Generalized elimination of the global translation from explicitly correlated Gaussian functions

This paper presents the multi-channel generalization of the center-of-mass kinetic energy elimination approach [B. Simmen et al., Mol. Phys. 111, 2086 (2013)] when the Schrödinger 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 Schrödinger equation in laboratory-frame Cartesian coordinates are demonstrated for the ground rovibronic state of the H₂⁺={p⁺,p⁺,e^-} ion and the H₂ = {p⁺, p⁺, e^-, e^-} molecule.