Confined helium atom low-lying S states analyzed through correlated Hylleraas wave functions and the Kohn-Sham model

Finite element method as an alternative to study the electronic structure of confined atoms

The finite element method (FEM) based on a nonregular mesh is used to solve Hartree-Fock and Kohn-Sham equations for three atoms (hydrogen, helium, and beryllium) confined by finite and infinite potentials, defined in terms of piecewise functions or functions with a well-defined first derivative. This approach's reliability is shown when contrasted with Roothaan's approach, which depends on a basis set. Therefore, its exponents must be optimized for each confinement imposed over each atom, which is a monumental task. The comparison between our numerical approach and Roothaan's approach is made by using total and orbitals energies from the Hartree-Fock method, where there are several comparison sources. Regarding the Kohn-Sham method, there are few published data and consequently the results reported here can be used as a benchmark for future comparisons. The way to solve Hartree-Fock or Kohn-Sham equations by the FEM is entirely appropriate to study confined atoms with any form of confinement potential. This article represents a step toward developing a fully numerical quantum chemistry code free of basis sets to obtain the electronic structure of many-electron atoms confined by arbitrary confinement.

An off-center endohedrally confined hydrogen molecule

In this study, we address the problem of a C₆₀ endohedrally confined hydrogen molecule through a configuration-interaction approach to electronic dynamics. Modeling the confinement by means of a combination of two Woods-Saxon potentials, we analyze the stability of the system as a function of the nuclei position through the behavior of the electronic spectrum. After studying the convergence of two different partial wave expansions, one related to the molecular Coulomb centers and the other related to the off-centering of the C₆₀ well, we found that the second approach provides a more accurate description of the system. Furthermore, we observed that the inter-atomic distance changes based on the position of the atoms inside the cavity. Thus, to obtain the most favourable energetic configuration for the molecule, it should be positioned inside the cavity next to the structure, where its size decreases.

Linear chains of hydrogen molecules under pressure: An extreme-pressure continuum model study

New analytical gradients of the electronic energy of a confined molecular system within the extreme-pressure continuum model are presented and applied to the study of the equilibrium geometries of linear chains of hydrogen molecules nH₂ under pressures. The decrease in inter- and intramolecular H-H distances with the increase in the pressure has been studied up to 80 GPa. We have also shown that the compression of the bond-lengths can be interpreted in terms of the effect of the confining potential of the electron density of the molecular systems.

Analytical calculation of pressure for confined atomic and molecular systems using the eXtreme-Pressure Polarizable Continuum Model

We show that the pressure acting on atoms and molecular systems within the compression cavity of the eXtreme-Pressure Polarizable Continuum method can be expressed in terms of the electron density of the systems and of the Pauli-repulsion confining potential. The analytical expression holds for spherical cavities as well as for cavities constructed from van der Waals spheres of the constituting atoms of the molecular systems. © 2018 Wiley Periodicals, Inc.

Correlation energy, correlated electron density, and exchange-correlation potential in some spherically confined atoms

We report correlation energies, electron densities, and exchange-correlation potentials obtained from configuration interaction and density functional calculations on spherically confined He, Be, Be²⁺ , and Ne atoms. The variation of the correlation energy with the confinement radius R_c is relatively small for the He, Be²⁺ , and Ne systems. Curiously, the Lee-Yang-Parr (LYP) functional works well for weak confinements but fails completely for small R_c . However, in the neutral beryllium atom the CI correlation energy increases markedly with decreasing R_c . This effect is less pronounced at the density-functional theory level. The LYP functional performs very well for the unconfined Be atom, but fails badly for small R_c . The standard exchange-correlation potentials exhibit significant deviation from the "exact" potential obtained by inversion of Kohn-Sham equation. The LYP correlation potential behaves erratically at strong confinements. © 2016 Wiley Periodicals, Inc.

Confined helium on Lagrange meshes

The Lagrange-mesh method has the simplicity of a calculation on a mesh and can have the accuracy of a variational method.