The hydrogen molecule and the H⁺₂molecular ion inside padded prolate spheroidal cavities with arbitrary nuclear positions

Abstract

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 Schrödinger 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.

Monte Carlo calculation of the potential energy surface for octahedral confined H$$_2^+$$2+

“…in [2]). As expected much attention has been devoted to H + 2 , the simplest molecular system [3][4][5][6][7][8][9][10][11][12][13]. Also this particular case, apart from its value as fundamental issue, may find several applications.…”

The H, H2+, and HeH2+ systems confined by an impenetrable spheroidal cavity: Revisited study via the Lagrange‐mesh approach

“…The first exact solutions to the Schrödinger problem—within the Born–Oppenheimer approximation—for the H atom, the H , and HeH molecular ions inside a hard and soft prolate spheroidal cavity have been commonly used as benchmark reference to validate the numerical assessment of other alternative approaches . However, the strategy followed in the aforementioned exact treatments demands as an input the exact electronic energy for a given state and interfocal distance and then find the box characteristics satisfying the appropriate boundary conditions.…”

“…[26,27] In this context, theoretical modeling of the simple system confined by prolate spheroidal boxes keeps renewed interest to explore the electronic and optical properties of hydrogenic donor impurities trapped in ovoidal QD's.The first exact solutions to the Schr€ odinger problem-within the Born-Oppenheimer approximation-for the H atom, the H 1 2 , and HeH 21 molecular ions inside a hard [28] and soft [29] prolate spheroidal cavity have been commonly used as benchmark reference to validate the numerical assessment of other alternative approaches. [15,[30][31][32][33] However, the strategy followed in the aforementioned exact treatments demands as an input the exact electronic energy for a given state and interfocal distance and then find the box characteristics satisfying the appropriate boundary conditions. This procedure becomes a bit cumbersome for practical applications making it desirable to establish first the box characteristics and then find the energy for a given state and interfocal distance, compliant with the boundary conditions.…”

Confinement effects on the electronic structure of M-shell atoms: A study with explicitly correlated wave functions

“…In a theoretical approach, hard wall confinement has been used as a model to understand changes in atomic sizes, energies and other properties . Penetrable surfaces that allow the electronic charge to extend beyond the confinement cavity, have also been considered in the literature …”