Generalized elimination of the global translation from explicitly correlated Gaussian functions

TL;DR

This paper extends a method for eliminating the global translation in quantum calculations using explicitly correlated Gaussian functions, enabling accurate solutions for many-particle systems without the Born--Oppenheimer approximation.

Contribution

It introduces a multi-channel generalization of the center-of-mass kinetic energy elimination approach for variational solutions with explicitly correlated Gaussian functions.

Findings

Successfully applied to the ground state of H₂⁺ ion.

Demonstrated effectiveness for the H₂ molecule.

Applicable to systems with Dirac-type Hamiltonians.

Abstract

This paper presents the multi-channel generalization of the center-of-mass kinetic energy elimination approach [Mol. Phys., 111 2086 (2013)] when the Schr\"odinger equation is solved variationally with explicitly correlated Gaussian functions. The approach has immediate relevance in many-particle systems which are handled without the Born--Oppenheimer approximation and can be employed also for Dirac-type Hamiltonians. The practical realization and numerical properties of solving the Schr\"odinger equation in laboratory-frame Cartesian coordinates are demonstrated for the ground rovibronic state of the H$_2^+=\lbrace\text{p}^+,\text{p}^+,\text{e}^+\rbrace$ ion and the H$_2=\lbrace\text{p}^+,\text{p}^+,\text{e}^+,\text{e}^+\rbrace$ molecule.