The Franck-Condon Principle and Its Application to Crystals

Abstract

The semiclassical Franck-Condon principle is shown to be related to the more rigorous (``exact'') quantum-mechanical perturbation formula in the following ways: (1) the Franck-Condon formula can be derived from the ``exact'' formula by using a mean value approximation or by neglecting certain commutators; (2) if the electric dipole moments are treated as approximately independent of position, the Franck-Condon and the ``exact'' absorption (or emission) spectrum have the same zeroth, first, and second moments, i.e., the same integrated spectrum, mean absorption frequency, and breadth; (3) the errors in higher moments than the second become relatively unimportant at high temperatures. If the electron-nuclear interaction is sufficiently strong the errors are unimportant even at absolute zero. The use of a quasi-molecular description in a many particle problem is found to be possible only if the masses or stiffnesses are allowed to be temperature dependent. A detailed analysis is made of the case in which the energy difference between the two electronic states is a linear function of the vibrational coordinates—and the latter are describable by normal modes. ``Exact'' formulas for the absorption and emission spectrum are obtained.

Scalable High-Performance Algorithm for the Simulation of Exciton Dynamics. Application to the Light-Harvesting Complex II in the Presence of Resonant Vibrational Modes

“…49,50 The absorption spectra I(ω) of a monomer with excitation frequency ω eg is given by the Fourier transform of the lineshape function 51…”

Solvent Reorganization Entropy of Electron Transfer in Polar Solvents

“…NVE simulations in acetonitrile were done in a cubic cell with the side length of 27.99 Å with 250 acetonitrile molecules and one p-nitroaniline molecule. In both cases, the simulation box is chosen to reproduce the solvent density at ambient conditions, F ) 0.997 g/cm 3 for water and F ) 0.782 g/cm 3 for acetonitrile. The cutoff radius for LJ interactions is equal to half of the box length.…”

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

“…modes whose quantum state can change upon transition, and solving numerically the associated time-dependent Schrödinger equation; ii) to resort to time-dependent perturbation theory for approximate solutions of the Schrödinger equation, retaining the whole space of coordinates or momenta. [7][8][9][10][11][12] Obviously, the choice between the two alternative approaches should be based on a careful analysis of the potential energies of the two electronic states involved in the transition.…”