The functional dependence of excited-state geometries and normal modes calculated with time-dependent density functional theory (TDDFT) is investigated on the basis of vibronic structure calculations of the absorption spectra of large molecules. For a set of molecules covering a wide range of different structures including organic dyes, biological chromophores, and molecules of importance in material science, quantum mechanical simulations of the vibronic structure are performed. In total over 40 singlet−singlet transitions of neutral closed-shell compounds and doublet−doublet transitions of neutral radicals, radical cations, and anions are considered. Calculations with different standard density functionals show that the predicted vibronic structure critically depends on the fraction of the “exact” Hartree−Fock exchange (EEX) included in hybrid functionals. The effect can been traced back to a large influence of EEX on the geometrical displacement upon excitation. On the contrary, the dependence of the results on the choice of the local exchange-correlation functional is found to be rather small. On the basis of detailed comparisons with experimental spectra conclusions are drawn concerning the optimum amount of EEX mixing for a proper description of the excited-state properties. The relationship of the quality of the simulated spectra with the errors for 0−0 transition energies is discussed. For the investigated singlet−singlet π → π* transitions and the first strongly dipole-allowed transitions of PAH radical cations some rules of thumb concerning the optimum portion of EEX are derived. However, in general no universal amount of EEX seems to exist that gives a uniformly good description for all systems and states. Nevertheless an inclusion of about 30−40% of EEX in the functional is found empirically to yield in most cases simulated spectra that compare very well with those from experiment and thus seems to be necessary for an accurate description of the excited-state geometry. Pure density functionals that are computationally more efficient provide less accurate spectra in most cases and their application is recommended solely for comparison purposes to obtain estimates for the reliability of the theoretical predictions.

Calculations of the vibronic structure in electronic spectra of large organic molecules based on density functional methods are presented. The geometries of the excited states are obtained from time-dependent density functional (TDDFT) calculations employing the B3LYP hybrid functional. The vibrational functions and transition dipole moment derivatives are calculated within the harmonic approximation by finite difference of analytical gradients and the transition dipole moment, respectively. Normal mode mixing is taken into account by the Duschinsky transformation. The vibronic structure of strongly dipole-allowed transitions is calculated within the Franck-Condon approximation. Weakly dipole-allowed and dipole-forbidden transitions are treated within the Franck-Condon-Herzberg-Teller and Herzberg-Teller approximation, respectively. The absorption spectra of several organic pi systems (anthracene, pentacene, pyrene, octatetraene, styrene, azulene, phenoxyl) are calculated and compared with experimental data. For dipole-allowed transitions in general a very good agreement between theory and experiment is obtained. This indicates the good quality of the optimized geometries and harmonic force fields. Larger errors are found for the weakly dipole-allowed S0 --> S1 transition of pyrene which can tentatively be assigned to TDDFT errors for the relative energies of excited states close to the target state. The weak bands of azulene and phenoxyl are very well described within the Franck-Condon approximation which can be explained by the large energy gap (>1.2 eV) to higher-lying excited states leading to small vibronic couplings. Once corrections are made for the errors in the theoretical 0-0 transition energies, the TDDFT approach to calculate vibronic structure seems to outperform both widely used ab initio methods based on configuration interaction singles or complete active space self-consistent field wave functions and semiempirical treatments regarding accuracy, applicability, and computational effort. Together with the parallel computer implementations employed, the present approach appears to be a valuable tool for a quantitative description and detailed understanding of electronic excitation processes in large molecules.

A general and efficient approach for the calculation of Franck-Condon integrals (FCIs) of large molecules is presented. In a first step, by exploiting the diagonally dominant and sparse structure of the Duschinsky matrix, a model system is constructed for which the Duschinsky matrix takes a block-diagonal form. For each of these blocks separately, the FCIs are calculated discarding all below a certain threshold. From those integrals retained the FCIs of the model system are obtained by simple multiplication. These serve as an estimate for the FCIs of the exact system which are calculated for those integrals which lie above a certain threshold. By systematically decreasing the threshold, the simulation can be reliably converged to the exact result with an arbitrary accuracy. Using this scheme, a considerable reduction of the number of FCIs which have to be calculated is achieved which leads to an improved scaling behavior of the computational effort with system size. The approach has been tested thoroughly for a set of molecules including difficult cases. For the larger systems a speedup of up to three orders of magnitude compared to an exact calculation is observed while the errors can be kept negligible. With this approach accurate calculations of FCIs are feasible also for large molecules encountered in "real-life" chemistry, especially biochemistry and material science.

There has been a considerable interest in the chiroptical properties of molecules whose chirality is exclusively due to an isotopic substitution and numerous examples for the electronic circular dichroism (CD) spectra of isotopically chiral systems have been reported in literature. Four different explanations have been proposed for the mechanism as to how the isotopic substitution induces a chiral perturbation of the otherwise achiral electronic wave function; however, up to now no conclusive answer has been given about the dominating effect responsible for the experimental observations. In this study we will present, for the first time, fully quantum-mechanical calculations of the CD spectra of three different molecular systems with isotopically engendered chirality. As examples, we consider the spectra of organic molecules with ketone and alpha-diketone carbonyl and diene chromophores. The effect of vibronic couplings for the reorientation of the electric and magnetic transition dipole moments is taken into account within the Herzberg-Teller approximation. The ground and excited state geometries and vibrational normal modes are obtained with (time-dependent) density functional theory [(TD)DFT], while the vibronic coupling effects are calculated at the TDDFT and density functional theory/multireference configuration interaction (DFT/MRCI) levels of theory. Generally, the band shapes of the experimental CD spectra are reproduced very well, and also the absolute CD intensities from the simulations are of the right order of magnitude. The sign and the intensity of the CD band are determined by a delicate balance of the contributions of a large number of individual vibronic transitions, and it is found that the vibrational normal modes with a large displacement are dominant. The separation of the calculated CD spectrum into the different contributions due to the overlap of the in-plane and out-of-plane components (regarding the symmetry plane of the unsubstituted molecule) of the electric and magnetic transition dipole moments yields information about the influence of the vibronic coupling effects for the reorientation of the corresponding transition dipole moments. In conclusion, the calculations clearly show that vibronic effects are responsible or at least dominant for the chiroptical properties of isotopically chiral organic molecules.

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