Ab Initio Calculations of Vibronic Spectra and Dynamics for Small Polyatomic Molecules:  Role of Duschinsky Effect

Abstract

The Duschinsky effect has been shown to be significant in spectroscopy and dynamics of molecules that involve the π−π* transitions. In this paper, we present a derivation of exact expressions for optical absorption and radiationless transitions in polyatomic molecules with displaced−distorted−rotated harmonic potential surfaces. In the formulation, we take into account the temperature effect exactly. The application of this new formulation is demonstrated for ethylene and allene, where the Duschinsky effect in the first singlet excited electronic state is very strong.

Ground and excited states of zinc phthalocyanine, zinc tetrabenzoporphyrin, and azaporphyrin analogs using DFT and TDDFT with Franck-Condon analysis

“…[48][49][50] Performing such first-principles calculations is challenging because each excited state needs to be optimized separately, which can produce mode mixing first described by Duschinsky. 51 In some cases, after the calculation of the TDDFT frequency, the solution produces imaginary frequency solutions, which indicates that the optimization for that excited state did not find the true minimum on the PES. One must then employ symmetry breaking to find the true minimum, and in turn the correct minimum on the PES, in order for the FC analysis to calculate the correct transition.…”

“…50,51,[57][58][59][60] A few key equations from the harmonic solution are given here, but the entire solution is calculable, and can be found in Santoro et al 57 The basic idea is that the molar absorption is produced by the absorption equation, which gives the transition between two electronic states |Ψ w ′⟩ and |Ψ w ⟩,…”

Quantum Dynamics of Radiationless Electronic Transitions Including Normal Modes Displacements and Duschinsky Rotations: A Second-Order Cumulant Approach

“…[32][33][34] Second-order effects such as variations of vibrational frequencies and the directions of normal vibrations, are usually not included in most of the Hamiltonian models used in qunatum dynamics, though a number of works suggest that their effect can be quite relevant. [35][36][37][38][39][40] The coupling operator V AF is in general a function of the vibrational coordinates of the system, although it is quite common to assume its value constant, since electronic transitions take place in a restricted region of the nuclear coordinates. 41 Another approximation of V AF , widely used in the study of photoexcited decays where conical intersections play a major role, is the so called linear vibronic model 1,42,43 in which the coupling operator is a linear function of the nuclear coordinates.…”

Theoretical investigations on valence vibronic transitions

“…When we write the vibrational ground state wave function as a product of harmonic functions, and use the completeness for the excited state vibrational wave functions, we neglect the intermode coupling in both electronic states [22]. Besides, if we use the normal coordinates for the ground state along with the completeness for the excited state, i.e., we use only the ground state normal modes, as we have done, we neglect rotation of the normal coordinates with respect to each other, the so-called Duschinsky effect [22,34] and anaharmonic effects. The accuracy of these approximations, including the fitting of the transition dipole moment calculated along the normal coordinates, is given by the comparison between the calculated OOS per mode and the experimental results, when available.…”