Deformation Potentials: Towards a Systematic Way beyond the Atomic Fragment Approach in Orbital-Free Density Functional Theory

Abstract

This work presents a method to move beyond the recently introduced atomic fragment approximation. Like the bare atomic fragment approach, the new method is an ab initio, parameter-free, orbital-free implementation of density functional theory based on the bifunctional formalism that treats the potential and the electron density as two separate variables, and provides access to the Kohn–Sham Pauli kinetic energy for an appropriately chosen Pauli potential. In the present ansatz, the molecular Pauli potential is approximated by the sum of the bare atomic fragment approach, and a so-called deformation potential that takes the interaction between the atoms into account. It is shown that this model can reproduce the bond-length contraction due to multiple bonding within the list of second-row homonuclear dimers. The present model only relies on the electron densities of the participating atoms, which themselves are represented by a simple monopole expansion. Thus, the bond-length contraction can be rationalized without referring to the angular quantum numbers of the participating atoms.

Detailed analysis of deformation potentials with application in orbital-free density functional theory

“…The first test case with c = 0 and d = 0 is the bare atomic fragment approach itself, in which case the equilibrium bond distances directly follow the size of the core shells, which decrease from Li to Ne and thus, yield a very short bond length in the case of Ne 2 [for a detailed explanation see Finzel (2021)]. The construction of a deformation potential with c = 2 and d = 0 means that one electron pair interacts constructively, while there are no destructive terms at all.…”

“…It has been shown recently that reliable approximations for the Pauli kinetic energy can be obtained via bifunctional formalism, involving the electron density and an approximate Pauli potential employing the bare atomic fragment approach (Finzel, 2018a(Finzel, ,b, 2019(Finzel, , 2020 and a so-called deformation potential that takes the interaction between two atoms into account (Finzel, 2021). The present work is a direct follow-up paper of the latter publication (Finzel, 2021), in which the recently proposed ansatz is subjected to further investigations. Therefore, a detailed analysis of those deformation potentials is given here.…”

“…As in recently published papers (Finzel, 2018a(Finzel, , 2019(Finzel, , 2020(Finzel, , 2021, the Pauli kinetic energy is evaluated from the so-called bifunctional expression:…”

“…Obviously, in an orbital-free formalism, the KS eigenfunctions and eigenvalues are of course not available. However, as recently shown (Finzel, 2021), sufficiently accurate approximations for the molecular Pauli potential can be found in order to properly describe chemical bonding by choosing the following ansatz v def P ðrÞ for the Pauli potential:…”

“…In the present work, energy minimization has been performed by optimizing the respective exponents 1s and 2s , while keeping the corresponding shell occupations fixed [for details see Finzel (2021)].…”