Nonadiabatic wavefunctions as linear expansions of correlated exponentials. A quantum Monte Carlo application to H2+ and Ps2

We propose to expand the nonadiabatic solution of the Schrödinger equation as a linear combination of explicity correlated exponentials. A series of trial wavefunctions has been optimized minimizing the variance of the local energy for the H2+ and dipositronium (Ps2) molecules in their ground state, without resorting to the Born-Oppenheimer approximation: the calculations have been performed using the variational Monte Carlo method. In a diffusion Monte Carlo simulation a 6-term wavefunction allowed us to compute the exact energy of the Ps2 system −0.51601 hartree with a variance of 0.00001 hartree.