Radiationless Transitions in Polyatomic Molecules. I. Calculation of Franck—Condon Factors

Abstract

Radiationless transitions between two electronic states are studied for a system consisting of a polyatomic molecule in a medium where vibrational relaxation is rapid. The transition rate is then governed by a vibronic matrix element and a vibrational overlap factor. Only the latter, known as the Franck—Condon factor and denoted by F, is investigated in detail. For harmonic oscillators F derives from shifts in equilibrium distance (displacements) and shifts in frequency (distortions). It is shown that for radiationless transitions involving large energy gaps (E), F is dominated by distortions, whereas for optical transitions it is dominated by displacements of the oscillators. These distortions lead to an approximately exponential decrease of F with increasing E. An isotope rule for F is derived which is valid for both displaced and distorted oscillators provided E is not too small. Since all formulas are of the form F (E), where E is the principal variable, comparison with experiment is only possible for a class of related molecules. Within this class E should vary a great deal but all other parameters should either be constant or vary in a simple, systematic manner. The dependence of some of these parameters on the number of oscillators involved in the transition is examined. Finally the theory is extended to molecular crystals and the corresponding liquids. It is concluded that in these systems the rate constant of an intramolecular radiationless transition must be equal to or smaller than that in dilute solutions, except when excited dimers are present in the initial state.

Electronic Spectroscopy of PAHs

“…However, the full mechanism underlying the PAH hypothesis takes place on timescales up to seconds. To fully explore the dynamical behaviour of PAHs and (Siebrand 1967), squares are those for IC (internal conversion) measured neutral (azulene derivatives from Murata et al 1972 and phenanthrene from Ohta & Baba 1986) and cationic PAHs (for a detailed list of the references, see Salama 2007). Circles are for the neutral fullerenes.…”

“…In particular the energy gap law (EGL) was inferred from measurement of fluorescence lifetime of PAHs in solution and proved to involve ISC (Siebrand 1967). The EGL states that in the statistical limit an exponential dependence of the nonradiative rates versus the energy gap between the prepared state and the electronic states immediately below is to be found (Englman & Jortner 1970).…”

“…A few examples illustrate the importance of PAH science and their profound impact on molecular science. The study of their quantum yield of fluorescence during the sixties and early seventies (Hunt et al 1962;Siebrand 1967) led to major developments in the understanding of intramolecular dynamics and radiationless transitions in particular (Englman & Jortner 1970). At the beginning of the eighties, with the advances of molecular beam techniques, the first systematic studies of their gas-phase electronic spectra were performed.…”

Symmetry forbidden vibronic spectra and internal conversion in benzene

“…Within the harmonic or anharmonic framework, further approximations such as displaced oscillator model, distorted oscillator model, and the mode-mixing effect or the Duschinsky effect can be introduced. Though a great deal of theoretical works 1,[6][7][8][9][10] have been done on IC, practical calculations based on ab initio wave functions are still scarce. In the present work, we have considered the distorted oscillator effect in spectrum simulation and the rate constants of the IC based on the ab initio computation of the vibronic coupling.…”

Absolute quantum efficiencies

“…We enumerate here a few areas where such informa· tion could be decisive. In theoretical chemistry, studies of radiative and especially radiationless processes have been proliferating [14][15][16][17][18]. The role of various terms within the Hamiltonian (vibronic, spin·orbit) [19][20][21][22] and the effect of substituents on both radiative and radiationless rate constants of isolated molecules are under scrutiny [23][24][25].…”