Algorithm for quantum-mechanical finite-nuclear-mass variational calculations of atoms with two $p$ electrons using all-electron explicitly correlated Gaussian basis functions

A new algorithm for calculating the Hamiltonian matrix elements with all-electron explicitly correlated Gaussian functions for quantum-mechanical calculations of atoms with two $p$ electrons or a single $d$ electron have been derived and implemented. The Hamiltonian used in the approach was obtained by rigorously separating the center-of-mass motion and it explicitly depends on the finite mass of the nucleus. The approach was employed to perform test calculations on the isotopes of the carbon atom in their ground electronic states and to determine the finite-nuclear-mass corrections for these states.