Systematic study of confinement induced effects on atomic electronic structure

Abstract

We point out that although a litany of studies have been published on atoms in hard-wall confinement, they have not been systematic or have not used robust numerical methods. We report a methodical study of atoms in hard-wall confinement employing a robust finite element method (FEM) in HelFEM that guarantees variational results and allows easily finding the numerically exact solution. Our fully numerical calculations are non-relativistic and are carried out at three levels of density functional theory with spherically averaged densities: the PW92, PBE, and r${}^2$SCAN functionals. The three are in excellent agreement, confirming the physicality of our results. We systematically examine low lying configurations of the H-Xe atoms and their monocations, and investigate how the configurations - especially the ground state - behave as a function of the position of the hard-wall boundary. We consider both spin-polarized as well as spin-restricted densities, and demonstrate that spin-polarization effects are significant in open shell configurations, even though some previous studies have only considered the spin-restricted model. We demonstrate the importance of considering ground state changes for confined atoms by computing the ionization radii for the H-Xe atoms and observe significant differences to earlier studies. Confirming previous observations, we identify electron shifts on the outermost shells for a majority of the elements: valence $s$ electrons are highly unfavored under strong confinement, and the high-lying $3d$ and $4f$ orbitals become occupied in atoms of periods 2-3 and 3-4, respectively. We also comment on deficiencies of a commonly used density based estimate for the van der Waals (vdW) radius of atoms, and propose a better behaved variant in terms of the number of electrons outside the vdW radius that we expect will prove useful in future studies.

28 pages, 8 figures. Redefined alternative vdW radius estimate and added results with PW92 and r2SCAN to show that the results are similar regardless of the functional

References in corpus (15)

• Large scale and linear scaling DFT with the CONQUEST code
• A review on non-relativistic fully numerical electronic structure calculations on atoms and diatomic molecules
• Heats of formation of perchloric acid, HClO${}_4$, and perchloric anhydride, Cl${}_2$O${}_7$. Probing the limits of W1 and W2 theory
• The heat of atomization of sulfur trioxide, SO${}_3$ - a benchmark for computational thermochemistry
• Many recent density functionals are numerically ill-behaved
• Fully numerical calculations on atoms with fractional occupations. Range-separated exchange functionals
• Fully numerical Hartree-Fock and density functional calculations. I. Atoms
• Fully numerical electronic structure calculations on diatomic molecules in weak to strong magnetic fields
• Meta-GGA density functional calculations on atoms with spherically symmetric densities in the finite element formalism
• Atomic electronic structure calculations with Hermite interpolating polynomials
• Ensemble v-representable ab-initio density functional calculation of energy and spin in atoms: atest of exchange-correlation approximations
• High-order finite element method for atomic structure calculations
• Insight on Gaussian basis set truncation errors in weak to intermediate magnetic fields with an approximate Hamiltonian
• A numerical study of the extended Kohn-Sham ground states of atoms
• The importance of tight $f$ basis functions for heavy p-block oxides and halides: a parallel with tight $d$ functions in the second row

Cited by in corpus (2)

• OpenOrbitalOptimizer -- a reusable open source library for self-consistent field calculations
• Atomic Confinement Potentials and the Generation of Numerical Atomic Orbitals