7/27/2019 Absorption of UV-Visible Ligh http://slidepdf.com/reader/full/absorption-of-uv-visible-ligh 1/14 2 Absorption of UV–visible light La lumie `re (...) donne la couleur et l’e ´clat a ` toutes les productions de la nature et de l’art; elle multiplie l’univers en le peignant dans les yeux de tout ce qui respire. Abbe ´ Nollet, 1783 [Light (...) gives color and brilliance to all works of nature and of art; it multiplies the universe by painting it in the eyes of all that breathe.] The aim of this chapter is to recall the basic principles of light absorption by mol- ecules. The reader is referred to more specialized books for further details. 2.1 Types of electronic transitions in polyatomic molecules An electronic transition consists of the promotion of an electron from an orbital of a molecule in the ground state to an unoccupied orbital by absorption of a photon. The molecule is then said to be in an excited state. Let us recall first the various types of molecular orbitals. A s orbital can be formed either from two s atomic orbitals, or from one s and one p atomic orbital, or from two p atomic orbitals having a collinear axis of sym- metry. The bond formed in this way is called a s bond. A p orbital is formed from two p atomic orbitals overlapping laterally. The resulting bond is called a p bond. For example in ethylene (CH 2 b CH 2 ), the two carbon atoms are linked by one s and one p bond. Absorption of a photon of appropriate energy can promote one of the p electrons to an antibonding orbital denoted by p à . The transition is then called p !p à . The promotion of a s electron requires a much higher energy (absorption in the far UV) and will not be considered here. A molecule may also possess non-bonding electrons located on heteroatoms such as oxygen or nitrogen. The corresponding molecular orbitals are called n or- Molecular Fluorescence: Principles and Applications . Bernard Valeur > 2001 Wiley-VCH Verlag GmbH ISBNs: 3-527-29919-X (Hardcover); 3-527-60024-8 (Electronic) 20
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The aim of this chapter is to recall the basic principles of light absorption by mol-ecules. The reader is referred to more specialized books for further details.
2.1
Types of electronic transitions in polyatomic molecules
An electronic transition consists of the promotion of an electron from an orbital of
a molecule in the ground state to an unoccupied orbital by absorption of a photon.
The molecule is then said to be in an excited state. Let us recall first the various
types of molecular orbitals.
A s orbital can be formed either from two s atomic orbitals, or from one s and
one p atomic orbital, or from two p atomic orbitals having a collinear axis of sym-
metry. The bond formed in this way is called a s bond. A p orbital is formed from
two p atomic orbitals overlapping laterally. The resulting bond is called a p bond.
For example in ethylene (CH2 b CH2), the two carbon atoms are linked by one s and
one p bond. Absorption of a photon of appropriate energy can promote one of the p
electrons to an antibonding orbital denoted by pÃ. The transition is then called
p! pÃ. The promotion of a s electron requires a much higher energy (absorption
in the far UV) and will not be considered here.
A molecule may also possess non-bonding electrons located on heteroatoms
such as oxygen or nitrogen. The corresponding molecular orbitals are called n or-
Molecular Fluorescence: Principles and Applications . Bernard Valeur> 2001 Wiley-VCH Verlag GmbH
bitals. Promotion of a non-bonding electron to an antibonding orbital is possible
and the associated transition is denoted by n ! pÃ.
The energy of these electronic transitions is generally in the following order:
n ! pà < p ! pà < n ! sà < s ! pà < s! sÃ
To illustrate these energy levels, Figure 2.1 shows formaldehyde as an example,
with all the possible transitions. The n ! pà transition deserves further attention:
upon excitation, an electron is removed from the oxygen atom and goes into the pÃ
orbital localized half on the carbon atom and half on the oxygen atom. The n–pÃ
excited state thus has a charge transfer character, as shown by an increase in the
dipole moment of about 2 D with respect to the ground state dipole moment of
C b O (3 D).
In absorption and fluorescence spectroscopy, two important types of orbitals areconsidered: the Highest Occupied Molecular Orbitals (HOMO) and the Lowest
Unoccupied Molecular Orbitals (LUMO). Both of these refer to the ground state of
the molecule. For instance, in formaldehyde, the HOMO is the n orbital and the
LUMO is the pà orbital (see Figure 2.1).
When one of the two electrons of opposite spins (belonging to a molecular orbital
of a molecule in the ground state) is promoted to a molecular orbital of higher en-
ergy, its spin is in principle unchanged (Section 2.3) so that the total spin quantum
number (S ¼ Ss i, with s i ¼ þ 12 or À 1
2) remains equal to zero. Because the multi-
Fig. 2.1. Energy levels of molecular orbitals in formaldehyde
plicities of both the ground and excited states ðM ¼ 2Sþ 1Þ is equal to 1, both are
called singlet state (usually denoted S0 for the ground state, and S1; S2; . . . for the
excited states) (Figure 2.2)1). The corresponding transition is called a singlet–singlet
transition. It will be shown later that a molecule in a singlet excited state may un-
dergo conversion into a state where the promoted electron has changed its spin;
because there are then two electrons with parallel spins, the total spin quantum
number is 1 and the multiplicity is 3. Such a state is called a triplet state because it
corresponds to three states of equal energy. According to Hund’s Rule, the triplet
state has a lower energy than that of the singlet state of the same configuration.
In a molecule such as formaldehyde, the bonding and non-bonding orbitals arelocalized (like the bonds) between pairs of atoms. Such a picture of localized or-
bitals is valid for the s orbitals of single bonds and for the p orbitals of isolated
double bonds, but it is no longer adequate in the case of alternate single and double
carbon–carbon bonds (in so-called conjugated systems). In fact, overlap of the p
orbitals allows the electrons to be delocalized over the whole system (resonance
Fig. 2.2. Distinction between
singlet and triplet states, using
formaldehyde as an example.
1) In some cases, the ground state is not asinglet state, e.g. dioxygen, anion and cationradicals of aromatic molecules.
effect). Butadiene and benzene are the simplest cases of linear and cyclic con-
jugated systems, respectively.
Because there is no overlap between the s and p orbitals, the p electron system
can be considered as independent of the s bonds. It is worth remembering that the
greater the extent of the p electron system, the lower the energy of the low-lying
p ! pà transition, and consequently, the larger the wavelength of the correspond-ing absorption band. This rule applies to linear conjugated systems (polyenes) and
cyclic conjugated systems (aromatic molecules).
2.2
Probability of transitions. The Beer–Lambert Law. Oscillator strength
Experimentally, the efficiency of light absorption at a wavelength l by an absorbing
medium is characterized by the absorbance A ðlÞ or the transmittance T ðlÞ, defined
as
A ðlÞ ¼ log I 0l
I l¼ Àlog T ðlÞ
ð2:1Þ
T ðlÞ ¼I lI 0l
where I 0l and I l are the light intensities of the beams entering and leaving the ab-
sorbing medium, respectively2).
In many cases, the absorbance of a sample follows the Beer–Lambert Law
A ðlÞ ¼ logI 0lI l¼ eðlÞlc ð2:2Þ
where eðlÞ is the molar (decadic) absorption coefficient (commonly expressed inL molÀ1 cmÀ1), c is the concentration (in mol LÀ1) of absorbing species and l is the
absorption path length (thickness of the absorbing medium) (in cm). Derivation of
the Beer–Lambert Law is given in Box 2.1.
2) The term intensity is commonly used but isimprecise. According to IUPAC recommen-dations (see Pure & Appl. Chem. 68, 2223–2286 (1996)), this term should be replaced bythe spectral radiant power P l, i.e. the radiantpower at wavelength l per unit wavelength
interval. Radiant power is synonymous withradiant (energy) flux. The SI unit for radiantpower is J sÀ1 ¼ W; the SI unit for spectralradiant power is W mÀ1, but a commonlyused unit is W nmÀ1.
2.2 Probability of transitions. The Beer–Lambert Law. Oscillator strength 23
Box 2.1 Derivation of the Beer–Lambert Law and comments on its practical use
Derivation of the Beer–Lambert Law from considerations at a molecular scale is
more interesting than the classical derivation (stating that the fraction of light
absorbed by a thin layer of the solution is proportional to the number of ab-
sorbing molecules). Each molecule has an associated photon-capture area, called
the molecular absorption cross-section s, that depends on the wavelength. A
thin layer of thickness dl contains dN molecules. dN is given by
dN ¼ N acS dl
where S is the cross-section of the incident beam, c is the concentration of the
solution and N a is Avogadro’s number. The total absorption cross-section of the
thin layer is the sum of all molecular cross-sections, i.e. s dN . The probability of
photon capture is thus s dN =S and is simply equal to the fraction of light
ðÀdI =I Þ absorbed by the thin layer:
ÀdI
I ¼
s dN
S¼ N asc dl
Integration leads to
ln I 0I ¼ N ascl or log I 0
I ¼ 1
2:303N ascl
where l is the thickness of the solution. This equation is formally identical to Eq.
(2.2) with e ¼ N as=2:303.
The molecular absorption cross-section can then be calculated from the ex-
perimental value of e using the following relation:
s ¼2:303e
N a¼ 3:825 Â 10À19e ðin cm2Þ
Practical use of the Beer–Lambert law deserves attention. In general, the sample
is a cuvette containing a solution. The absorbance must be characteristic of theabsorbing species only. Therefore, it is important to note that in the Beer–Lam-
bert Law ðA ðlÞ ¼ log I 0=I ¼ eðlÞlc Þ, I 0 is the intensity of the beam entering the
solution but not that of the incident beam I i on the cuvette, and I is the intensity
of the beam leaving the solution but not that of the beam I S leaving the cuvette
(see Figure B2.1). In fact, there are some reflections on the cuvette walls and
these walls may also absorb light slightly. Moreover, the solvent is assumed to
have no contribution, but it may also be partially responsible for a decrease in
intensity because of scattering and possible absorption. The contributions of the
2.2 Probability of transitions. The Beer–Lambert Law. Oscillator strength 25
value is 1. For n ! pà transitions, the values of e are in the order of a few hundreds
or less and those of f are no greater than@10À3. For p! pà transitions, the values
of e and f are in principle much higher (except for symmetry-forbidden tran-
sitions): f is close to 1 for some compounds, which corresponds to values of e that
are of the order of 10 5. Table 2.1 gives some examples of values of e.
In the quantum mechanical approach, a transition moment is introduced for
characterizing the transition between an initial state and a final state (see Box 2.2).
The transition moment represents the transient dipole resulting from the dis-
placement of charges during the transition; therefore, it is not strictly a dipolemoment.
The concept of transition moment is of major importance for all experiments
carried out with polarized light (in particular for fluorescence polarization experi-
ments, see Chapter 5). In most cases, the transition moment can be drawn as a
vector in the coordinate system defined by the location of the nuclei of the atoms4);
therefore, the molecules whose absorption transition moments are parallel to the
electric vector of a linearly polarized incident light are preferentially excited. The
probability of excitation is proportional to the square of the scalar product of the
transition moment and the electric vector. This probability is thus maximum when
the two vectors are parallel and zero when they are perpendicular.
For p ! pà transitions of aromatic hydrocarbons, the absorption transition mo-
ments are in the plane of the molecule. The direction with respect to the molecular
axis depends on the electronic state attained on excitation. For example, in naph-thalene and anthracene, the transition moment is oriented along the short axis for
the S0 ! S1 transition and along the long axis for the S 0 ! S2 transition. Various
examples are shown in Figure 2.3.
Tab. 2.1. Examples of molar absorption coefficients, e (at the wavelength corresponding to the
maximum of the absorption band of lower energy). Only approximate values are given, because
the value of e slightly depends on the solvent
Compound e /L mol À1 cmÀ1 Compound e /L mol À1 cmÀ1
Benzene A200 Acridine A12000
Phenol A2 000 Biphenyl A16000
Carbazole A4 200 Bianthryl A24000
1-Naphthol A5 400 Acridine orange A30000
Indole A5 500 Perylene A34000
Fluorene A9 000 Eosin Y A90000
Anthracene A10 000 Rhodamine B A105000
Quinine sulfate A10000
4) Note that this is not true for moleculeshaving a particular symmetry, such asbenzene ðD6hÞ, triphenylene ðD3hÞ and C60
ðIhÞ.
2.2 Probability of transitions. The Beer–Lambert Law. Oscillator strength 27
There are two major selection rules for absorption transitions:
1. Spin-forbidden transitions. Transitions between states of different multiplicities
are forbidden, i.e. singlet–singlet and triplet–triplet transitions are allowed, but
singlet–triplet and triplet–singlet transitions are forbidden. However, there is
always a weak interaction between the wavefunctions of different multiplicities
via spin–orbit coupling5). As a result, a wavefunction for a singlet (or triplet)
state always contains a small fraction of a triplet (or singlet) wavefunction
C ¼ a1Cþ b 3C; this leads to a small but non-negligible value of the intensity
integral during a transition between a singlet state and a triplet state or vice
versa (see Scheme 2.1). In spite of their very small molar absorption coefficients,
such transitions can be effectively observed.
Intersystem crossing (i.e. crossing from the first singlet excited state S1 to the
first triplet state T1) is possible thanks to spin–orbit coupling. The efficiency of
this coupling varies with the fourth power of the atomic number, which explains
why intersystem crossing is favored by the presence of a heavy atom. Fluores-
cence quenching by internal heavy atom effect (see Chapter 3) or external heavy
atom effect (see Chapter 4) can be explained in this way.
2. Symmetry-forbidden transitions. A transition can be forbidden for symmetry
reasons. Detailed considerations of symmetry using group theory, and its con-
sequences on transition probabilities, are beyond the scope of this book. It isimportant to note that a symmetry-forbidden transition can nevertheless be ob-
served because the molecular vibrations cause some departure from perfect
symmetry (vibronic coupling). The molar absorption coefficients of these tran-
sitions are very small and the corresponding absorption bands exhibit well-
defined vibronic bands. This is the case with most n ! pà transitions in solvents
that cannot form hydrogen bonds (eA100–1000 L molÀ1 cmÀ1).
2.4
The Franck–Condon principle
According to the Born–Oppenheimer approximation, the motions of electrons are
much more rapid than those of the nuclei (i.e. the molecular vibrations). Promo-
tion of an electron to an antibonding molecular orbital upon excitation takes about
10À15 s, which is very quick compared to the characteristic time for molecular vi-
5) Spin–orbit coupling can be understood in aprimitive way by considering the motion of an electron in a Bohr-like orbit. The rotationaround the nucleus generates a magneticmoment; moreover, the electron spins about
an axis of its own, which generates anothermagnetic moment. Spin–orbit couplingresults from the interaction between thesetwo magnets.
Birks J. B. (1970) Photophysics of Aromatic Molecules , Wiley, London.
Herzberg G. (1966) Molecular Spectra andMolecular Structure. III Electronic Spectraand Electronic Structure of PolyatomicMolecules, Van Nostrand ReinholdCompany, New York.
Jaffe H. H. and Orchin M. (1962) Theory and Applications of Ultraviolet Spectroscopy ,John Wiley & Sons, New York.
Turro N. J. (1978) Modern Molecular Photochemistry , Benjamin/Cummings,Menlo Park, CA.