Exact and model exchange-correlation potentials for open-shell systems

Abstract

The conventional approaches to the inverse density functional theory problem typically assume non-degeneracy of the Kohn-Sham (KS) eigenvalues, greatly hindering their use in open-shell systems. We present a generalization of the inverse density functional theory problem that can seamlessly admit degenerate KS eigenvalues. Additionally, we allow for fractional occupancy of the Kohn-Sham orbitals to also handle non-interacting ensemble-v-representable densities, as opposed to just non-interacting pure-v-representable densities. We present the exact exchange-correlation (XC) potentials for six open-shell systems -- four atoms (Li, C, N, and O) and two molecules (CN and ${\text{CH}}_2$) -- using accurate ground-state densities from configuration interaction calculations. We compare these exact XC potentials with model XC potentials obtained using non-local (B3LYP, SCAN0) and local/semi-local (SCAN, PBE, PW92) XC functionals. Although the relative errors in the densities obtained from these DFT functionals are of $\mathcal{O}(10^{-3}-10^{-2})$, the relative errors in the model XC potentials remain substantially large -- $\mathcal{O}(10^{-1}-10^0)$.

References in corpus (14)

• Complexity in Strongly Correlated Electronic Systems
• SCAN-based hybrid and double-hybrid density functionals from models without fitted parameters
• DFT-FE -- A massively parallel adaptive finite-element code for large-scale density functional theory calculations
• Higher-order adaptive finite-element methods for Kohn-Sham density functional theory
• Optimized Effective Potentials in Finite Basis Sets
• Machine Learning the Physical Non-Local Exchange-Correlation Functional of Density-Functional Theory
• Numerical Methods for the Inverse Problem of Density Functional Theory
• Reduction of Electronic Wavefunctions to Kohn-Sham Effective Potentials
• Inverse Kohn-Sham Density Functional Theory: Progress and Challenges
• Kohn-Sham potentials in exact density-functional theory at non-integer electron numbers
• Improved method for generating exchange-correlation potentials from electronic wave functions
• Optimized Unrestricted Kohn-Sham Potentials from Ab Initio Spin Densities
• Accurate Kohn-Sham auxiliary system from the ground state density of solids
• Exchange Correlation Potentials from Full Configuration Interaction in a Slater Orbital Basis

Cited by in corpus (1)

• Exchange-Correlation Potentials and Energy Densities through Orbital Averaging and Aufbau Integration