Dynamical symmetry of vibronic transitions in polyatomic molecules and the Franck-Condon principle

In this work, rigorous prescreening conditions for the calculation of Franck-Condon factors (FCFs) are derived and implemented. These factors play an important role in numerous applications including the prediction and simulation of vibronic spectra, electron transfer rates, and nonradiative transition probabilities. For larger systems it is crucial to calculate only relevant FCFs, as the computational burden becomes otherwise prohibitive due to the sheer number of Franck-Condon integrals. By exploiting rigorous prescreening criteria one can significantly reduce the computational effort and systematically refine results to the desired target accuracy. In this work, such criteria are derived via the use of sum rules obtained through a coherent state generating function for the FCFs in the harmonic oscillator approximation, following the prescription of Doktorov et al. These sum rules allow efficient and rigorous prescreening prior to the calculation of entire batches of Franck-Condon integrals, reducing the subsequent computational burden. To illustrate the benefit of employing such conditions, they are applied in this work to calculate FC profiles for vibronic spectra of formic acid, thymine, anthracene, and a polycyclic aromatic hydrocarbon derivative containing about 450 vibrational degrees of freedom. Since the prescreening step gives stringent upper and lower bounds for the loss of FC intensity in these spectra arising from the neglected FCFs, the present approach renders most previous a priori selection schemes obsolete and has the potential to complement or even replace other approximate treatments.

Vibronic transitions in large molecular systems: Rigorous prescreening conditions for Franck-Condon factors

Reviews the vibronic properties of point defects (i.e. impurities and radiation-induced defects) in diamond. Cases discussed are: defects where the totally symmetric electron-lattice interaction dominates; cases of dynamic Jahn-Teller distortions; vibronic interactions between nearly degenerate states and a statically deformed defect. Before discussing each of these topics the relevant theory is outlined at an introductory level with the emphasis on features relevant to understanding data. It is shown that a good understanding of the vibronic data is now available in diamond. Compared to defects in silicon, defects in diamond are less prone to static deformations, partly as a result of the high-energy transverse acoustic modes in diamond.

https://iopscience.iop.org/article/10.1088/0034-4885/44/7/003/pdf

The Jahn-Teller effect and vibronic coupling at deep levels in diamond

The density of states functions, which describe the vibrational structure in PE spectra, are calculated with the help of Green's functions In addition to the exact solution of the one‐body problem, two different approaches to calculate reorganization and many‐body effects are presented In all cases no data of the ion are required, and all transitions except those between linear and bent configurations are included It is shown that the density of states is well approximated by using only the first‐order coupling constants in the one‐particle approximation This means that already a simple calculation becomes a powerful tool in interpreting PE spectra

On the vibrational structure in photoelectron spectra by the method of Green's functions

Second quantization is used to derive the overlap integral between two harmonic-oscillator wave functions on different centres and with different force constants. The appropriate dipole moment and kinetic-energy integrals are also obtained.

Second quantization and the general two-centre harmonic oscillator integrals

Second quantization of the harmonic oscillator is used to derive two-centre overlap, dipole moment and kinetic energy integrals.

J Katriel

Papers

On the use of second quantization for the calculation of two-centre harmonic oscillator integrals