Basis set effects on the Hartree–Fock description of confined many-electron atoms

Abstract

In this work, the basis sets designed by Clementi, Bunge and Thakkar, for atomic systems, have been used to obtain the electronic structure of confined many-electron atoms by using Roothaan's approach in the Hartree-Fock context with a new code written in C, which uses the message-passing interface library. The confinement was imposed as Ludeña suggested to simulate walls with infinity potential. For closed-shell atoms, the Thakkar basis set functions give the best total energies (TE) as a function of the confinement radius, obtaining the following ordering: TE(Thakkar) < TE(Bunge) < TE(Clementi). However, for few open-shell atoms this ordering is not preserved and a trend, for the basis sets, is not observed. Although there are differences between the TE predicted by these basis set functions, the corresponding pressures are similar to each other; it means that changes in the total energy are described almost in the same way by using any of these basis sets. By analysing the total energy as a function of the inverse of the volume we propose an equation of state; for regions of small volumes, this equation predicts that the pressure is inversely proportional to the square of the volume.

Electron‐density delocalization in many‐electron atoms confined by penetrable walls: A Hartree–Fock study

“…In the same direction of Gadre et al, we use HF wave functions to get the electron‐density by solving the corresponding one‐electron equations with the MEXICA‐C code, with Equation as the basis set. To obtain , in this work, the spherical average of the electron‐density is obtained for each confinement radius.…”

“…In this case, the hydrogen atom was clamped at the center of one sphere, of radius R c , with impenetrable walls and consequently, wave‐function or electron‐density satisfy Dirichlet's boundary conditions. On this line, walls with infinite potential have been applied to study many‐electron atoms, using wave‐function techniques or the density functional theory, and some of these results have been contrasted with experimental values to predict s – d electronic transitions observed when some metals are submitted to high pressures . In early stages of the quantum mechanics, Sommerfeld proposed that positive eigenvalues found under this model indicate an electron delocalization .…”

Confinement effects on the electronic structure of M-shell atoms: A study with explicitly correlated wave functions

“…Here, the following form for g ( r ) is employed which has shown to work properly for atoms, see for example, Refs. [, , ].…”

“…In a theoretical approach, hard wall confinement has been used as a model to understand changes in atomic sizes, energies and other properties . Penetrable surfaces that allow the electronic charge to extend beyond the confinement cavity, have also been considered in the literature …”

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

“…It is worth noting that the confined atoms model gives many features of this process without the necessity to use sophisticate solid state techniques. [7][8][9][10][11][12][13][14] For the s-d transition, an infinite potential has been used to mimic the pressure exerted over the electrons of alkali DOI: 10.1002/andp.201800476 metals. Thus, nucleus and electrons are confined by an external potential.…”