Explicitly Correlated Gaussian Functions and Rovibrational Spectra of Diatomic Molecules

Explicitly correlated Gaussian functions are implemented in order to calculate the rovibrational spectra of various diatomic molecules with and without the Born- Oppenheimer approximation. Matrix elements and gradients for the overlap, potential, and kinetic energy are derived for two different bases corresponding to the second rotationally excited state, one with the approximation that the rotational excitation of the system is due primarily to the excitation of the nuclei and the other allowing all particles to contribute to the rotational excitation. Matrix elements of the nuclear nuclear correlation function and interparticle distance are also derived in the former basis. Comparisons with experimental data and other computational work are provided. Implemented improvements in the Born-Oppenheimer code are also introduced, with results shown for the HeH$^+$ molecule. A new project involving confined molecules will be briefly introduced