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.
Categories: physics.comp-ph cond-mat.str-el physics.atom-ph physics.chem-ph