An algorithm for computation of diatomic spectra

Abstract

In principle, an atomic or molecular spectrum would be computed as follows: Upper and lower Hamiltonians would be enumerated in a complete basis, and numerically diagonalized to give the upper and lower energy eigenvalues and eigenvectors. The transition moments for the appropriate operator, e.g., the electric dipole transition moments, would be evaluated from the eigenvectors. The vacuum wavenumbers , i.e., energy eigenvalue differences, would be found for all non-vanishing transition moments. And the line strengths for each spectral line of wavenumber would be determined as sum of the squares of the transition moments over all transitions producing the same . A line list that includes line strengths would be generated by repeating the above computations over the required range of upper and lower total angular momentum quantum numbers. The spectrum from min to max would be separated into a number of pixels, subsequently, the contribution of each line to each pixel is calculated using the line list. We show how this algorithm can be implemented for a diatomic spectrum if the required molecular parameters are available.