Correlation between Franck-condon Factors and Average Internulcear Separations for Diatomics Using the Fourier Grid Hamiltonian Method

Abstract

The Fourier Grid Hamiltonian (FGH) method is used to compute the vibrational eigenvalues and eigenfunctions of bound states of diatomic molecules. For these computations, the Hulburt and Hirschfelder (HH) potential model for diatomics is used. These potential energy functions are used for constructing and diagonalizing the molecular Hamiltonians. The vibrational wave functions for the ground and the excited states are used to calculate the Franck-Condon factors (FCFs), r-Centroids and average internuclear separations which play a significant role in determining the intensity of the bands in electronic transitions. The results of FCFs and r-Centroids for diatomic molecules such as H2, N2, CO, I2 and HF using the FGH method are compared with other methods. The Franck-Condon profiles indicate a strong correlation between the values of Franck-Condon factors and the mean internuclear separations for the corresponding transitions.