The hydrogen molecule and the H2+ molecular ion inside padded prolate spheroidal cavities with arbitrary nuclear positions

A generalization of previous theoretical studies of molecular confinement based on the molecule-in-a-box model for the H-2(+) and H-2 systems whereby the confining cavity is assumed to be prolate spheroidal in shape is presented. A finite height for the confining barrier potential is introduced and the independent variation of the nuclear positions from the cavity size and shape is allowed. Within this scheme, the non-separable Schrodinger problem for the confined H-2(+) and H-2 molecules in their ground states is treated variationally. In both cases, an important dependence of the equilibrium bond length and total energy on the confining barrier height is observed for fixed cavity sizes and shapes. It is also shown that-given a barrier height-as the cavity size is reduced, the limit of stability of the confined molecule is attained for a critical size. The results of this work suggest the adequacy of the proposed method for more realistic studies of electronic and vibrational properties of confined one-and two-electron diatomics for proper comparison with experiment.