Diagonal Born-Oppenheimer Correction Based on Spin-Free Relativistic Hamiltonians

Abstract

Methodologies beyond the Born-Oppenheimer (BO) approximation are nowadays important to explain high precision spectroscopic measurements. Our work is the first development and application of the diagonal BO correction (DBOC) based on spin-free relativistic Hamiltonians. We used the second and infinite-order Douglas-Kroll-Hess Hamiltonians at their spin-free levels. Our test calculations of noble atoms (He – Xe) show that the DBOC energy (EDBOC) is approximately proportional to atomic number Z. Hence the BO correction generally increases when a molecule contains heavier atoms. We also computed the adiabatic corrections to the barrier heights for linearization of H₂X molecules where X = O, S, Se, and Te, to discuss DBOC corrections for heavy elements.