Modeling of the time-resolved vibronic spectra of polyatomic molecules:   the formulation of the problem and analysis of kinetic equations
  A semiempirical parametric method is proposed for modeling three-dimensional (time-resolved) vibronic spectra of polyatomic molecules. The method is based on the use of the fragment approach in the formation of molecular models for excited electronic states and parametrization of these molecular fragments by modeling conventional (one-dimensional) absorption and fluorescence spectra of polyatomic molecules. All matrix elements that are required for calculation of the spectra can be found by the methods developed. The time dependencies of the populations of a great number (>10^3) of vibronic levels can be most conveniently found by using the iterative numerical method of integration of kinetic equations. Convenient numerical algorithms and specialized software for PC are developed. Computer experiments showed the possibility of the real-time modeling of three-dimensional spectra of polyatomic molecules containing several tens of atoms. 
S.A.Astakhov, V.I.Baranov