The effect of confinement on the electronic energy and polarizability of a hydrogen molecular ion

Abstract

The electronic energy and the polarizability of a confined hydrogen molecular ion in the ground state and the first excited state, for cavities of different volumes, are calculated using the variational method. In the treatment adopted an alternative molecular wave function is introduced with only one variational parameter and based on wave functions used for confined atoms.

Benchmark values of Shannon entropy for spherically confined hydrogen atom

“…There are still many questions that are not easily solved or yet unknown for the simplest confined hydrogen atom investigated here, for example, the limit of entropy sum at zero confinement radius, the variation of entropies for highly excited Rydberg states, the combination effect with external field, and so forth. Furthermore, the investigation of confinement for multielectron atoms and small molecules based on elaborate methods beyond the density functional theory may reveal more fundamental interests in atomic and molecular physics as well as quantum chemistry. It is hoped that our present work could provide useful information's for further studies in this area.…”

Comment on “The effect of confinement on the electronic energy and polarizability of a hydrogen molecular ion” by Josimar Fernando da Silva, Fabricio Ramos Silva and Elso Drigo Filho, Int. J. Quantum Chem. 2016, 116, 497–503

“…In Ref. [ ], the hydrogen molecular ion confined by a hard prolate spheroidal box is studied variationally (within the Born‐Oppenheimer approximation) employing a two‐center ansatz molecular wavefunction consisting of a LCAO approach using two atomic s‐type hydrogenic orbitals with a single variational parameter. Unfortunately, in its grounds, the paper is full of conceptual and numerical errors which force us to make pertinent comments.…”

Ground-state energy for confined H2: a variational approach

“…The Laplacian, in prolate spheroidal coordinates, considering an azimuthal symmetry, is given by: and the barrier of potential, V c , is: From the conditions of the problem under analysis, the ansatz wave functions proposed for the atomic function, in complete analogy to Eq. 4, are written following those suggested by da Silva et al [15]:…”

“…In the study of confined molecules, special attention has been devoted to the ionic hydrogen molecule (H 2 + ) [10][11][12][13][14][15] and the neutral hydrogen molecule (H 2 ) [16][17][18][19]. Small polyatomic molecules have also been analyzed [20][21][22][23].…”

“…Recently, the eigenvalues of energy for a confined hydrogen ion molecule [15] have been obtained by the variational method using a molecular function described as a linear combination of atomic orbitals of 1 s state with just one variational parameter. In this work, the methodology adopted by da Silva et al [15] is extended for the hydrogen molecule, as previously suggested [24]. In this way, a molecular function of the valence bond type [25] is proposed for a confined hydrogen molecule.…”