Ground state calculations of the confined molecular ions H2+ and HeH⁺⁺ using variational Monte Carlo method

Abstract

AbsractThe ground state energy of hydrogen molecular ion confined by a hard prolate spheroidal cavity is calculated. The case in which the nuclear positions are clamped at the foci is considered. Our calculations are based on using the variational Monte Carlo method with an accurate trial wave function depending on many variational parameters. The calculations were extended also to include the molecular ion. The obtained results are in good agreement with the recent results.Key words: Variational methods, Monte Carlo methods, Molecular structure, Ground state of the and HeH ++ confined quantum systems. 1-IntroductionRecently, studies of quantum objects confined by different forms of external potentials have attracted the attention of both physicists and quantum chemists. This is due to the unusual physical and chemical properties observed in such systems when submitted to narrow spatial limitation as compared to their free cases. Also, confined systems are widely used to model a variety of problems in physics and chemistry. Examples of these problems occur in the study of the synthesis of nanostructure materials such as carbon nanotubes [1,2], buckyballs and zeolitic nanochannels which serve as ideal containers for molecular insertion and storage with promising applications [3][4][5][6]. The increasing pace at which research is being carried out in the aforementioned systems demands many powerful and sophisticated methodologies (Hartree-Fock, quantum chemical density functional theory, quantum molecular dynamics, to mention a few [1,[7][8][9]) and also, complementary exploratory models aimed at understanding the basic mechanisms of the changes in the electronic and structural properties of confined molecules. Various theoretical models have been proposed in the past to analyze the confinement effects on the confined systems, particularly those based on boxed-in molecules. Box models of confinement with hard and soft boundaries have been widely used to survey the effect of spatial limitation in the case of simple molecules such as molecular ion, molecule and some small polyatomics as , , and . Since, the molecular ion is considered as one of the first non-trivial quantum mechanical systems, many studies have been presented to investigate the effect of compression on its properties. In Ref [10], Molinar-Tabares et al. studied the confined by spheroids of size using prolate spheroidal coordinates. In frame of Born-Oppenheimer approximation, the Schrödinger equation was solved by the method of separation of variables to obtain the equilibrium distance between nuclei and the corresponding energy as a

Compressed lithium atom under Debye screening

“…In this context, we specifically examine two highly effective methods: the variational Monte Carlo (VMC) method and the diffusion Monte Carlo (DMC) method. While we have previously discussed the VMC method in our earlier works (see References [18, 19, 45]), our focus here is solely on the DMC method. The DMC method's approach seeks to transform the time‐dependent Schrödinger's equation into an imaginary‐time diffusion equation.…”

“…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].…”