Abstract
Computational codes based on the diffusion Monte Carlo method can be used to determine the quantum state of two-electron systems confined by external potentials of various natures and geometries. In this work, we show how the application of this technique in its simplest form, that does not employ complex analytic guess functions, allows to obtain satisfactory results and, at the same time, to write programs that are readily adaptable from one type of confinement to another. This adaptability allows an easy exploration of the many possibilities in terms of both geometry and structure of the system. To illustrate these results, we present calculations in the case of two-electron hydrogen-based species (hbox {H}_{2} and hbox {H}_{3}^{+}) and two different types of confinement, nanotube-like and octahedral crystal field.Graphic abstract
Highlights
The fundamental relevance and concrete applications of the confined quantum systems have been established since the early days of quantum physics [13,28,41], up to the present day [23,35,39,40]
We show the application of the method to the ground state of two-electron systems (H2 and H+3 ) with non-trivial confinement geometries
We underline that while we have studied the collinear geometry of H+3, nothing in the code prevents the consideration of any nuclear geometry, since the code high flexibility with regard to the changing of geometry
Summary
The fundamental relevance and concrete applications of the confined quantum systems have been established since the early days of quantum physics [13,28,41], up to the present day [23,35,39,40]. Atoms imprisoned in zeolite traps, clusters and fullerene cages provide good examples of confined systems in atomic physics and inorganic chemistry [6,10,18,42] Many of these studies on the physical–chemical properties of confined systems focus on systems with a small number of electrons: for example, species with small molecules containing hydrogen, helium and lithium. A trial wavefunction is employed; instead, some efficient solutions to accelerate calculations and reduce noise are employed Thanks to this method, it is possible to study different systems, with different orientations, and even quickly change the geometry of the potential well, from spherical to elliptical, from cylindrical to cubical, using Cartesian coordinates and implementing few modifications to the starting code. The molecular hydrogen confined in a rigid spheroidal box, with fixed and not fixed nuclear positions, was studied with variational calculations and quantum Monte Carlo techniques [9,14,15,21,22,31], with Monte Carlo methods beyond the Born– Oppenheimer approximation [37]
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