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 [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${}_2^{+}=\{{\text{p}}^{+},{\text{p}}^{+},{\text{e}}^{+}\}$ ion and the H${}_2=\{{\text{p}}^{+},{\text{p}}^{+},{\text{e}}^{+},{\text{e}}^{+}\}$ molecule.