Excited state geometry optimizations by analytical energy gradient of long-range corrected time-dependent density functional theory

Abstract

An analytical excitation energy gradient of long-range corrected time-dependent density functional theory (LC-TDDFT) is presented. This is based on a previous analytical TDDFT gradient formalism, which avoids solving the coupled-perturbed Kohn-Sham equation for each nuclear degree of freedom. In LC-TDDFT, exchange interactions are evaluated by combining the short-range part of a DFT exchange functional with the long-range part of the Hartree-Fock exchange integral. This LC-TDDFT gradient was first examined by calculating the excited state geometries and adiabatic excitation energies of small typical molecules and a small protonated Schiff base. As a result, we found that long-range interactions play a significant role even in valence excited states of small systems. This analytical LC-TDDFT gradient was also applied to the investigations of small twisted intramolecular charge transfer (TICT) systems. By comparing with calculated ab initio multireference perturbation theory and experimental results, we found that LC-TDDFT gave much more accurate absorption and fluorescence energies of these systems than those of conventional TDDFTs using pure and hybrid functionals. For optimized excited state geometries, LC-TDDFT provided fairly different twisting and wagging angles of these small TICT systems in comparison with conventional TDDFT results.

Computational design of faster rotating second-generation light-driven molecular motors by control of steric effects

“…Such a scenario would be consistent with 1 H-NMR data on the rotary cycle of a second-generation motor with a dibenzocyclohepten-5-ylidene stator, 26 but is not a common feature for second-generation motors. 26 Specifically, the first piece of evidence that the stator-rotator folding changes Performing excited-state geometry optimizations using time-dependent DFT (TD-DFT) [77][78][79][80][81][82][83][84][85] within the Tamm-Dancoff approximation (TDA) [86][87][88][89] and also using the ab initio approximate coupled-cluster singles and doubles (CC2) method 90 as implemented in the Turbomole 6.3 suite of programs, 91,92 key results from these calculations are presented in Table 1. From Table 1, it is found that the stator-rotator folding relative to the olefinic Finally, as to verifying that the photochemical steps sustain rotary motion, this can indeed be inferred from the observation in Table 1 that the changes in the α dihedral angle during the FC relaxation have the same sign (…”

How Method-Dependent Are Calculated Differences between Vertical, Adiabatic, and 0–0 Excitation Energies?

“…Furthermore, for most of the current excited states, expanding the basis set from double-ζ to triple-ζ quality, or including diffuse basis functions, has a marginal effect on the excitation energies obtained with TD-DFT. 29 Second, excited-state geometries were optimized using analytic TD-DFT [45][46][47] and CC2 43 excited-state gradients. Then, adiabatic excitation energies were obtained as electronic energy differences between ground and excited states at their respective equilibrium geometries, to which were subsequently added ZPVE corrections derived from ground and excited-state frequency calculations at optimized ground and excitedstate structures, respectively.…”

“…Although much more expensive than ground-state geometry optimizations, such calculations are today feasible for many excited-state methods, including TD-DFT. [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] Adding a further dimension to efforts along those lines and of relevance for determining which type of transition (vertical or adiabatic) best corresponds to experimental absorption maxima, are simulations of vibrationally resolved electronic absorption spectra reported by a number of research groups. [49][50][51][52][53] Such simulations require computation of vibrational wavefunctions and their overlap (Franck-Condon factors), and may also include a dependence of the electronic dipole moment operator on nuclear coordinates (Herzberg-Teller corrections).…”

Absorption and fluorescence properties of oligothiophene biomarkers from long-range-corrected time-dependent density functional theory

“…In contrast to conventional hybrid functionals which incorporate a constant fraction of HF exchange, the LC scheme for DFT 11,24,28,31,32 …”