On the inclusion of cusp effects in expectation values with explicitly correlated Gaussians

TL;DR

This paper enhances the calculation of expectation values in quantum systems by incorporating cusp effects using integral transformation techniques, with applications to helium and H3+ ions.

Contribution

It extends existing integral transformation methods to include cusp effects in expectation value calculations for both non-relativistic and relativistic operators.

Findings

Accurate expectation values for helium's ground state.

New results for H3+ molecular ion near equilibrium.

Validation of techniques for relativistic corrections.

Abstract

This paper elaborates the integral transformation technique of [K. Pachucki, W. Cencek, and J. Komasa, J. Chem. Phys. 122, 184101 (2005)] and uses it for the case of the non-relativistic kinetic and Coulomb potential energy operators, as well as for the relativistic mass-velocity and Darwin terms. The techniques are tested for the ground electronic state of the helium atom and new results are reported for the ground electronic state of the H$_3^+$ molecular ion near its equilibrium structure.