Molecular structure calculations: a unified quantum mechanical description of electrons and nuclei using explicitly...

We elaborate on the theory for the variational solution of the Schrödinger equation of small atomic and molecular systems without relying on the Born-Oppenheimer paradigm. The all-particle Schrödinger equation is solved in a numerical procedure using the variational principle, Cartesian coordinates, parameterized explicitly correlated Gaussian functions with polynomial prefactors, and the global vector representation. As a result, non-relativistic energy levels and wave functions of few-particle systems can be obtained for various angular momentum, parity, and spin quantum numbers. A stochastic variational optimization of the basis function parameters facilitates the calculation of accurate energies and wave functions for the ground and some excited rotational-(vibrational-)electronic states of H(2) (+) and H(2), three bound states of the positronium molecule, Ps(2), and the ground and two excited states of the (7)Li atom.