Calculation of the line shapes of electronic transitions at defects using the frozen Gaussian technique

Abstract

Calculations of the optical properties of defects in semiconductors or multiphonon transition rates presently make far more severe approximations than standard electronic structure calculations. One major challenge is how one can handle realistically the lattice vibrations, including quantum nuclear dynamics when those are necessary. The semi-classical frozen Gaussian technique allows us to calculate the line shapes of electronic transitions at defects using molecular dynamic simulation data from the initial and final states. Approximate nuclear wave functions are constructed from classical trajectories on nuclear potential energy surfaces for the two states. The method expands the system initial and final states (functions of position and momentum), as a sum of Gaussians, whose centres evolve classically on the relevant potential surface. An expression for the transition probability is then derived from the time-dependent overlap of the two wave functions. The frozen Gaussian method has been tested on the core exciton in diamond. The potential energy surfaces are calculated using an approximate but self-consistent molecular orbital technique, while simultaneously performing molecular dynamics. The results of our calculations show a Stokes shift of 3.64eV, similar to the value of “up to 5eV” obtained experimentally. We predict a fine structure with much narrower lines than those observable in the (low-resolution) experimental spectra.