Integrated experimental and computational spectroscopy study on π-stacking interaction: the anisole dimer

This journal is c the Owner Societies 2010 Phys. Chem. Chem. Phys., 2010, 12, 13547–13554 13547

Integrated experimental and computational spectroscopy study

on p-stacking interaction: the anisole dimer

Nicola Schiccheri,a Massimiliano Pasquini,wa Giovanni Piani,a

Giangaetano Pietraperzia,wa Maurizio Becucci,w*a Malgorzata Biczysko,*bc

Julien Bloinobc

and Vincenzo Baronec

Received 11th February 2010, Accepted 5th July 2010

DOI: 10.1039/c002992k

Integrated experimental and computational results help to clarify the nature of the intermolecular

interactions in a simple, isolated p-stacked dimer prepared in a molecular beam. The properties of

bimolecular anisole complexes are examined and discussed in terms of the local/supramolecular

nature of the electronic wavefunctions. Experimental resonance-enhanced multi-photon ionization

spectra of clusters with different isotopic compositions confirmed the fundamentally localized

nature of the S1 ’ S0 electronic transition. A detail analysis of the experimental results however

shows the existence of non-negligible excitonic coupling for the excited-state wavefunctions

leading to the doubling of the single-molecule vibronic levels in the S1 state, with a splitting of

about 30 cm�1. Theoretical simulation of the vibrationally resolved electronic spectra and

computations of the excitonic coupling convincingly support the experimental findings.

The overall combined experimental/theoretical study allows a detailed description of the stacking

interaction in the anisole dimer.

1. Introduction

Intermolecular interactions are among the most fundamental

forces, which strongly influence the physical-chemical properties of

matter. In this context, we can recall the cases of condensed

phases or the formation of supramolecular systems, as well as

self-assembly or molecular recognition processes, which all

depend on the mechanisms of information and energy transport

between molecules.1 It is already widely recognized that the

nature of weak intermolecular interactions present in

macromolecular systems of biological2–4 and technological

interest5–7 can be effectively explored with the aid of electronic

spectroscopy experiments accompanied by the analysis of

possible excitonic coupling. However, studies on such complex

systems are not able to reveal the character of a specific

intermolecular interaction, which requires molecular

aggregates isolated from any possible external perturbation.

In this respect, great efforts have recently been devoted to the

experimental studies of dimers of aromatic molecules

produced in molecular beam environments.8 Highly resolved

spectroscopic studies are able to directly probe electronic

properties such as the supramolecular/local character of

electronic excitations, which result in strong/weak excitonic

couplings. In general, the coupling efficiency is greatly

enhanced for complexes formed by equivalent units, namely

partners of a given complex, having exactly the same isotopic

composition and electronic density. Perhaps the most studied

case so far has been the benzene dimer, investigated by

microwave and electronic spectroscopy methods.9,10 For the

benzene dimer a small excitonic coupling between the two

units has been reported by Schlag et al.,10 resulting in a

splitting of about 2 cm�1: this is in line with the presence of

two equivalent benzene units, resulting in a C2v structure of the

dimer, in contrast with the T-shaped structure evidenced by

microwave spectroscopy.9

As an example of molecular complexes where the two units

are equivalent we can mention the 2-pyridone dimer: a planar

and center-symmetric cluster stabilized by two hydrogen

bonds between the N–H and O atoms with a 2.7 A inter-

molecular distance. Indeed, the high-resolution electronic

spectroscopy study carried out by Held and Pratt clearly

demonstrated the supramolecular nature of this complex,11

characterized by a strong coupling of the electronic wavefunction

of the two units, resulting in the complete delocalization of the

excitation. Moreover, the isotopic substitution of a single unit

in the complex removes the equivalence of both moieties,

leading to the observed excitonic splitting. This has been

observed by Leutwyler’s group,12 which reported the excitonic

splitting (of about 50 cm�1) of the vibronic energy levels for

the molecular complex in the excited electronic S1 state, caused

by symmetry breaking in the system after a single H/D or12C/13C isotopic exchange. An analogous splitting of 11 cm�1

was demonstrated for 2-aminopyridine.13 In this case, the

effect was also observed for isotopically equivalent species,

but has been enhanced by a single 12C/13C substitution. It

should be noted that in some cases, e.g. for the 2-pyridone/

2-hydroxypyridine complex and the phenol dimer, a delocalized

nature of the excited state has been suggested14,15 even if the

a LENS, Polo Scientifico e Tecnologico, Universita di Firenze,via N. Carrara 1, 50019 Sesto Fiorentino, Italy.E-mail: [email protected]

bDipartimento di Chimica ‘‘Paolo Corradini’’ and CR-INSTMVillage, Universita di Napoli ‘‘Federico II’’, Complesso Univ.Monte S. Angelo, via Cintia, 80126 Napoli, Italy.E-mail: [email protected]

c Scuola Normale Superiore, piazza dei Cavalieri 7, 56126 Pisa, Italyw Also at Dipartimento di Chimica, Universita di Firenze, Italy

PAPER www.rsc.org/pccp | Physical Chemistry Chemical Physics

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13548 Phys. Chem. Chem. Phys., 2010, 12, 13547–13554 This journal is c the Owner Societies 2010

two units are not equivalent. Additionally, it should be

stressed that all these studies probed complexes stabilized by

hydrogen bonding, either planar or non-planar.

The present work is devoted instead to studying the nature

of the p-stacking interaction taking place when two aromatic

molecules are superimposed on parallel planes. This very

common phenomenon plays an important role in the crystal

structure of aromatic compounds in the solid state16 and in

liquid crystals which are known to form columnar structures

with superimposed aromatic groups.17 This weak interaction

can also be used as a molecular self-assembly technique in

bottom-up nanotechnology1 or can be effectively exploited in

gas sensors to detect the presence of aromatic chemicals.18

Moreover, p-stacking strongly affects the properties of

polymers of different natures, such as polystyrene, aramids,

RNA, DNA, proteins, peptides,19 and undoubtedly plays a

fundamental role in other systems of biological interest. The

most famous example is the double strand helix of DNA,

where the p-stacking occurs between adjacent nucleotides and

contributes to the overall stability of the structure.20

Despite its importance and wide appearance, the p-stackinginteraction is not well understood yet and different aspects are

pointed out depending on the scientific field in which such a

phenomenon is studied. For example, in the area of molecular

biology, stacking is sometimes referred to as a hydrophobic

interaction, to distinguish it from the dipolar interactions

and hydrogen bonding typical in a water environment.21

Moreover, the description of the p-stacking interaction is

commonly given in classical terms, while its exact nature is

quantum mechanical (QM). Within the QM framework,

p-stacking is attributed to a partial overlap of p-orbitals

and/or electron correlation in p-conjugated systems placed in

a suitable geometry. It is worth noting that the correct

description of the p-stacking interaction is still a challenging

task for computational chemistry, and wavefunction-based

correlation methods with extended basis sets22,23 are required

to model it accurately. However, for larger systems, a correct

inclusion of the most relevant aspects of the process at a

reasonable computational cost has become possible using the

recent developments in density functional theory (DFT).24–27

It should also be stressed that a direct vis-a-vis comparison

between experimental and computed vibrationally resolved

electronic spectra, necessary to dissect the vibrational and

vibronic effects in the former, has become possible only

recently due to novel theoretical approaches,28,31–33 allowing

the simulation of the vibronic structure of electronic spectra

for medium-to-large molecular systems.

In this regard, anisole is a convenient model system for

the study of weak intermolecular interactions since different

possible mechanisms co-exist but no dominant terms are

present34–37 (unlike some molecules, such as phenol, which

tend to prefer hydrogen-bonding interactions). Here, we

present a discussion on the properties of the anisole dimer, a

simple isolated supramolecular system stabilized by p-stackinginteractions in the gas phase. The structure of this complex

was determined using the combined efforts of high-resolution

spectroscopy and theoretical modelling, as described in detail

in a previous report.38 The anisole dimer is a center-symmetric

system with the two units placed in a parallel configuration at

a distance of 3.4 A. This arrangement results mostly from

dispersion interactions between the two moieties.38 In this

work, special emphasis will be given to the nature of this

p-stacking interaction as derived by an integrated experimental

and computational evaluation of the molecular/supramolecular

properties of the wavefunction.

2. Experimental methods and data analysis

The experimental setup was reported previously.35,39 Here we

will provide only a brief summary and the most relevant

details.

This study of the anisole clusters was carried out using

species with different isotopic compositions. We used isotopically

substituted samples of anisole obtained from C/D/N Isotopes

(anisole-2,4,6-d3, from now on referred to as DOP, with

deuteration in the para and in the two ortho positions of the

aromatic ring) and Aldrich (anisole with 1H atoms only or H8;

anisole-2,3,4,5,6-d5 or D5, with full deuteration on the aromatic

ring; methoxy-d3-benzene or D3, with full deuteration on the

methyl group).

Resonance-enhanced multi-photon ionization experiments

(REMPI) were performed on jet-cooled samples. The gas

mixture used, composed of helium as a buffer gas at 300 kPa

stagnation pressure and vapors of anisole (at the equilibrium

pressure with liquid held at 255–260 K), is admitted in the

vacuum chamber through a pulsed valve (General Valve, series

9, 500 mm diameter nozzle, 220 ms pulse duration) with a

conical skimmer (Beam Dynamics, model 2, 1 mm diameter)

placed about 10 mm from the nozzle. The resulting molecular

beam, containing anisole as isolated molecules, dimers and a

few larger clusters, is probed by the interaction with laser

pulses of 5 ns duration, 0.1 cm�1 bandwidth, 50–500 mJ energyin a two photon–one color ionization scheme. The laser

frequency is tuned in the range 36 100–36 500 cm�1, about

the origin band of the first optically allowed electronic

transition for the anisole dimers. A non-negligible ion yield

is observed only when the laser frequency is in resonance for

the one-photon transition. The produced ions are analyzed

using a time-of-flight mass spectrometer (reflectron configuration)

and detected by microchannel plates. The detector is operated

in variable gain mode40 in order to obtain a good amplification

of the weak cluster signal without much distortion from the

strong monomer signal. The resulting mass spectrum is averaged

on a fast digital storage oscilloscope (500 MHz bandwidth)

and sent to a PC for further elaboration. The mass spectrum

shows a complex pattern due to the presence of anisole

molecules and clusters with different isotopic compositions.

However, mass resolution is far better than 1 atomic mass unit

(amu) in the mass range 100–300 amu, relevant for the study of

anisole and anisole dimers, allowing unambiguous assignment

of the different peaks in the mass spectrum (apart from those

from anisole D3 and DOP; for this reason these samples were

never used together in the same experimental run). The mass

spectrum transferred to the PC is elaborated in order to obtain

the signal relative to the different mass peaks for each data

point (corresponding to different laser excitation frequencies).

Therefore, when a complex gas mixture is used, such as when

all the different isotopic species are present, the REMPI

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spectra related to the different isotopomers are recorded at the

same time. This approach greatly improves the accuracy for

each frequency shift measurement in the spectra. The absolute

laser frequency is monitored, during the scan, using a Burleigh

Pulsed Wavemeter with 0.1 cm�1 accuracy.

3. Computational details

The structure of the anisole dimer is already known.38 The

calculated equilibrium structure giving the best agreement to

experimental rotational constants has been obtained by

computations at the M05-2X and TD-M05-2X levels with

the 6-31+G(d,p) basis set for the ground and excited state,

respectively. Thus, the same models have been applied to the

harmonic frequency and vibronic spectra calculations. The

TD-DFT harmonic frequencies have been evaluated by the

recently introduced numerical differentiation of analytical

energy gradients.41 The relative shifts of the zero-point

vibrational energies (ZPVE) computed with the M05-2X

functional have been compared to the results delivered by

the B3LYP functional42 which is known for its reliable

prediction of vibrational properties.

The one-photon absorption (OPA) spectrum was simulated

using the procedure described in detail in ref. 28 and 29, which

is based on an effective evaluation method32,33 able to select

a priori the relevant transitions to be computed. In view of the

strongly allowed character of the electronic transition, the

Franck–Condon (FC) approximation, which assumes that

the dipole moment remains constant during the transition,

has been applied in this work. The simulation of vibrationally

resolved electronic spectra is based on the computation of

overlap integrals (also known as FC integrals), between the

vibrational wavefunctions of the electronic states involved

in the transition. Within the adopted Franck–Condon

Adiabatic–Hessian (FC|AH) framework, the evaluation of

the FC integrals requires the computation of the equilibrium

geometry structures and the vibrational properties of both

electronic states. Mixing between the normal modes of the

initial and the final states has been taken into account, with the

linear transformation proposed by Duschinsky:30Q= JQ0+K,

where Q and Q0 represent the mass-weighted normal

coordinates of the initial and final electronic states, respectively.

The Duschinsky matrix J describes the rotation of the normal

coordinate basis vector of the initial state during the transition.

The shift vector K represents the displacement of the normal

modes between the initial- and final-state structures. It is

important to note that, as a result of our calculations, the

two anisole units in the excited-state equilibrium structure of

the cluster are not equivalent. The theoretical vibronic spectra

for isotopically substituted anisole dimers were obtained using

the following procedure. A batch of all possible dimers

composed of two identical or isotopically different (among

H8, DOP, D3 and D5) anisole molecules was generated.

For each complex, the frequencies were computed to generate

the corresponding theoretical vibronic spectrum. The final

theoretical spectra, which are compared to the experimental

ones, result from the addition of the two spectra corresponding

to the permutation of the anisole units in a given dimer.

Details about the nature of the electronic transitions have

been revealed by computation of the electronic densities at the

ground and excited states, and the subsequent natural bond

orbital43 analysis. For this purpose the recently introduced

polarized double-z basis set N07D44,45 was used. All calculations

were performed with a locally modified version of the

GAUSSIAN suite of quantum chemistry programs.47

4. Results and discussion

In order to perform a detailed analysis of the origin band for

the different isotopically substituted anisole dimers, we start

our discussion with the relative shift of the S1 ’ S0 electronic

transition origin band (0–0 band) observed for the anisole

monomers with different isotopic compositions.48 Then we will

focus on the REMPI data for the anisole dimer and the

assignment of the different observed origin bands. Finally,

we will discuss the excitonic coupling between the excited

states of this dimer.

Within the Born–Oppenheimer approximation, the energy

of an electronic transition can be described as a sum of two

contributions. The first term related to a purely electronic

transition is equal for molecules of different isotopic

compositions, while the second one, related to the change in

the zero-point vibrational energy (ZPVE), is different between

isotopic species.

The isotopic shift of the 0–0 band can easily be evaluated by

ab initio computation of the ZPVE in the ground and excited

states. For anisole, it has already been shown that QM

calculations provide an accurate description of its ground-

state structure and properties and its changes upon electronic

excitation.31,48,49 Table 1 compares the experimental data with

the computed ZPVE changes upon electronic excitation,

DZPVE, for the different anisole isotopomers and the

difference in DZPVE with respect to the reference system, H8.

A remarkable agreement is found between the experimental

shift of the 0–0 band for anisole molecules with different

isotopic compositions and the DZPVE values predicted by

different methods. The accuracy of these results is a necessary

step towards reliably evaluating the ZPVE for anisole dimers.

Anisole dimers with the same isotopic composition have a

center-symmetric structure in the ground state. Therefore, in

this text, we will refer to the anisole dimers made of two

identical moieties as symmetric clusters, and we will refer to

Table 1 Experimental frequencies and relative shifts of the S1 ’ S0

origin band for different anisole isotopomers in comparison withcalculated changes in the ZPVE with electronic excitation. Shifts werecalculated with respect to anisole–H8. Units: cm�1

Experimental DZPVE

0–0 Shift a b c

H8 36384.0 0.0 0.0 0.0 0.0DOP 36488.4 104.4 106.5 119.9 114.0D5 36555.4 171.4 176.4 187.4 180.5D3 36387.3 3.3 7.1 12.5 1.6

a: CIS/6-31G(d,p)-HF/6-31G(d,p). b: TD-B3LYP/6-311+G(d,p)-

B3LYP/6-311+G(d,p). c: TD-M05-2X/6-311+G(d,p)-M05-2X/

6-311+G(d,p).

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those made of two anisole molecules of different isotopic

compositions as asymmetric clusters.

The REMPI excitation spectra of diverse isotopically

substituted anisole dimers are shown on Fig. 1, and a brief

observation of the latter clearly indicates that only a single set

of transitions is present for the symmetric ones. This can also

be confirmed by comparison of the REMPI spectra between

the monomers and dimers, as shown on Fig. 2 for the H8

species. Indeed, for both dimer and monomer, the same

pattern of the most intense vibronic bands is present.

However, the spectrum of the dimer is more complicated

due to the existence of intermolecular vibrational modes.

The excitation spectra of the asymmetric dimers in Fig. 1

show two different sets of data, which are recognized by the

slightly higher peaks corresponding to their origins. In the case

of H8–DOP, for instance, the two origin bands are present at

36151.7 and 36262.0 cm�1. The origins of both sets of bands

are very close to that of the corresponding symmetrical dimer

(within 15 cm�1, see Table 2). This leads, at first glance, to a

picture of local character for the electronic excitation and the

weak interaction between the two almost independent molecular

units in anisole bimolecular clusters. Accordingly, we will

mark from now on the excited unit with an asterisk.

Further evidence for this picture is given by a uniform red-

shift in the frequency (216 cm�1) of the 0–0 band for the

symmetric clusters with respect to the relative monomeric unit.

Strong support for the local character of the electronic excitation

arises from the analysis of the experimental isotopic frequency

shifts of the transition origin. In Table 3 the 0–0 transition

frequencies are assigned to the different clusters considering

one molecule as a ‘‘spectator’’ and the second one as the active

site of the excitation. Then, taking as a reference the spectator

unit (either H8 or DOP or D5), the excitation-frequency shift

of the active unit corresponds, within a very good approximation,

to one of the isolated monomers reported in Table 1.

Further support for the local character of the excitation is

provided by the theoretical results, in particular, simulated

OPA spectra with the isotopic substitution on the excited or

spectator unit. An example is shown in Fig. 3, where the

experimental spectrum of the asymmetric cluster H8–D5 is

compared to its computed counterpart obtained by mixing

together the contributions from H8*–D5 and D5*–H8.

It should be noted that the computations of vibronic

spectra were performed in an adiabatic framework, so the

anisole dimer was treated as a supramolecular system when

considering structure and frequency changes upon transition to

the first optically accessible singlet-excited electronic state.

In such a case, the symmetry of the system was removed

and the excitation has a local character as clearly shown by the

results presented in Table 4, where almost 100% of the

electronic excitation is localized on a single unit of the dimer.

Such a situation can also be visualized by the difference

between the excited- and ground-state electron densities

(computed at the S1 optimized geometry) shown in Fig. 4.

Additionally, the changes in intramolecular geometry

parameters listed in Table 5 confirm the local character of

the electronic excitation. For the first anisole moiety the

C1–O7 bond becomes shorter and the O7–C8 one longer,

while the C3–C4–C5, C6–C1–C2 and C1–O7–C8 angles

increase. The character and magnitude of these changes are

in line with those observed for the isolated anisole31,48 in the

first singlet-excited electronic state. In contrast, no significant

geometry change was found for the second (spectator) anisole

moiety.

Fig. 1 REMPI spectra around the origin band of the S1 ’ S0

electronic transition of the anisole dimers formed in a jet-cooled gas

mixture containing H8, D5 and DOP.

Fig. 2 REMPI spectra of the anisole H8 monomer (lower trace) and

dimer (upper trace) in the first 1000 cm�1 above the origin band of the

S1 ’ S0 electronic transition.

Table 2 Transition wavenumbers for the assigned origin bands of theanisole monomers and dimers. In the different columns theexperimental transition frequencies are reported according to theirclassification, i.e. the character of local excitation in one of themolecular moieties. Numbers in parentheses are the frequency shiftsrelative to the excitation in the symmetric dimer. Units: cm�1

H8* DOP* D5*

Monomer 36384.0 (216.6) 36488.4 (214.3) 36555.4 (216.3)H8–H8 36167.4 (0.0) — —H8–DOP 36151.7 (�15.7) 36262.0 (�12.1) —H8–D5 36152.4 (�15.0) — 36324.8 (�14.3)DOP–DOP — 36274.1 (0.0) —DOP–D5 — 36257.4 (�16.7) 36329.0 (�10.1)D5–D5 — — 36339.1 (0.0)

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Thus, on the basis of both experimental and computational

analyses it can be concluded that the excited-state equilibrium

of an anisole dimer is characterized by electronic transitions

essentially localized on one moiety. However, a more detailed

analysis of the experimental data also reveals secondary effects

related to the excitonic coupling between the electronic system

of the two anisole units. As discussed above, the energy levels

in the complex are possibly shifted with respect to those of the

isolated molecules because of two contributions, the dimerization

shift and the excitonic shift. From the above discussion, it is

rather clear that the dimerization shift is the largest term,

common to all symmetric and asymmetric clusters. The

possible occurrence of excitonic coupling in the anisole dimer

was first discussed by Zehnacker et al.50 Here we discuss its

relevance keeping in mind the new experimental evidence.

In principle, a coupling term between zero-order wave-

functions, i.e. the single molecule in our case, results in a shift

in the energy levels; maximum shift occurs if the initial

wavefunctions are degenerate. This coupling affects only the

electronic part of the wavefunction which is, within the

Born–Oppenheimer approximation, the same even for isotopically

different clusters. However, the ZPVE deviation between

Table 3 The local nature of the electronic excitation in an anisole dimer. In the first column the spectator unit is reported, in columns 2–6the excited unit, followed by the experimental and computed (M05-2X//TD-M05-2X) absolute frequency and the relative shift with respect to theexcitation in the H8 unit of the corresponding dimer are reported. The observed shifts are closely comparable to those observed in thecorresponding excited monomers. Units: cm�1

Spectator unit Excited unit

Experimental Calculated

Transition wavenumber Shift Transition wavenumber Shift

H8 H8* 36167.4 0.0 40 328 0H8 DOP* 36262.0 94.6 40 436 108H8 D5* 36324.8 157.4 40 499 171DOP H8* 36151.7 0.0 40 332 0DOP DOP* 36274.1 122.4 40 437 105DOP D5* 36329.0 177.3 40 503 171D5 H8* 36152.4 0.0 40 327 0D5 DOP* 36257.4 105.0 40 435 108D5 D5* 36339.0 186.6 40 498 171

Fig. 3 Experimental REMPI spectrum of the H8–D5 cluster

compared with the absorption spectra calculated as the sum of

predicted transitions for local excitation in the H8 or D5 units of

the H8–D5 cluster (spectral region around the origin band of the

S1 ’ S0 electronic transition). Calculated spectra were all frequency

shifted by about �4180 cm�1 in order to coincide with the

experimental band origins.

Table 4 Atomic charges (with hydrogens summed into heavy atoms)from natural bond orbital43 analysis for the anisole dimer. Valuescomputed with M05-2X/N07D and TD-M05-2X/N07D for theground and excited states, respectively. The atom labels follow thoseon Fig. 4; the two anisole units are labelled as A1 and A2

Atom S0 S1 D(S1 � S0)

C1 0.325 0.394 0.069C2 �0.038 �0.106 �0.068C3 0.016 �0.085 �0.101C4 �0.042 0.096 0.137C5 0.027 �0.083 �0.110C6 �0.078 �0.108 �0.030O7 �0.549 �0.462 0.087C8 0.339 0.368 0.029sum on A1 0.00 0.01 97.2%C17 0.325 0.325 0.000C18 �0.038 �0.039 �0.001C19 0.016 0.012 �0.004C20 �0.042 �0.044 �0.003C21 0.027 0.024 �0.003C22 �0.078 �0.085 �0.006O23 �0.549 �0.549 0.000C24 0.339 0.341 0.002Sum on A2 0.00 �0.01 2.8%

Fig. 4 Plot of the electron density differences between the S1 and S0

electronic states and the atom numbering scheme. The regions that

have lost electron density as a result of the transition are shown in

bright green, and the darker magenta regions gained electron density.

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different isotopomers is of the order of a few thousand

wavenumbers according to our calculations,z thus the vibronicenergy levels of monomers are exactly coincidental only for the

symmetric clusters. Therefore, the maximum perturbation due

to excitonic coupling should occur for the symmetrical

clusters. Additionally, assuming a small coupling term, i.e.

less than 100 cm�1, given the large difference between vibronic

energy levels, for asymmetric clusters we should expect a truly

negligible shift in the energy levels.

Further considerations concern the symmetry effect on the

supramolecular wavefunctions and the associated electronic

transition selection rules. We have already shown that the

structure of the anisole cluster is characterized by the presence

of a center of symmetry in the ground state.38 Then the

supramolecular wavefunction, provided that a coupling

between the two units exists, shall be represented by the linear

combination of the two degenerate single molecule wave-

functions with identical weight: the most stable state is

symmetric (g), whereas the less stable one is antisymmetric (u).

Due to the optical transition selection rules, only states of

different parity can be connected by an allowed optical

transition (g 2 u). Thus, since the ground state has g

symmetry, as for any closed-shell system, the allowed optical

transition must couple to a state of u symmetry. Therefore

only one origin band is expected for the symmetric clusters.

Furthermore this band should be blue-shifted with respect to

the corresponding band in an asymmetric cluster, which is

unaffected by the excitonic coupling. Now, we would like to

focus on the experimentally observed shift of bands relative to

the same transitions observed in symmetric and asymmetric

dimers, as reported in Table 2. On average, transitions in the

symmetric clusters are blue-shifted by about 14–15 cm�1. This

shift is almost the same for all clusters, whatever their isotopic

composition; therefore it should reflect a purely electronic

term, that is to say the excitonic coupling, since vibrational

effects related to the change in the ZPVE should lead to a

much more sparse distribution in the results.

From a computational point of view, analysis of excitonic

coupling should be performed within a vertical framework,

considering electronic excitations for the centersymmetric

structure of the dimer in the ground electronic state, with fully

equivalent anisole moieties. In this frame of reference, the

HOMO and HOMO�1 as well as the LUMO and LUMO+1

are equivalent, while the analysis of the vertical excitation

energies (see Table 6) shows two close-lying excited states for

the dimer. Additionally as shown by the molecular orbitals

involved in the lowest singlet electronic excitations, for anisole

monomers and dimers, depicted in Fig. 5, both S1 and S2 are

related to the excitations between the molecular orbitals,

which are combinations of the HOMO and LUMO of the

Table 5 Selected (see text) intramolecular geometry parameters forthe anisole dimer. Values computed at the M05-2X/6-31+G(d,p) andTD-M05-2X/6-31+G(d,p) levels of theory for the ground and excitedstates, respectively. Bonds in A, angles in degrees

S0 S1 D(S1 � S0)Bonds

C1–O7 1.3585 1.3316 �0.027O7–C8 1.4216 1.4311 0.009C17–O23 1.3585 1.3561 �0.002O23–C24 1.4216 1.4226 0.001

Angles

C1–O7–C8 117.6 120.0 2.5C3–C4–C5 119.1 122.5 3.4C6–C1–C2 119.9 123.3 3.3C17–O23–C24 117.6 117.5 0.0C19–C20–C21 119.1 119.1 0.0C22–C17–C18 119.9 119.8 �0.1

Table 6 Calculated vertical excitation energies and oscillatorstrengths (f) for the lowest energy singlet-states of the monomer andstacked dimer of anisole. Excitonic shift and dimerization shift arederived as well, according to eqn (1) and (2), and compared to theexperimental values

State Transition Weight Evert/eV f

MonomerS1 H - L 0.62 5.33 0.0390

H �1 - L +1 0.30 — —DimerS1 H - L �0.41 5.28 0.0000

H �1 - L +1 0.46 — —S2 H - L 0.41 5.29 0.0756

H �1 - L +1 0.46 — —

Calculated Experimental

Eexc/cm�1 39 15 — —

D/cm�1 �393 �232 — —

Fig. 5 Molecular orbitals involved in the dominant configurations of

the monomer and dimer low-energy excited states.z Data available upon request.

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This journal is c the Owner Societies 2010 Phys. Chem. Chem. Phys., 2010, 12, 13547–13554 13553

monomers. The delocalized character of the electronic wave-

function is also confirmed by the analysis of atomic charges

which shows that about 50% of excitation is localized on each

moiety for both S1 and S2. Furthermore, the oscillator

strength of S1 ’ S0 vanishes for anisole dimers, at variance

with the S2 ’ S0 transition whose oscillator strength is twice

as large as the S1 ’ S0 transition for the single monomer.

Those findings clearly support the computation of the vibronic

splitting according to the simple scheme proposed by

Guthmuller et al.46 In this approach, the excitonic shift

responsible for the splitting of the zero-order excited states

Eexc and the dimerization shift describing the difference in

interaction energies between initial and final states D, are

derived from vertical excitation energies Evert (computed at

the TD-M05-2X/aug-cc-pVTZ level on the dimer/monomer

ground state structure), with the following relation,

Eexc ¼EDvertðS2Þ � ED

vertðS1Þ2

ð1Þ

D ¼ EDvertðS1Þ þ ED

vertðS2Þ2

� EMvertðS1Þ ð2Þ

where the M and D superscript labels refer to single molecule

(M) or dimer (D) properties. Results gathered in Table 6 show

that the computed excitonic splitting agrees qualitatively with

the experimental findings. Such results based on the analysis of

relative excitation energies are remarkable considering that

one does not expect absolute excitation energies to be

computed even within 100 cm�1 accuracy. It should also be

noted that, as expected, the shift of the 0–0 band of the dimer,

in comparison with the monomer (D), is described better by

the adiabatic approach adopted in the simulation of OPA

spectra.

Based on the above discussion we show that the excitonic

shift of the single-molecule vibronic energy levels has been

determined for a cluster formed by two independent aromatic

molecules with p-stacking geometry. This QM effect, which

results from the partial overlap of the molecular orbitals of

each monomer, is effective even at the typical van der Waals

binding distance (3.4 A) between two anisole units in a dimer.

This is far off the typical covalent or coordination bond

lengths. In fact, a clear measure of the pure electronic inter-

action between the two units in the cluster is possible only for

systems in a stacking configuration, with no direct (and

strong) atom–atom interaction. Such a picture of the system

fully agrees with the description of the interaction energies

already presented for the electronic ground state of the anisole

dimer.38 In fact, the energy decomposition derived with

symmetry-adapted perturbation theory (SAPT) confirms the

leading role of the dispersion interaction in the dimer binding

energy. Additionally, we note that in the excited electronic

state the overall strength of the cluster binding interaction is

not very large, as shown by the observed small excitonic shift.

Moreover, the change in the interaction energy between the

two units upon electronic excitation is depicted by the shift of

the 0–0 transitions observed for the dimers with respect to the

monomers. In fact, a small red-shift (about 216 cm�1)

indicates that the complex is bound more tightly in the excited

state. Thus, the overall picture, taking into account both

effects, demonstrates the weak interaction between anisole

moieties in both electronic states.

Finally, we want to discuss the results obtained for the

H8–D3 clusters. The H8–H8 and D3–D3 complexes show

regular REMPI spectra with a single origin band. These two

bands were separated by 3 cm�1 only. Additionally, a single

origin band was found for H8–D3 in the REMPI spectrum,

which falls in between those of the corresponding symmetric

clusters (see Fig. 6), despite a careful search carried out even

under high spectral resolution conditions.38 In our opinion,

this is consistent with the local character of the CH/CDmethyl

group vibrations with respect to the properties of the aromatic

ring. This local character is demonstrated by the very small

frequency shift for the S1 ’ S0 electronic transitions of the

H8 and D3 monomers,48 and for the symmetric dimers.

A significant shift should be expected if the vibrational

frequencies of the methyl group change with electronic

excitation. Thus, the properties of the aromatic ring system

for the H8 and D3 are practically identical and the H8–D3

complex can be described as originating from the interaction

of two identical chromophores.

5. Conclusions

A combined experimental and theoretical study performed for

p-stacked anisole dimers, formed by moieties with different

isotopic compositions, revealed the local nature of the electronic

excitation for the equilibrium structure. However, fast electronic

excitation within the non-equilibrium structure vertical frame-

work, resulting in a small (around 30 cm�1) excitonic splitting

for the lowest electronically excited-states, demonstrates the

supramolecular character of the anisole dimer. This exciton

splitting has been observed only for clusters made of identical

units and for mixed anisole dimers containing both anisole–H8

and anisole–D3 (anisole with full deuteration on the methoxy

group). This phenomenon can be explained within the frame-

work of the Born–Oppenheimer approximation by assuming

that the electronic and vibrational coordinates of the methyl

group are independent, while the aromatic ring vibrations are

Fig. 6 REMPI spectra around the origin band of the S1 ’ S0

electronic transition of the anisole dimers formed in a jet-cooled gas

mixture containing H8 and D3.

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13554 Phys. Chem. Chem. Phys., 2010, 12, 13547–13554 This journal is c the Owner Societies 2010

not fully decoupled from the electronic coordinates. We can

recognize two cases: first, for molecules of different H/D

substitutions on the aromatic ring, the excitonic coupling is

possible only for identical units in the cluster since, for

asymmetric dimers, the vibronic energy levels are well separated

due to the large ZPVE differences. Second, for molecules that

differ only by H/D substitution on the –CH3 group, the distance

of the methyl group from the chromophore and the local

character of the –CH3 vibrations lead to similar behavior as for

the truly symmetric dimers. This can be explained by considering

that the coupling between methyl and aromatic ring vibrations is

a second-order effect with respect to excitonic coupling, so that

the latter can be observed also for mixed clusters.

Acknowledgements

This work was supported by the Italian MIUR and by the

EU (under contract No. RII3-CT-2003-506350). The

large-scale computer facilities of the VILLAGE network

(http://village.unina.it) are also gratefully acknowledged.

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