Protonic Structure of Molecules. II. Methodology, Center-of-Mass Transformation, and the Structure of Methane, Ammonia, and Water

A center-of-mass-transformed Hamiltonian is used to study the molecular structure of methane, ammonia, and water, where the protons as well as the electrons are described by Slater determinants of one-particle Slater functions. The matrix elements of the Hamiltonian are given for a wave function constructed from a product between a sum of Slater determinants for the electrons and a sum of Slater determinants for the protons. The ground states of the protons were the ${}_{}{}^5{}_{}{}^{}S$ multiplet of the $s{p}^3$ configuration at -39.137 64 hartrees for methane, the ${}_{}{}^4{}_{}{}^{}P$ multiplet of the $s{p}^2$ configuration at -55.445 22 hartrees for ammonia, and the ${}_{}{}^3{}_{}{}^{}P$ multiplet of the $\mathrm{sp}$ configuration at -75.500 05 hartrees for water. The energies of the other protonic multiplets of the above configurations are given also, as are the energies of the protonic multiplet of the $s^2{p}^2$ and $p^4$ configurations in methane, of the $s^{2}p$ and $p^3$ configurations in ammonia, and of the $s^2$ and $p^2$ configurations in water. The errors in the wave functions are discussed.