Ground-state calculations of confined hydrogen molecule H₂ using variational Monte Carlo method

Abstract

The variational Monte Carlo method is used to evaluate the ground-state energy of the confined hydrogen molecule, . Accordingly, we considered the case of hydrogen molecule confined by a hard prolate spheroidal cavity when the nuclear positions are clamped at the foci (on-focus case). Also, the case of off-focus nuclei in which the two nuclei are not clamped to the foci is studied. This case provides flexibility for the treatment of the molecular properties by selecting an arbitrary size and shape of the confining spheroidal box. An accurate trial wave function depending on many variational parameters is used for this purpose. The obtained results are in good agreement with the most recent results.

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

“…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.…”

Compressed lithium atom under Debye screening

“…Many investigations have been conducted to examine atoms enclosed within spherical and non-spherical cavities, starting from hydrogen [1-4], and extending to helium [5][6][7][8][9][10][11][12][13][14][15] and molecules [16][17][18][19]. However, limited research has been presented on confined many-electron atoms up to neon atom in the literature [20][21][22][23][24][25][26].…”

“…Confined systems serve as valuable models for a wide range of physics problems. When atoms and molecules are spatially confined within either permeable or impermeable cavities, their properties change significantly compared with their unconfined counterparts.Many investigations have been conducted to examine atoms enclosed within spherical and non-spherical cavities, starting from hydrogen [1-4], and extending to helium [5][6][7][8][9][10][11][12][13][14][15] and molecules [16][17][18][19]. However, limited research has been presented on confined many-electron atoms up to neon atom in the literature [20][21][22][23][24][25][26].…”

Electron Density Analysis for the H2+ System Confined by Hard Walls: The Chemical Bond Under Extreme Conditions

“…Some people argue that this potential is realistic and its results can be compared with experimental data. In fact, to the best of our knowledge only four molecules, H + 2 , [21][22][23][24][25] HeH ++ , [21] H 2 , [26][27][28][29] and LiH [30] have been studied when they are submitted to spatial restrictions and all of them deal with one or two electrons (See a recent review by Ley-Koo [31] ). [16] Besides, this model has been useful to test exchange-correlation functionals designed within the Kohn-Sham density functional theory.…”