Spin-dependent terms of the Breit-Pauli Hamiltonian evaluated with an explicitly correlated Gaussian basis set for molecular computations

TL;DR

This paper calculates spin-dependent relativistic corrections for molecules using an explicitly correlated Gaussian basis, enabling high-precision predictions of fine-structure effects in small systems.

Contribution

It introduces a method to compute spin-dependent relativistic corrections with high accuracy using explicitly correlated Gaussian basis sets for molecular systems.

Findings

High-precision energy corrections for triplet Be, H2, and H3+ states.

Accurate magnetic coupling curves for excited states of He2.

Validation against no-pair Dirac-Coulomb-Breit Hamiltonian energies.

Abstract

This work collects the spin-dependent leading-order relativistic and quantum-electrodynamical corrections for the electronic structure of atoms and molecules within the non-relativistic quantum electrodynamics framework. We report the computation of perturbative corrections using an explicitly correlated Gaussian basis set, which allows high-precision computations for few-electron systems. In addition to numerical tests for triplet Be, triplet H$_2$, and triplet H$_3^+$ states and comparison with no-pair Dirac-Coulomb-Breit Hamiltonian energies, numerical results are reported for electronically excited states of the helium dimer, He$_2$, for which the present implementation delivers high-precision magnetic coupling curves necessary for a quantitative understanding of the fine structure of its high-resolution rovibronic spectrum.