181] G.D. Scholes, K.P. Ghiggino. J. Chem. Phys. 101 (1994) 1251.

[182] R.D. Harcourt, G.D. Scholes, K.P. Ghiggino. J. Chem. Phys. 101 (1994) 10521.

[183] G.D. Scholes, R.D. Harcourt. J.Chem.Phys. 104 (1996) 5054.

[184] G.D. Scholes. J.Phys.Chem. 100 (1996) 18731.

[185] Terenin, V. Ermolaev. Trans. Faraday Soc. 52 (1956) 1042.

[186] N. J. Turro. Modern molecular photochemistry. University Science Books, Sausalito,

1991.

[187] Z.-Q. You, C.-P. Hsu, G.R. Fleming. J. Chem. Phys. 124 (2006) 44506.

[188] L.M. Frutos, O. Castaño. J. Chem. Phys. 123 (2005) 104108.

[189] P.H. Krupenie. J. Phys. Chem. 1 (1972) 423.

[190] F. Nyasulu, J. Macklin, W. Cusworth III. J. Chem. Ed. 79 (2002) 356.

[191] D. Tudela, V. Fernández. J. Chem. Ed. 80 (2003) 1381.

[192] M.J. Paterson, O. Christiansen, F. Jensen, P. R. Ogilby. Photochem. Photobiol. 82

(2006) 1136.

[193] G. D. Scholes, K. P. Ghiggino. J. Chem. Phys. 101 (1994) 1251.

[194] G. D. Scholes, R. D. Harcourt, K. P. Ghiggino. J. Chem. Phys. 102 (1995) 9574.

[195] G.D. Scholes, R.D. Harcourt. J. Chem. Phys. 104 (1996) 5054

[196] D.G. Truhlar. J. Phys. Chem. 83 (1979) 188.

[197] D.G. Truhlar, B.C. Garrett. Acc. Chem. Res. 13 (1980) 440.

[198] A.D. Isaacson, D.G. Truhlar. J. Chem. Phys. 76 (1982) 1380.

[199] D.G. Truhlar, W.L. Hase, J.T. Hynes. J. Phys. Chem. 87 (1983) 2664.

[200] D.G. Truhlar, B.C. Garrett, S.J. Klippenstein. J. Phys. Chem. 100 (1996) 12771. PROOFS ONLY

PROOFS ONLY

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