Transition dipole moments of charge transfer excitations in one-component molecular crystals

Transition dipole moments of charge transfer excitations in one-component

molecular crystals

Grzegorz Mazur

_{, Piotr Petelenz}

_{, Michał Slawik}

a

Department of Computational Methods in Chemistry, Jagiellonian University, Ingardena 3, 30-060 Cracow, Poland b

K. Gumin`ski Department of Theoretical Chemistry, Jagiellonian University, Ingardena 3, 30-060 Cracow, Poland c

Department of Applied Chemistry, National Chiao Tung University, 1001 Ta Hsueh Rd., 30010 Hsinchu, Taiwan

a r t i c l e

i n f o

Article history:

Received 14 December 2011 In final form 18 January 2012 Available online 27 January 2012 Keywords: Charge-transfer excitons CT transition dipoles Oligothiophenes Absorption spectra Electroabsorption spectra

a b s t r a c t

Owing to the peculiar structure of oligothiophene crystals, their low-energy b-polarized spectra are dom-inated by the contributions from charge transfer states almost free from Frenkel state admixtures, offer-ing a unique opportunity for in-depth studies of the former. Here, a simple model, rooted in the Mulliken theory of charge transfer transitions, is proposed to estimate the relevant transition dipole moments. For sexithiophene, the resultant estimate agrees with the value used in the recent detailed theoretical repro-duction of the absorption and electroabsorption spectra, and is found to be consistent with other input parameters. The approach presented here is readily applicable for other one-component molecular crys-tals, providing a simple method to estimate the intrinsic transition dipoles of charge transfer configurations.

Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction

Owing to the (potential and actual) applications of organic molecular crystals in optoelectronics, theoretical description of these systems is being revisited nowadays with new goals in mind. In the new context, the charge-transfer (CT) excitations, character-ized by a finite distance between the electron and the hole, come into focus, constituting a bridge between the intramolecular (Fren-kel) excitons, which (being endowed with large transition intensi-ties) couple the system to the radiation field, and the unbound electron–hole pairs where the two charge carriers are separated by a distance large enough to make their interaction negligible, which couple the system to the electric field and charge carrier reservoirs.

The recently rediscovered crucial role of CT states for Frenkel exciton energetics in oligoacenes[1] is one of the facets of this new perspective. As noticed about twenty years ago[2], the inter-action with the CT states, mediated by electron- and hole-transfer integrals, substantially affects the dispersion of Frenkel states (to the extent of changing the sequence of Davydov components). This was originally reported for tetracene and pentacene [2], to be experimentally confirmed (in the latter case) a few years back[3]. While the original finding was based on a very simplistic model

[2], somewhat extended later[4], the present computational results

obtained for tetracene[1]are rooted in full-fledged first-principles theory, leaving no doubt regarding their validity.

However, this recent development is focused specifically on the properties of the eigenstates of Frenkel origin, with the CT mani-fold acting merely as a perturber of the energy levels naturally de-fined by the resonance interaction between the molecules. In this way, the CT states are probed only indirectly, with their own spec-tral contributions tentatively ignored. Admittedly, in oligoacene absorption they are certainly very weak, probably diffuse and masked by the vibronic replicas of the Frenkel state, which makes their observation practically impossible. They are accessible to electroabsorption (EA) spectroscopy, but for the time being an up-dated reproduction of the corresponding experimental data has been relegated to future work[1].

Meanwhile, a complete approach which allows one to treat the electroabsorption[5]and absorption spectra[5,6]within the same consistent framework has been proposed and applied for the sexi-thiophene crystal (6T)[7]. Owing to the peculiar lattice geometry, in oligothiophenes the b-polarized Frenkel absorption is negligible in the range corresponding to charge transfer excitons whose con-tribution is therefore not masked[6,8]. By the same token, the b-polarized transition dipole moment borrowed by the CT states from the Frenkel states is marginal, in contrast to the situation in oligoacenes.

In consequence, for 6T and other oligothiophenes there is an en-ergy range where the intensity of b-polarized absorption is entirely due to the intrinsic transition dipole moment carried by the CT configurations, which evidently is not negligible and, being the sole

0301-0104/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2012.01.012

⇑Corresponding author.

E-mail addresses: mazur@chemia.uj.edu.pl (G. Mazur), petelenz@chemia.uj. edu.pl(P. Petelenz),slawik@chemia.uj.edu.pl(M. Slawik).

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contributor, is becoming important in this new context. However, it is rather an elusive quantity. Its estimates for other systems were crude, and its actual value for oligothiophenes has never been the-oretically estimated. This is the objective of the present paper.

In the pioneering theoretical papers on CT excitons[9–11], the intrinsic CT absorption was consistently disregarded. It was no-ticed at that time that the eigenstates of CT origin are bound to borrow some transition moment from Frenkel excitons, owing to the coupling mediated by charge transfer integrals (in this context called dissociation integrals), but the contribution from the intrin-sic CT transition dipole was not invoked. The fact that this latter contribution, although admittedly small, might in principle be comparable to the former, was to become apparent only later, when the first attempt was made to predict the intensities of anthracene electroabsorption features, based on a model explicitly including the off-diagonal couplings within the CT manifold (as well as with Frenkel states) and accounting for the translational symmetry of the crystal[12]. Based on a crude numerical estimate

[13], the intrinsic contribution (on the order of a few hundredths of eÅ) was later included in the successful simulation of the experi-mental EA spectra of oligoacenes [4], and was subsequently adopted in papers that followed. The approach was inherently sim-plistic; among other inherent shortcomings, the underlying approximations forced the predicted CT transition dipole to be di-rected along the line joining the centers of the molecules involved in charge transfer, i.e. to be strictly parallel to the permanent (diag-onal) dipole moment of the corresponding CT state.

Somewhat later, the issue got revisited for a different system (perylenetetracarboxylic anhydride, PTCDA) using a more sophisti-cated methodology. Within a more realistic model at the semi-empirical ZINDO level, Hoffmann[14–16]found the direction of the CT transition dipole to deviate from the axis joining the centers of the two molecules and used his conclusions to extract the effec-tive value of the corresponding transition dipole moment by fitting the experimental absorption spectra [14–16]. In passing, he insightfully alluded to the description of CT states proposed by Mulliken for donor–acceptor complexes[14]and extensively re-ferred to in the literature.

Here we will explore his idea, applying the Mulliken approach in a new context. It will enable us to relate the CT transition dipole moment to other input parameters (for which more accurate esti-mates are available) used in the successful theoretical reproduc-tion of the sexithiophene absorpreproduc-tion and electroabsorpreproduc-tion spectra[7]. Our study is focused on the lowest (nearest neighbor) CT configuration, crucial for b-polarized oligothiophene spectra where interference from other states is practically negligible, which makes this particular state perfectly suited for testing the intensity scale.

2. Model

Typically, theoretical description of excitons in molecular crys-tals operates within the subspace of electronic excited states, essentially ignoring their coupling to the ground state of the sys-tem. This is one of the crucial advantages of the exciton concept, enormously reducing the formal and computational burden. Were the approach formulated in the basis of Hartree–Fock states of the crystal as a whole, by virtue of the Brillouin theorem it would also be a nearly perfect approximation. Yet, in order to avoid major complications, it is in fact normally couched in terms of molecular states, crystal eigenstates being the sought result.

In the molecular basis, there is no general reason for the non-diagonal matrix elements of the intermolecular interaction opera-tor between the ground and excited states to vanish. In energy terms, their neglect is entirely justified, since the relevant energy

separation is large as a rule so that the resultant shifts are marginal. However, the mixing between the ground state and the excited states has also an effect on absorption intensities, which for some weak transitions may be significant. This is the case for charge transfer states, as illustrated by the following argument, rooted in the Mulliken model[17].

Let us consider a pair AB of centrosymmetric molecules which we tentatively assume to be different (this limitation will be re-laxed later). As a first approximation, the environment (e.g. the rest of the crystal in which the model dimer is embedded) is not explic-itly included in the model, but its electrostatic effect is implicexplic-itly accounted for in the effective diagonal energies of the relevant CT states.

Suppose that molecule A has a low ionization potential and low electron affinity, while molecule B has a high ionization potential and large electron affinity. Then the energy gap between the A+_B_{and A}_B+_{CT states is large and each of them may be treated}

separately. We will focus on the first configuration. The unperturbed wavefunction of the pair jA+_B_i

0is built from

the molecular orbitals of the isolated moieties (presumably orthog-onalized). When the distance between A and B is finite, but not too small, the matrix element of the pair Hamiltonian V =0hABjHjA+Bi0

does not vanish, yet it is (by assumption) much smaller than the energy gapD= ECT Egbetween the CT state and the ground state

of the pair. In that case, the intermolecular interaction may be con-sidered as a perturbation and (correct to first order) the eigenstates of the pair may be approximated as

jAþBi ¼ jAþBi0þ V

D

D

The transition dipole moment from the perturbed ground state to the perturbed CT state is then given by

hABjMjAþBi ¼ 1 V 2

D

D

D

As the moieties are centrosymmetric, the last integral vanishes. If the molecules are embedded in a crystal, their distance RABis

usu-ally very large by molecular standards, and so is the permanent (diagonal) dipole moment of the CT configuration0hA+BjMjA+Bi0.

Hence, on the right-hand side the second term is expected to dom-inate. It is worth noting that its direction coincides with that of the permanent dipole moment of the charge transfer configuration in hand. As noticed by Hoffmann[14–16], the leading contributions to the integral in the first right-hand side term come from the re-gions where the orbitals of the two moieties strongly overlap; in general, these regions are not oriented in any special manner with respect to the radius vector joining the centers of the molecules, which results in deviations of the CT transition dipole from the direction of the corresponding permanent dipole moment. The deviations are not expected to be very large, but are not necessarily negligible.

The same line of reasoning may be applied for the configuration with reversed charges jA_B+

i. If the two moieties are identical, the unperturbed energies of the two configurations are the same. How-ever, an elementary estimate shows that the splitting in the CT man-ifold, induced by the interaction with the ground state, is marginal (103_{eV) and may be safely neglected in comparison with other}

interactions, as long as the CT excitation energy and the CT integral V are of the order of those encountered in typical one-component molecular crystals (such as oligoacenes or oligothiophenes).

In effect, there is no need to invoke explicitly the coupling of the exciton subspace with the ground state, provided that the intrinsic transition dipole of CT configurations is identified with that of Eq.(2). The total value from Eq.(2)is usually quite small compared to typical transition dipole moments of Frenkel states. Although only a fraction of the latter is lent to the eigenstates of CT origin (the lending being mediated by exciton dissociation integrals), it suffices to account for most of the observed CT state intensity; at least in oligoacenes, the intrinsic CT transition dipoles were appar-ently a mere correction [18]. However, with present perspective their original a priori estimates [12,13] seem to have been too low, so that this statement should be taken with a grain of salt. As no single-crystal electroabsorption spectra were available for those systems, confrontation with experiment was then possible only for film samples, which precluded more stringent tests based on the different polarization of Frenkel and CT transition dipoles, whereas some potential discrepancies might have been absorbed in the values of dissociation integrals, known only approximately. The situation is different in oligothiophenes. For 6T the b-polar-ized electroabsorption spectrum is available and the absence of Frenkel b-polarized contribution to optical absorption of the eigen-states of CT parentage exposes the intrinsic CT contribution, allowing one to test its estimate almost quantitatively. Here, we are taking advantage of this opportunity.

3. Dependence on intermolecular overlap

Some of the input parameters needed to estimate the transition dipole moment of Eq.(2)are ready to hand. The permanent dipole moment of a CT configuration is determined by the positions of the two molecules in the lattice and may be obtained from the known crystal structure. The energy gap Dmay be identified with the diagonal energy of the corresponding CT configuration prior to its mixing with other CT and Frenkel states, described by exciton the-ory such as that presented e.g. in Ref.[7](it might alternatively be approximated by the energy of the resultant eigenstate of CT par-entage, owing to the modest size of the splittings induced in this manifold by the interactions within exciton subspace).

The order of magnitude of the matrix element0hABjMjA+Bi0, as

well as that of the charge transfer integral V =0hABjHjA+Bi0, is

lim-ited by intermolecular overlap. In the following, we will use an approximate approach to focus on this dependence. Reduced to orbital basis, both integrals of interest engage the HOMO of mole-cule A and the LUMO of molemole-cule B. These can be easily found using a standard quantum chemistry program package.

According to Tanaka[19], a rough estimate of the CT integral is given by

V ¼ KS; ð3Þ

where S = hAHOMO_jBLUMO_{i is the overlap integral between the HOMO}

of the donating molecule A and the LUMO of the electron-accepting molecule B.

The constant K, obviously depending on the level of approxima-tion used to evaluate the overlap integral, should be adjusted to the specific basis set applied here. Based on the Mulliken approxima-tion, the scaling factor K for the HOMO–LUMO integral is approxi-mated as the mean of those appropriate for the HOMO–HOMO (Kh)

and LUMO–LUMO (Ke) cases, which are bound to differ significantly.

The requisite electron and hole transfer integrals Je= hABjHjABi =

hALUMO_BjHjABLUMO_{i and J}

h= hA+BjHjAB+i = hAHOMOBjHjABHOMOi are

available as a reference, having been evaluated in the past from a tight-binding fit to the results of band structure calculations in a large plane-wave basis set[7,20].

The estimate of the HOMO–LUMO matrix element needs to be corrected in one respect. As noted earlier, the perturbation

approach leading to Eq.(2)is strictly valid in an orthogonal basis set. To compensate for the fact that the basis functions used in Eqs.(1b), (2)are not orthogonalized, we follow the standard prac-tice[21] of replacing V in the actual estimates by the effective value

Veff¼ V 

1

2S

D

The other needed ingredient, i.e. the off-diagonal matrix element of the dipole moment [the first term on the right-hand side of Eq.(2)] is approximated according to Mulliken[17]

0hABjMjAþBi0¼

ffiffiffi 2 p

eðRA R0ÞS; ð5Þ

where e is the electron charge, RAis the radius vector of the center

of moiety A, and R0is the radius vector of the center of gravity of the

transition density between the two states, for the sake of simplicity tentatively identified with the midpoint between the geometric centers of the two molecules, which yields RA R0¼12RAB.

(Admit-tedly, this approximation is inherently unable to capture the small contribution perpendicular to RAB).

Summarizing, the effective intrinsic transition dipole moment carried by a CT configuration in the exciton subspace is directed approximately along the axis joining the centers of the molecules involved in charge transfer and (neglecting second order correc-tions) is reasonably approximated by

hABjMjAþB i ¼ 212_{eS 1 }V 2 eff

D

D

D

D

D

Evidently, it is limited (linearly) by the intermolecular overlap inte-gral, which depends (roughly exponentially) on the intermolecular distance. As noted above, the same applies to the CT integrals Je

and Jhrelevant for the coupling of CT excitons with Frenkel excitons,

mediating intensity transfer between these states. Accordingly, inclusion of the transition moment carried by the CT configurations is indispensable for internal consistency of the exciton approach such as that of Ref.[7].

4. Transition dipoles in crystal lattice

It follows from Eq.(6)that (apart from special relative orienta-tions of the moieties where equality results e.g. from point symme-try) the transition dipoles to the two conceivable CT configurations jA+B

i and jAB+

i, engaging the same pair of molecules, may differ even in length. This is a direct consequence of the fact that the corresponding transition moments are proportional to different overlap integrals hAHOMO

jBLUMOi and hALUMOjBHOMOi. It should be noted in passing that the same statement is valid for the corre-sponding Hamiltonian matrix elements V (hAHOMO_jHjBLUMO_{i and}

hALUMOjHjBHOMOi) approximated by Eq. (3), in contrast to the standard electron

Je¼ hA LUMO

jHjBLUMOi ¼ hBLUMOjHjALUMOi

and hole

Jh¼ hA HOMO

jHjBHOMOi ¼ hBHOMOjHjAHOMOi

transfer integrals, where the same kind of orbital (either HOMO or LUMO) of both molecules is involved. The integrals Jeand Jhgovern

exciton dissociation integrals. For the latter, similar equalities hold approximately:

De¼ hABjHjAþBi ¼ hABjHjABþi

Dh¼ hABjHjABþi ¼ hABjHjAþBi

as long as the molecular excited state A⁄_{, B}⁄_{results from}

HOMO-to-LUMO promotion and orbital relaxation in the excited state is disre-garded. In effect, although for a given pair of molecules the CT states with reversed polarities couple to other states in the exciton sub-space by analogous matrix elements, their transition dipole moments from the ground state may in general differ.

For pairs of molecules related by symmetry operations some consequences of the explicit dependence of the transition dipole on overlap integrals, as stipulated by Eq. (6), are nontrivial and may be quite relevant for detailed interpretation of the spectra. There is a natural tendency to identify the sense of the transition dipole moment with the direction of actual charge transfer (which we also did in our earlier papers[2,4,12,18,20]), i.e. with the sense of the permanent dipole moment of the generated CT state. This is not always correct, because the overlap integral S in Eq.(6)may be negative, as illustrated inFig. 1.

In the figure, a centrosymmetric stack of centrosymmetric mol-ecules is generated by translation (which is the constitutive feature of all crystals); in addition, it is endowed with a center of symme-try (which is very common in molecular crystals). The phases of the orbitals are consistently generated by translation (note that HOMO and LUMO belong to different irreducible representations of the molecule point group). It follows from symmetry that the overlap integrals between the HOMO of the central molecule A and the LUMOs of molecules B and C, respectively, have opposite signs. The senses of the corresponding radius vectors RABand RAC

are also mutually opposite; in consequence, according to Eq.(6), the senses of the corresponding transition dipoles hABjMj A+B_i

and hACjMjA+_C

i are the same, as shown in the figure. Likewise, the sense is also the same for hABjMjA_B+_{i and for hACjMjA}_C+_i.

Paradoxically, the sense of the transition dipoles of all the CT states considered above is identical, irrespective of the sense of their permanent dipole moments, set by the relative arrangement of the two created charges. Of course, this fact influences the selec-tion rules. Contrary to simplistic intuitive expectaselec-tions, it is the sum, not the difference of the transition dipoles of the CT states with opposite polarities that does not vanish (in contrast to some expectations in the literature[22–24]).

The significance of the above observations is rather conceptual than practical; in view of their resolution, in most experimental spectra available to date the differences between the predictions based on differently set phases of CT transition dipole moments are probably hidden in the overall width of the spectral bands. On the other hand, in the model studies of Refs.[22–24], correct-ness of the predictions is restored by the arbitrary setting of the signs of some transfer integrals (unphysical for the systems studied

there, but compensating the effect of the implicit assumptions con-cerning the relative phases of the transition dipoles).

However, by highlighting the role of the actual shape and nodal structure of the underlying molecular orbitals, the present study shows that parametrization of the models applied at the level of exciton theory may need more insight into the features of the indi-vidual molecules forming the crystal and more input from quan-tum chemistry calculations than practiced hitherto.

5. Numerical estimates

Although this paper is focused on sexithiophene for which a complete set of reference data is available, for comparative pur-poses we have extended our estimates also for quaterthiophene (4T) where, owing to the smaller size of the molecule, the compu-tations are more reliable. We concentrate our attention on the near-est neighbor CT state (engaging the translationally non-equivalent molecules located in the same plane of tight herringbone packing). The transition dipoles for higher CT excitations are less relevant, being much smaller or not contributing in the critical b polariza-tion; for these reasons they are not suitable for the ultimate test. Nevertheless, for the sake of completeness we also present the re-sults for the CT configurations engaging the translationally equiva-lent molecules along the c (in 6T) or a (in 4T) direction, where the anomalously large intermolecular LUMO overlap gives rise to large transition dipoles; for all other CT states they are negligibly small. The molecular orbitals of 6T and 4T were obtained from Har-tree–Fock calculations in the 6-311G⁄⁄

basis, wherefrom the sought overlap integrals were generated. The stability of the re-sults was confirmed by repeating the runs in shorter basis sets. The reference values of the electron and hole transfer integrals Je,

Jhwere ready to hand, evaluated earlier from a tight-binding fit

to the results of band structure calculations in a large plane-wave basis set [7,20]. Their scaling according to Eq. (3) provided the respective values of the constants Ke, Khfor electron and hole

trans-fer, listed inTable 1along with the resultant averaged constants K and other relevant quantities. For the energies of the CT states we took the values used previously to reproduce the electroabsorption spectra [7], which had been found to agree rather well with independent a priori estimates. The permanent (diagonal) dipole moment of CT configurations ensues from the known crystal structure.

As mentioned in the preceding section, in a general relative ori-entation of the molecules A and B (no point symmetry) even the absolute values of the integrals for HOMO-to-LUMO transfer may depend on whether the electron is transferred from A to B or from B to A. This is the case for the nearest neighbors in oligothiophene

Fig. 1. HOMO–LUMO overlap between translationally equivalent centrosymmetric molecules, and CT transition dipole moment. Different shading tints indicate different sign of the orbital.

Table 1

CT transition dipole moments and relevant input data. 4T, n.n.a 4T, ka 6T, n.n.a 6T,kc Je, eV 0.040 0.088 0.038 0.09 SHOMOLUMO 0.00330 0.0258 0.00314 0.0261 Ke, eV 12.13 3.41 12.10 3.45 Jh, eV 0.017 0.019 0.017 0.01 SHOMOHOMO 0.00353 0.0030 0.00324 0.00161 Kh, eV 4.81 6.33 5.10 6.21 K, eV 8.47 4.87 8.60 4.83 D, eV 3.04 3.24 2.75 2.78 RAB, Å 4.90 6.09 4.95 6.03 SHOMOLUMO1 0.00666 0.00594 0.00724 0.00377 m1, Å 0.0515 0.098 0.0688 0.067 S_HOMOLUMO2 0.00368 0.00548 0.00609 0.00409 m2, Å 0.0284 0.090 0.0578 0.073 jmeffj, Å 0.042 0.094 0.064 0.070 a n.n. = nearest neighbor.

lattices, which generates two sets of transfer integrals V1, V2and

transition dipoles m1, m2, both collected inTable 1. However, the

exciton model underlying the recent theoretical reproduction of the sexithiophene spectra[7] is simplified in this regard, as the pertinent CT transition dipoles are assumed there to be equal. In order to maintain the total intensity balance, we define the effec-tive transition dipole moment (to be compared with that of Ref.

[7]) by the relationship m2

eff¼12 m21þ m22

 

. By repeating the exciton calculations of Ref. [7]we have checked that differentiation be-tween the two kinds of transition dipoles affects the predicted spectra to a marginal extent.

It is surprising to note that the difference between the transi-tion moments to the CT states of opposite polarities varies so much from one system to the other: while for quaterthiophene there is a disparity of almost a factor of 2, for sexithiophene the two mo-ments differ by a mere 20%. It cannot be ruled out that the effect is genuine, resulting from the difference in orbital structures and lattice geometries of 4T and 6T. In fact, for orbitals with rich nodal structure even minor variations in relative orientation may lead to substantial changes in intermolecular overlap integrals, as we learned in the past for PTCDA and related systems[25]. It is equally possible, though, that the inordinately increased value of the smal-ler transition moment in 6T is a computational artifact, stemming from uncontrollable mixing in the bloated space of virtual orbitals, rapidly growing with the size of the molecule. The smaller molec-ular size favors the 4T result as the more reliable one, and the over-all close similarity of the two systems (manifested e.g. in the values of electron and hole transfer integrals) might suggest that for sex-ithiophene a somewhat smaller value of the CT transition dipole would be more credible.

In this situation some caution in the interpretation is impera-tive, but the overall conclusions are rather reassuring. Even if the sexithiophene result is to be taken at face value, the estimated transition dipole length of 0.064 Å exceeds by some 40% that used to reproduce the absorption and electroabsorption spectra (0.045 Å

[7]), which may be viewed as a provisional ‘‘experimental’’ result. This accuracy is perfectly reasonable for an order-of-magnitude estimate. In fact, Eq.(3)is indubitably quite crude, and so is the Mulliken approximation which justifies the relationship between the scaling constants K for the various charge transfer integrals. The inherent errors are probably compounded by the Gaussian ba-sis used in our calculations, poorly suited to reproduce the crucial large-distance tails of atomic orbitals. Then, within the overall lim-its of the applied approach, the agreement with experiment seems better than fair. If, on the other hand, the large discrepancy between the 4T and 6T cases is indeed a computational artifact, the net value for the latter system should be reduced, so that it would be even closer to the target result.

The transition dipole moment for charge transfer along the lat-tice period (i.e. between translationally equivalent molecules) is more difficult to compare with experiment, since it contributes only in c polarization (for 6T), dominated by very intense absorp-tion of Frenkel origin. Nonetheless, the value of about 0.07 eÅ ob-tained here (larger than for the nearest-neighbor CT state, in accordance with the large electron transfer integral and large LUMO overlap) substantially exceeds the previously assumed value of 0.02 eÅ[7], providing extra intensity in the region about 2.8– 3.1 eV where some intensity was evidently missing in the simu-lated profile (cf. Fig. 4 of Ref.[7]). Although this piece of evidence is inconclusive in view of the sensitivity of the c-polarized spec-trum to potential discrepancies in reproducing the contributions of Frenkel parentage (which are very likely to result especially from the simplistic description of the background absorption to the exciton-phonon continuum[26]), the general trend is rather encouraging.

6. Discussion

Intrinsic charge transfer absorption of one-component molecu-lar crystals, normally masked by Frenkel transitions and their vib-ronic replicas, came into limelight in the case of oligothiophenes, where, owing to the peculiar lattice geometry, it dominates the b-polarized spectra. It appears even more prominently in the elec-troabsorption spectrum, also measured for this particular polariza-tion[5]. Combined, these two spectroscopies offer a considerable body of experimental data calling for theoretical interpretation.

Electroabsorption however, being based on a differential signal, is very sensitive to any shortcomings of the underlying theoretical description; in consequence, it is not yet possible to date to plau-sibly predict EA spectra based on first principles alone. At the pres-ent stage, a successful interpretation consists in fitting the experimental spectrum with a set of parameters enclosed within the bounds resulting from inherent inaccuracies of the theoretical methods used for their a priori estimates. So far, the estimate of the transition dipole moments of CT configurations was by far the least reliable, being based primarily on analogies.

This paper, although intended to provide merely order-of-mag-nitude estimates, represents some progress in this regard. It may be viewed as a consistency test. In the calculations of Ref.[7], where nearly quantitative agreement with experiment was achieved both for the absorption and electroabsorption spectra, the value of the CT state intrinsic transition dipole moment was an independent parameter, a priori known rather vaguely and ulti-mately adjusted by fitting the spectra.

The main goal of the present work consists in the fact that the value of this elusive quantity is now related to other input param-eters used in Ref.[7], and is found to be consistent with them. Admittedly, the approximations that allow one to express the CT transition dipole moment in terms of the electron and hole transfer integrals and CT state energies of Ref.[7]are inherently crude. On this view, the nominal 40% discrepancy between the present esti-mate for 6T and the value found optimal for reproducing the exper-imental spectra may be considered surprisingly small. Moreover, the lower value obtained for quaterthiophene is encouraging in suggesting that a part of the discrepancy may be due to error cumulation resulting from the large size of the sexithiophene mol-ecule, and might potentially be eliminated in the future by using a more sophisticated scheme of quantum chemical calculations.

It would be a worthy task which would complete the set of parameters needed to simulate the absorption and electroabsorp-tion spectra of this model system. Other input data being known with better accuracy, this would be an important step on the way to a predicting power comparable to that recently attained for Frenkel states[1].

Acknowledgements

This work was financed from the Polish national resources allotted for research in the years 2010/2011 as statutory allocation (DS21) to the Faculty of Chemistry of the Jagiellonian University.

The research was carried out with the equipment purchased thanks to the financial support of the European Regional Develop-ment Fund in the framework of the Polish Innovation Economy Operational Program (Contract No. POIG.02.01.00-12-023/08).

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