Nonadiabatic variational calculations for the ground state of the positronium molecule

For a four-particle system consisting of two electrons and two positrons, the nonadiabatic wave function is constructed with the use of an expansion in terms of explicitly correlated Gaussian-type basis functions and a Cartesian-coordinate laboratory frame. Motions of all particles are correlated at the same time in the wave function. The energy of the center-of-mass motion is effectively eliminated from the total nonrelativistic energy of the system by defining the variational principle based on the internal Hamiltonian. The ground-state energy is computed for different lengths of Gaussian expansions and values are compared with previous literature results. Our best estimation of the binding energy of the positronium molecule is 0.435 eV.