Leading relativistic corrections for atomic P states calculated with a finite-nuclear-mass approach and all-electron explicitly correlated Gaussian functions

Abstract

In this work we report progress in the development and implementation of quantum-mechanical methodsforcalculating bound groundand excitedstates of smallatomic systems. Theworkconcerns singlet states with the L=1 total orbital angular momentum (P states). The method is based on the f inite-nuclear-mass (non-Born-Oppenheimer; non-BO) approach and the use of all-particle explicitly correlated Gaussian functions for expanding the non-relativistic wave function of the system. The development presented here includes derivation and implementation of algorithms for calculating the leading relativistic corrections for singlet states. The corrections are determined in the framework of the perturbation theory as expectation values of the corresponding effective operators using the non-BO wave functions. The method is tested in the calculations of the ten lowest 1P states of the helium atom and the four lowest 1P states of the beryllium atom.