Impact of the Computational Method on the Geometric and Electronic

J. Phys. Chem. B 2005, 109, 20237-20243

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Impact of the Computational Method on the Geometric and Electronic Properties of Oligo(phenylene vinylene) Radical Cations V. M. Geskin,† F. C. Grozema,§ L. D. A. Siebbeles,§ D. Beljonne,†,‡ J. L. Bre´ das,*,†,‡ and J. Cornil†,‡ SerVice de Chimie des Mate´ riaux NouVeaux, Centre de Recherche en Electronique et Photonique Mole´ culaires, UniVersite´ de Mons-Hainaut, Place du Parc 20, B-7000 Mons, Belgium, School of Chemistry and Biochemistry and Center for Organic Photonics and Electronics, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, and Opto-Electronic Materials Section, DelftChemTech, Faculty of Applied Sciences, Delft UniVersity of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands ReceiVed: April 14, 2005; In Final Form: August 23, 2005

We report on a quantum-chemical study of the electronic and optical properties of unsubstituted oligo(phenylene vinylene) (OPV) radical cations. Our goal is to distinguish the impact of the choice of molecular geometry from the impact of the choice of quantum-chemical method, on the calculated optical transition energies. The geometry modifications upon ionization of the OPV chains are found to depend critically on the theoretical formalism: Hartree-Fock (HF) geometry optimizations lead to self-localization of the charged defects while pure density functional theory (DFT) results in a complete delocalization of the geometric modifications over the whole conjugated backbone. The electronic structure and vertical transition energy associated with the lowest excited state of the radical cations have been calculated at the post-Hartree-Fock level within a configuration interaction (HF-CI) scheme and using the time-dependent DFT (TD-DFT) formalism for different radical cation geometries. Interestingly, the changes in the calculated optical properties obtained when using different geometric structures are less important within a given method than the differences between methods for a given structure. The optical excitation is localized with HF-CI and delocalized with TD-DFT, almost irrespective of the molecular geometry; as a result, HF-CI excitation energies tend to saturate as the chain length increases, in contrast to the results from TD-DFT.

1. Introduction The changes brought into a conjugated oligomer or polymer chain by introducing an excess charge (upon doping, charge injection, or photoinduced charge transfer) are significant and reversible, opening the way to many applications.1 In the absence of strong interchain interactions, the excess charge and unpaired spin density in π-conjugated chains are expected to not be equally distributed over the entire chain but rather to concentrate on a limited portion of the chain (i.e., they are “selftrapped”). A local geometric distortion then accompanies the electronic relaxation upon charge injection in order to reach the equilibrium geometry of the charged state. This leads to the formation of a localized defect on the conjugated chain,2 referred to as a “polaron” in solid-state physics, with its own charge, spin, and geometric characteristics. Poly(phenylene vinylene) (PPV), its derivatives, and their oligomers (OPVn, with n corresponding to the number of phenylene rings) are among the most theoretically and experimentally studied conjugated systems. This is due to their increasing use in electroluminescent devices and solar cells, convenient synthetic methods, and good processability.3,4 Much attention has been given at the theoretical level to the nature of charged species in PPV systems, in particular to their geometric structure and optical properties. This information results from * Corresponding author. E-mail: [email protected]. † Universite ´ de Mons-Hainaut. ‡ Georgia Institute of Technology. § Delft University of Technology.

disentangling different characteristics of the polaron (i.e., its spin and charge distribution and its geometry) inferred by complementary approaches. In particular, our knowledge on the extent of geometric relaxation associated with a polaron primarily relies on theory since experimental structural data on radical cations are by and large unavailable. Charge distributions are readily obtained from quantum-chemical calculations but cannot be trusted in absolute values since they are generated from arbitrary partitioning schemes. Assessment of the results of such theoretical studies are complicated by the fact that different quantum-chemical methods are often used to calculate the geometric structure (mainly ab initio and semiempirical Hartree-Fock (HF) and density functional theory (DFT) approaches), the electronic spectra (generally a configuration interaction (CI) scheme with HF calculations and a timedependent formalism (TD-DFT) with DFT), and spin distributions (most often based on unrestricted Hartree-Fock and DFT methods). Changing the computational method sometimes leads to significant changes in the calculated properties, as is typically the case for charge distributions.5 Self-localized distortions in charged conjugated chains were first described by calculations based on the tight-binding π-electron Su-Schrieffer-Heeger (SSH) Hamiltonian.6 At a higher level of sophistication, restricted Hartree-Fock semiempirical and ab initio calculations usually result in a very sharp self-localization of the defect, with maximal distortions in its center and a similar width whatever the chain length.2 However, the extent of geometric distortions in radical cations is likely to be overestimated in restricted open-shell Hartree-Fock

10.1021/jp0519417 CCC: $30.25 © 2005 American Chemical Society Published on Web 10/05/2005

20238 J. Phys. Chem. B, Vol. 109, No. 43, 2005 (ROHF) calculations, as has been indicated by Bally and Borden.7 On the other hand, unrestricted Hartree-Fock (UHF) wave functions of conjugated chains are highly spin contaminated, in particular for the neutral segments of the molecules; thus, they yield optimized structures that are unreliable.8,9 Treatments beyond Hartree-Fock are therefore required, yet post-HF calculations on oligomers long enough to assess selflocalization were until recently hardly feasible. An alternative is DFT, which takes into account electron correlation at affordable computational costs. DFT calculations predict that the excess charge, spin, and structural distortion spread over the entire chain in OPVs10 as well as in other systems;11 thus, pure DFT provides no intrinsic self-localization. The structures provided by hybrid DFT approaches, including a part of HF exchange, are intermediate.12 On a similar ground, the difficulties in describing at the quantum-chemical level neutral solitons in polyenyl radicals have been discussed by Bally et al.13 The experimental approach used to estimate the extent of a polaron is to determine the spin distribution by ENDOR (electron nuclear double resonance) and ESR (electron spin resonance); it was successfully applied to PPV in the absence of dopants.14 The results were explained by assuming the formation of localized polaronic defects. Theoretical simulations based on spin densities obtained from semiempirical PariserParr-Pople (PPP) calculations at the UHF level (which yield a sharp polaron centered on a vinylene unit and extending over about six repeat units) reproduce to a large extent the measured ENDOR spectrum of PPV.15 An apparent contradiction arises when different geometries are used10,16 to simulate the optical absorption spectra of charged OPVs with the same computational technique (namely, the semiempirical Hartree-Fock intermediate neglect of differential overlap (INDO) Hamiltonian coupled to a single configuration interaction (SCI) scheme). In both works,10,16 the simulated optical spectra display two new subgap features following the emergence of a singly occupied molecular orbital. However, Grozema et al. find that the optical absorption spectra compare much better to the experimental data when using as input the geometries they obtained at the density functional theory (DFT) level10 rather than the geometries optimized at the HartreeFock semiempirical Austin Model 1 (AM1) level by Cornil et al.16 Since at the DFT level, in contrast to the AM1, there are almost no self-localization effects leading to the formation of polaronic structures, this agreement might suggest that polarons originate from extrinsic effects (linked, for instance, to the presence of dopants or impurities). However, the appearance of two new subgap transitions in the spectra of doped PPV, at around ∼1 and ∼2 eV,17,18 is well reproduced by correlated semiempirical quantum-chemical calculations performed on the singly charged five-ring PPV oligomer (OPV5+) on the basis of the AM1-optimized geometry: values of 0.96 and 1.81 eV are obtained at the INDO-SDCI level (involving single and double excitations) and of 0.82 and 1.92 eV at the AM1-CAS (complete active space) level (where a full CI is applied within a limited active space).19 The agreement in that work between the experimental and theoretical data would point rather to the localized nature of the defect due to the injected charge. It is important to stress at this stage that the appearance of a “subgap” transition in a radical cation does not necessarily imply the presence of a geometric relaxation. As a matter of fact, upon ionization, a low-energy transition is expected even in the absence of nuclear and electronic relaxations, due to the possibility of promoting an electron from the new highest doubly

Geskin et al. occupied molecular orbital (HOMO) to the new singly occupied molecular orbital (SOMO). In addition, it should be borne in mind that, in the solid state, the more ordered the material and the stronger the interchain couplings, the more delocalized the polaron (in perfect crystals, polarons are expected not to be stable but rather to be completely delocalized).20,21 The primary goal of our work is to solve the geometry/optical property discrepancy and, more generally, to assess for isolated chains to what extent the calculated optical properties and hence the electronic structure are determined by the geometry of the conjugated system. To do so, we investigate here the interplay between the quantum-chemical methods used for geometry optimizations and those used for the simulation of optical spectra. Somewhat unexpectedly, we demonstrate that the calculated electronic structures and optical properties are more sensitive to the choice of the theoretical method for a given geometry than to the details of the molecular structure for a given method. Our discussion is structured as follows: We start by comparing the optimized geometries of OPV radical cations versus those of its neutral oligomers and the corresponding chain-length evolution, as obtained by Hartree-Fock, DFT, and hybrid DFT methods; we show that distinctly different molecular structures are produced. We then concentrate on the lowest optical transition of the radical cations and analyze how its energy, as calculated at the INDO-SCI and TD-DFT levels, depends on the input geometry and varies with increasing chain length. 2. Theoretical Methodology Unconstrained AM1 geometry optimizations of isolated OPV oligomers in the neutral state yield nonplanar structures, with the phenylene and vinylene planes tilted with respect to each other by about 20°. The amplitude of the torsion angle is, however, sensitive to the choice of the theoretical method; highly correlated calculations lead to a planar structure for transstilbene, in full agreement with highly resolved gas-phase fluorescence spectra.22 The disparity of the results is reconciled by the fact that the torsional profile is very flat,23 thus favoring the planarization of the chains in the solid state.24 Accordingly, we have exclusively considered planar structures for the neutral PPV oligomers. In the radical cations, the positively charged portion of the chain is strictly coplanar whatever the computational approach. Geometry optimizations were performed with the AM1 Hamiltonian, in both the ROHF (as previously done by Cornil et al.16) and UHF schemes. AM1/CAS optimizations carried out with various sizes of the active space yield results very similar to ROHF. The DFT geometries were obtained with the VWNBP functional and a DZP III STO basis set using the ADF program.10 We have also used Gaussian 9825 to optimize geometries with a 3-21G* basis set in the framework of pure DFT and hybrid DFT approaches, using the BLYP and the BHandHLYP (including one-half of exact Hartree-Fock exchange26) functionals, respectively. DFT calculations for radical ions were spin-unrestricted, which is in accordance with the general spirit of DFT. The spin contamination in pure DFT, calculated formally from the Kohn-Sham determinant, was found to be insignificant: the solutions are practically pure doublets, with S2 differing marginally from the correct value of 0.75. Spin contamination in the BHandHLYP solutions is somewhat higher, apparently due to the admixture of an unrestricted Hartree-Fock contribution; however, it remains acceptable, with S2 never exceeding 0.9. The vertical excitation energies and associated transition dipole moments have been calculated with the INDO/S Hamil-

Oligo(phenylene vinylene) Radical Cations tonian coupled to an SCI scheme27 and with the TD-DFT formalism with Gaussian 98.25 The INDO-SCI calculations generate the singly excited configurations from an ROHF wave function for the ground state. Note that Brillouin’s theorem does not hold for the doublet ground state of the radical ions: the ground-state ROHF determinant does mix with single excitations, thus implying that the SCI doublet ground state is correlated. For this reason, it appears that the role of double excitations is insignificant when calculating the optical properties of radical cations. In the case of closed-shell systems, the impact of double excitations is much more pronounced and usually leads to appreciable blue shifts since correlation effects become generally not properly balanced between the ground state and the excited states. Moreover, the inherent size inconsistency of CI techniques, that is, the impossibility of describing systems of different sizes with the same precision, manifests itself in the case of open-shell systems: changing the CI size can alter the energy of the ground and excited states differently and lead to some irregularities in the evolution of the excitation energies as a function of chain length. In this study, we find deviations that are lower than 0.1 eV for the calculated excitation energies; we deem those to be acceptable, given that they are obtained as a difference between two (very large) total energies that both depend on the size of the CI active space and of the system. The first excited state of the radical cations is one-photonallowed. According to INDO-SCI calculations, this excited state mostly originates from an electronic transition between the HOMO and SOMO levels; its properties are therefore relatively robust with respect to correlation effects. In contrast, the higher lying optically allowed excited states are more strongly correlated (on the basis of the ground-state molecular orbitals), since they are described by the mixing of several configurations. Furthermore, we note that the calculated second transition energy is only weakly influenced by chain length10,28 and hence by the polaron geometry. Since the main objective of this work is to determine the extent to which quantum-chemical calculations of optical properties are related to the polaron geometry in OPVs, in the following, we focus on the first optical transition. The TD-DFT calculations were performed with the BHandHLYP functional (since hybrid functionals are known to be superior to pure functionals in TD calculations) and a 3-21G* basis set. While extended basis sets with diffuse functions are often required in TD-DFT calculations on small molecules and for excited states lying at high energy, smaller and less diffuse basis sets are sufficient for larger systems, in particular when they are positively charged, due to the contraction of the π-electronic cloud; they are actually even preferable to avoid convergence problems in TD-DFT. 3. Results and Discussion 3.1. Geometric Structures. It is instructive to compare first how different methods describe the geometric structures of the radical cations for a given chain length and the structural evolution with chain size. Figure 1 illustrates the C-C bondlength alternation in OPV7+ (defined for phenylene and vinylene groups separately as the difference between the average length of the “single” and “double” bonds, as illustrated in the neutral structure 0 in Scheme 1). The structures optimized with pure DFT methods do not show any tendency of self-localization of the defect: the BLA and charge patterns are uniform along the chain. The hybrid BHandHLYP functional introduces a slight localization that may peak around the middle of the molecule. However, the geometric distortion gets more extended with increasing chain length, thus suggesting that localization is not

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Figure 1. Bond-length alternation in the phenylene and vinylene groups of a charged (filled circles) and neutral (open circles) OPV7, as obtained at the ab initio ROHF (a), AM1-ROHF (b), DFT-BHandHLYP (c), and DFT-BLYP (d) levels. The chemical structure of the molecule is displayed on top.

SCHEME 1

intrinsic but rather imposed by finite-size effects. In contrast, the structures optimized with the ab initio and semiempirical ROHF methods display a well-localized defect. In the region where the excess charge resides, the phenylene rings acquire some quinoid character (the C-C bond lengths become more alternated) while the C-C bond alternation is reduced in the vinylene linkages. These changes in the bonding pattern for the radical cation are consistent with a dominant contribution of the valence-bond canonical structure of type (•+) over several units; see Scheme 1. A clear manifestation of self-localization is molecular symmetry breaking. In long chains, there is no reason for the defect to be pinned in the middle of the chain and maintain the symmetry of the neutral molecule. The maximum amplitude of the geometry distortions peaks around either a phenylene or a vinylene unit, irrespective of the parity of the oligomer. The geometry distortion can be centered at different positions along the chain. The structure obtained for OPV7 at the ab initio level supports this picture. Despite the fact that there is a phenylene in the middle of this chain, the self-localized polaron turns out to be centered on a vinylene unit, thus breaking the molecular symmetry. Note that within the polaron itself the charge and

20240 J. Phys. Chem. B, Vol. 109, No. 43, 2005 bonding patterns are symmetric with respect to the central vinylene unit. We find such a symmetry breaking with all the HF-based methods: for chain lengths beyond OPV6 with ROHF/3-21G*, beyond OPV7 with AM1/ROHF, and beyond OPV4 with AM1/UHF. Though the energy difference between vinyleneand phenylene-centered polarons is very small in long chains (on the order of 0.5 kcal/mol with ROHF/3-21G* and 0.05 kcal/ mol with AM1/ROHF calculations), we consider symmetry breaking to be an important indicator for the completion of the defect formation; the latter implies that its structure does not change further with an increase in the chain length and that the additional units adopt a neutral geometry. Similar symmetrybreaking effects have been observed for oligothiophene radical cations.29 Symmetry breaking does not occur either with the BLYP functional (at least up to OPV9) or with the B3LYP and BHandHLYP functionals that introduce an increasing fraction of HF exchange; this points to the absence of intrinsic polaron localization at the DFT level. Though artifactual symmetry breakings can occur with ROHF calculations, as documented for allyl radicals,30 we believe that our results exhibit an intrinsic effect. This is supported by the following aspects: (i) Symmetry is also broken at the UHF level, whereas artifactual breaking is typical of ROHF only. (ii) In contrast to polyene radicals, symmetry breaking in OPV•+ is not observed in short chains but is initiated for a chain length at which the geometry of the polaron defect is complete. (iii) There is a smooth transition between the structures before and after symmetry breaking. (iv) Artifactual symmetry breaking is corrected by post-HF treatments; however, ROHF geometry optimizations performed at the AM1/CI level with an increasing size of the active space still yield broken-symmetry structures virtually identical to those obtained with ROHF. For a long oligomer, several brokensymmetry structures are actually obtained, with the polaron centered on different vinylene units for each. It is also worth stressing that the interpretation of ENDOR and ESR results suggests that a polaron in PPV is indeed centered on a vinylene moiety;15 this is an independent confirmation of the intrinsic and nonartifactual character of the symmetry-breaking effects observed in our calculations. We have also analyzed the degree of geometric localization and its chain-length evolution for the different methods. For this purpose, it is convenient to define a coarse-grained descriptor allowing us to compare at a glance numerous geometries. Here, we consider this parameter to be the difference B between the average bond-length alternation (BLA) values in adjacent vinylene and phenylene groups. In the middle of a neutral chain, the average BLA value within the vinylene and phenylene groups is 0.107 and 0.014 Å at the AM1 level, respectively, so that B is equal to 0.093 Å. Similar B values are obtained for neutral PPV with pure and hybrid DFT functionals (0.074 and 0.105 Å, respectively). In the presence of a selflocalized defect, BLA decreases in the vinylene units and increases in the phenylene rings, which makes B smallest in the middle of the geometric distortion. We have plotted in Figure 2 the values of B at the end of the chain B(end) and in the middle of the defect B(middle) as a function of chain length. This graph provides information on (i) the degree of polaron localization (from the difference between B(end) and B(middle)) and (ii) the size of the defect (from the chain length at which the difference between B(end) and B(middle) starts to saturate). With pure DFT methods, irrespective of the chosen functional

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Figure 2. Chain-length evolution of the B(end) and B(middle parameters) in OPV radical cations, as obtained by various optimization methods.

Figure 3. Evolution of the energy of the lowest optically allowed vertical transition in OPV radical cations as a function of chain length plotted vs direct (a) and inverse (b) number of phenylene rings in the chains, as obtained by different formalisms. The first acronym represents the method used for the electronic-structure calculations and the second that for the geometry optimizations.

(BLYP or VWN-BP) and basis set, B(end) and B(middle) are close and increase with chain length toward values characteristic of the neutral molecule; the absence of saturation reflects the

Oligo(phenylene vinylene) Radical Cations

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Figure 4. Illustration of the LCAO (linear combination of atomic orbitals) pattern of the HOMO level of the neutral OPV6 (a) and of the SOMO level of unrelaxed (b) and fully relaxed (c) OPV6+. The geometries have been initially optimized at the AM1 level. The size and color of the circles reflect the amplitude and sign of the LCAO coefficients, respectively.

fact that no self-localization occurs. For ab initio and semiempirical ROHF structures, B(end) increases and saturates for a size of six to seven phenylene units while B(middle) decreases and also tends to saturate when the defect formation is completed. The partial incorporation of HF exchange in the framework of hybrid DFT techniques introduces some degree of localization and leads to intermediate B values; note, however, that B(middle) follows an evolution similar to that observed with pure DFT. 3.2. Optical Properties. It is not unusual in quantum chemistry to use different methods for geometry optimizations and for subsequent determinations of the molecular properties. In the second stage of the calculations, the nuclear configuration is therefore not in equilibrium with the electronic structure. We now investigate the optical properties of OPV radical cations by putting a special emphasis on the dependence of the results with respect to the molecular geometry and the method used to compute the excitation energies. We will focus here exclusively on the lowest excited state of the radical cations since its description is not affected by subtle correlation effects. We report in Figure 3 the chain-length evolution of the lowest transition energy, as computed with different methods and/or different molecular geometries. At the INDO-SCI level, the transition energies obtained for the AM1 geometries saturate quickly with increasing chain length and level off around OPV79. (We note that these values are somewhat different from those initially reported in ref 16: the latter were found, after careful reexamination, to be affected by convergence problems.) The same saturation is observed for radical cations at the AM1 geometry of neutral OPV chains, except that the transition energies are red-shifted (by up to 0.4 eV for the longest oligomers). In both cases, the transition is mostly described by the (doubly occupied) HOMO f SOMO excitation (the corresponding CI coefficient is 0.89 in the shortest oligomers and goes down to 0.69 in OPV9); other determinants involving

excitations from several lower occupied orbitals to the SOMO come into play in the longest oligomers. The transition is strongly optically allowed, as indicated by the increase in the oscillator strength from 0.47 to 1.31 throughout the series. Figure 4 illustrates the shape of the HOMO in neutral OPV6 and that of the SOMO in the unrelaxed (i.e., in the neutral geometry) and fully relaxed singly charged OPV6 (AM1-optimized geometry), as provided by INDO calculations. The HOMO of the neutral molecule tends to concentrate in the middle of the chain; this behavior is amplified for the SOMO of the unrelaxed radical cation which exhibits a very similar nodal pattern compared to the HOMO of the neutral molecule. Interestingly, the geometry relaxation characteristic of the polaron brings practically no changes to the shape of the SOMO level. A similar evolution is obtained for the transition energies computed at the INDO-SCI level on the basis of pure DFT geometries. In contrast, the transition energies calculated with the TD-DFT formalism for geometries obtained at the AM1 and pure DFT (VWN-BP) levels evolve in a very different way (see Figure 3); in both cases, there is no sign of saturation with increasing chain length. Note that the different lines are crossing for oligomer lengths corresponding to those typically investigated at the experimental level; the assessment of the most reliable technique would thus require data collected for longer chains. Nevertheless, we clearly see at the long-chain limit that the calculated transition energies decrease in the following order: HF-CI//HF > HF-CI//DFT > TD-DFT//HF > TD-DFT// DFT (where the latter acronym represents the method used for geometry optimizations and the former that used for electronicstructure calculations). Combining DFT geometries with a TDDFT formalism provides very low excitation energies in long chains. The rapid saturation of the INDO-SCI transition energies suggests that the structure of the frontier orbitals is already converged in short chains. The larger values calculated for the fully relaxed radical cations compared to the unrelaxed systems

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Figure 5. Charge distribution on the phenylene and vinylene units of OPV7+, as obtained with the INDO (bottom) and hybrid DFTBHandHLYP (top) methods for various starting geometries.

point to a reinforcement of the electronic localization, though this effect is not readily seen in the shape of the SOMO (see Figure 4). Altogether, the AM1//INDO-SCI values, which saturate around 0.8-0.9 eV, provide the best agreement with the experimental value for PPV (∼1 eV);17,18 the other theoretical values saturate slowly with chain length and are too low in energy or, even worse, show an unphysical chain-length dependence. It thus appears that it is primarily the choice of the method used for the electronic-structure calculations rather than the molecular geometry that drives the observed evolutions. This is fully supported by Figure 5, which illustrates the charge distributions calculated for OPV7+, from a Mulliken population analysis, at the INDO and BHandHLYP-DFT levels for different input geometries. Strikingly, we observe that, starting from a delocalized DFT structure, a well-localized AM1 geometry, or an intermediate hybrid DFT structure, the charge is systematically sharply localized when INDO calculations are performed and weakly localized for the hybrid DFT results. We have further analyzed the charge localization in Figure 6, where we plot the participation ratio P for different cases.10 The participation ratio is defined as P ) 1/ΣQi2, where Qi is the charge present on the ith unit; the sum runs over all monomer units. The lowest possible value of P is 1 when the excess charge is localized on a single unit. P reaches its highest possible value of N when the charge is spread evenly over all N units of the chain. This limiting value is displayed as a solid line in Figure 6a, where phenylene and vinylene units are considered on an equal footing. For pure DFT-optimized geometries, the DFT values of P approach the higher limit, indicating extensive

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Figure 6. (a) Chain-size evolution of the participation ratio calculated for OPV radical cations for different computational schemes and molecular geometries. The solid line represents the limiting case of uniform delocalization. (b) Evolution of the transition energies calculated at the INDO/SCI level as a function of the participation ratio estimated with INDO; the starting geometries considered here are those optimized at the pure DFT level.

charge delocalization; the limit is not reached due to the fact that the charges are not the same on the phenylene and vinylene units. For the same geometries, the corresponding INDO values P tend to saturate around 8; this matches the typical extent of the geometric defect provided by HF calculations (four phenylene units and the three vinylene linkages connecting them, i.e., seven units). Intermediate values are again obtained with hybrid DFT approaches. It is also interesting to observe in Figure 6b that there exists a linear correlation between the INDO transition energies computed for different chain sizes on the basis of pure DFT geometries and the corresponding INDO participation ratios. We thus conclude that the variations in the molecular geometries among the various approaches only exert a minor influence on the calculated transition energies compared to the choice of the postoptimization method. We rationalize this finding by the fact that the electronic distribution is a robust feature of a given method. 4. Synopsis Using various quantum-chemical approaches, we have investigated the geometry and optical properties of oligo(phenylene vinylene) radical cations to assess the interplay between

Oligo(phenylene vinylene) Radical Cations geometric relaxation effects and calculated transition energies. The extent of the geometric distortion varies as a function of the method used to optimize the geometry: it evolves from a sharp localization with ab initio or semiempirical HF methods to complete delocalization with pure DFT, passing by an intermediate localization with hybrid DFT approaches (which lead, however, to a spreading of the defect over the whole backbone). The chain-length evolution of the lowest transition energy depends primarily on the degree of electronic localization of the SOMO level; the latter is to a large extent decoupled from the details of the actual geometry, making the calculated results mostly dependent on the nature of the method used to generate the electronic structure. We believe that these conclusions are of general applicability for conjugated polymers. In the range of oligomer sizes typically studied experimentally (up to five to seven unit cells), the absolute values of the lowest transition energy calculated with different techniques on the basis of different geometries do not differ significantly due to the confinement of the charged species by the chain ends. Thus, these cannot be exploited to assess the best theoretical approach. The chain-size evolution of the transition energies is, however, more sensitive to the choice of the theoretical approach when going to longer oligomers. We find as a rule of thumb that the higher the charge (or SOMO) localization, the faster the saturation and the larger the transition energies. To establish the relative performance of HF-CI and TD-DFT calculations, experimental optical transition energies for excess charges on long conjugated chains are needed. Acknowledgment. The work in Mons has been partly supported by the Belgian Federal Government “Service des Affaires Scientifiques, Techniques et Culturelles (SSTC)” in the framework of the “Poˆle d’Attraction Interuniversitaire en Chimie Supramole´culaire et Catalyse Supramole´culaire (PAI 5/3)”, the Belgian National Fund for Scientific Research (FNRS/FRFC), and by the European commission project NAIMO ((NMP4-CT2004-500355). J.C. and D.B. are FNRS research associates. The work at Georgia Tech is partly supported by the National Science Foundation (through Grant CHE-0342321 and STC Award DMR-0120967) and the IBM Shared University Research Program. References and Notes (1) Handbook of Conducting Polymers, 2nd ed.; Skotheim, T. A., Reynolds, J. R., Elsenbaumer, R. L., Eds.; Marcel Dekker: New York, 1997. (2) Bre´das, J. L.; Street, G. B. Acc. Chem. Res. 1985, 18, 309-315. (3) Friend, R. H.; Gymer, R. W.; Holmes, A. B.; Burroughes, J. H.; Marks, R. N.; Taliani, C.; Bradley, D. D. C.; dos Santos, D. A.; Bre´das, J. L.; Lo¨gdlund, M.; Salaneck, W. R. Nature 1999, 397, 121.

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