The hydrogen molecule inside prolate spheroidal boxes: full nuclear position optimization

The ground-state energy of the H(2) molecule confined by a hard prolate spheroidal box is studied variationally by uncoupling the nuclear positions from the foci. The (uncorrelated) two-electron ansatz wavefunction is constructed as a product of one-electron terms associated with the H(2)(+) ion with arbitrary nuclear positions and under the same confinement conditions. It is shown that by making the cavity size and shape independent of the nuclear positions, optimum equilibrium bond lengths and energies are obtained as compared with corresponding on-focus calculations. This procedure allows for a controlled treatment of molecular properties by selecting an arbitrary size and shape of the confining spheroidal box. As an example, pilot calculations are presented for the energy evolution and vibrational properties of the H(2) molecule confined in boxes of varying size but keeping the same aspect ratio.