Simple model for time-dependent vibrational relaxation using MathCad software

CHED 1441

Kushal D. Shah, arman81us@yahoo.com, Rajat Nanda, rajat_nanda@ben.edu, and Timothy W. Marin, tmarin@ben.edu. Department of Chemistry, Benedictine University, 5700 College Road, Lisle, IL 60532-0900
A simple vibrational relaxation model is presented for molecules that have undergone electronic excitation, using both a kinetic 'stepladder' mechanism and Franck-Condon factors. Implications of one and two excited vibrational modes are discussed. The stepladder kinetic model describes a series of consecutive, irreversible, first-order relaxations, and predicts the population of each species over time. Overlap integrals of the harmonic oscillator wave functions for the excited and ground states give the Franck-Condon factors for both modes and generate the absorption spectrum. Time-dependent absorption spectra are then obtained by combining the absorption spectra with the kinetic model. An existing simple vibrational relaxation model has been greatly optimized using Mathcad and Sigmaplot software to allow for determination of the time-dependent absorption spectra and present them as 3D plots and animations.