Quantum states of H2+ and H2 in an icosahedral potential well

Abstract

We investigate the potential energy surfaces (PESs) of the hydrogen-based cation H2+ and the neutral molecule H2 confined inside an infinite potential well in the shape of a regular icosahedron. The numerical computations are performed using the diffusion Monte Carlo method and are based on an analytical technique for obtaining simple equations of the surfaces of convex polyhedra proposed by S. Onaka. Different states and different orientations of the molecules inside the confining potential well, as well as various sizes of the latter, are studied. We provide a detailed symmetry analysis and consistent labeling of the H2+ states considered. The results show that the icosahedral confinement is closely isotropic in its inner region, leading to PESs that develop pronounced minima, as in the case of simpler confinement geometries. Shape-specific effects can be evidenced when the nuclei are in contact with the confining wall.

Static field ionization of the spherically confined hydrogen atom

“…This allows a considerable code acceleration [48]. The method can be used to study a great variety of systems, even different geometries of the potential well (from spherical to octahedral and icosahedral, from cylindrical to cubical) [50][51][52], using Cartesian coordinates and with minimal modifications to the algorithm.…”

“…Two cases of study are presented: the first one with the hydrogen nucleus fixed at the center of the confining sphere, the second one with the nucleus placed in different positions along the x axis, and in particular the equilibrium one. Using a direct calculation method based on diffusion Monte Carlo (DMC) [46][47][48], we will consider strong electric fields and different positions of the nucleus, especially the one that corresponds to the minimum overall energy, taking into account both the ground and excited states, 1s and 2p.…”

Electron density analysis of two-electron systems confined by prolate spheroids with hard walls

“…The change of the electronic structure of atoms and molecules by confinement is an active field in physics and chemistry, where many confinement effects have been studied using model potentials to mimic spatial restrictions [1][2][3][4][5][6]. The hard walls model has been used for atoms and molecules to simulate the confinement by imposing Dirichlet boundary conditions such that the wave function or electron density is canceled on the system's boundaries.…”

“…Confined one-and two-electron molecules have been studied considering different shapes and methods [6,[24][25][26][27][28][29][30][31]. However, the main interest in such reports is related to energy analysis, and the chemical bond has not been the main target.In this sense, Ley-Koo and Cruz solved analytically the Schrödinger equation for the + H 2 molecule confined by prolate spheroids with hard walls [24].…”

“…This behavior is a consequence of confinement, where the kinetic energy commands the potential energy when hard walls confine this molecule. In addition to the + H 2 molecule, some efforts have been made to study molecules with more than one electron confined by hard walls, in particular for H 2 [6,[25][26][27][28][29][30] and He 2 [34].This article aims to analyze the electron density in two-electron systems, He and H 2 , confined by prolate spheroids with hard walls. The solution of the Hartree-Fock equations is through the Roothaanʼs approach using a basis set defined within the prolate spheroidal coordinate system.…”