Exchange correlation potentials from full configuration interaction in a Slater orbital basis

Abstract

Ryabinkin–Kohut–Staroverov (RKS) theory builds a bridge between wave function theory and density functional theory by using quantities from the former to produce accurate exchange-correlation potentials needed by the latter. In this work, the RKS method is developed and tested alongside Slater atomic orbital basis functions for the first time. To evaluate this approach, full configuration interaction computations in the Slater orbital basis are employed to give quality input to RKS, allowing full correlation to be present along with correct nuclei cusps and asymptotic decay of the wavefunction. SlaterRKS is shown to be an efficient algorithm to arrive at exchange-correlation potentials without unphysical artifacts in moderately-sized basis sets. Furthermore, enforcement of the nuclear cusp conditions will be shown to be vital for the success of the Slater-basis RKS method. Examples of weakly and strongly correlated molecular systems will demonstrate the main features of SlaterRKS.

Discontinuities of Kinetic Energy Densities within Finite and Complete Basis Sets

“…In other situations, however, discontinuities of kinetic energy densities may have tangible consequences. For instance, when imposing nuclear cusp conditions on molecular orbitals − it might be beneficial to go beyond the standard equations for spherically averaged quantities and try to impose cusp conditions with explicit directional dependence. The fact that, in H 2 , discontinuities of τ­( r ) can be as large as 75% of the value of τ­( r ) at the nucleus (Figure ) may explain why the spherically averaged nuclear cusp condition is harder to impose for hydrogens than for heavier nuclei …”

Kohn–Sham Density in a Slater Orbital Basis Set

“…The difficulty can partly be traced to the inherent limitations of finite basis sets (e.g., atom-centered orbitals), where KS orbitals are insufficiently flexible to precisely represent densities coming from wave function theory. While one option is to turn to complete basis sets to produce more precise KS orbitals, − the present work deliberately chooses to stay within the finite-basis framework. , Finite basis sets consisting of atom-centered orbitals are not only ubiquitous, but are utilized by most high-accuracy wave function theories. , The present study therefore focuses on the finite basis case, and does so at the cost of not being able to strictly reproduce wave function densities in the KS framework.…”

“…While one option is to turn to complete basis sets to produce more precise KS orbitals, 24−26 the present work deliberately chooses to stay within the finite-basis framework. 27,28 Finite basis sets consisting of atom-centered orbitals are not only ubiquitous, but are utilized by most high-accuracy wave function theories. 29,30 The present study therefore focuses on the finite basis case, and does so at the cost of not being able to strictly reproduce wave function densities in the KS framework.…”

Exact and Model Exchange-Correlation Potentials for Open-Shell Systems

“…The inverse DFT problem is solved as an iterative procedure ,,,, or constrained optimization. ,,,, While most of these approaches suffer from numerical instabilities ,, and/or are based on electron densities with incorrect asymptotic behavior, ,− recent efforts have worked to address these challenges. In particular, one strategy uses the two-electron density matrix instead of just the density − and another employs constrained optimization in a complete finite-element (FE) basis. , The latter strategy finds XC potentials from densities containing the correct asymptotics, giving highly accurate potentials that can be used in learning XC functionals.…”