Structural information is extracted from the all-particle (non-Born-Oppenheimer) wave function by calculating radial and angular densities derived from n-particle densities. As a result, one-and two-dimensional motifs of classical molecular structure can be recognized in quantum mechanics. Numerical examples are presented for three-(H(-), Ps(-), H(2) (+)), four-(Ps(2), H(2)), and five-particle (H(2)D(+)) systems. Extracting elements of molecular structure from the all-particle wave function Structural information is extracted from the all-particle (non-Born-Oppenheimer) wave function by calculating radial and angular densities derived from n-particle densities. As a result, one-and twodimensional motifs of classical molecular structure can be recognized in quantum mechanics. Numerical examples are presented for three-(H − , Ps − , H + 2 ), four-(Ps 2 , H 2 ), and five-particle (H 2 D + ) systems.

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 H={p,p,e} ion and the H = {p, p, e, e} molecule.