Kohn-Sham potentials in exact density-functional theory at non-integer electron numbers

Abstract

Within exact electron density-functional theory, we investigate Kohn-Sham (KS) potentials, orbital energies, and non-interacting kinetic energies of the fractional ions of Li, C and F. We use quantum Monte Carlo densities as input, which are then fitted, interpolated at non-integer electron numbers $N$, and inverted to produce accurate KS potentials $v_s^N(r)$. We study the dependence of the KS potential on $N$, and in particular we numerically reproduce the theoretically predicted spatially constant discontinuity of $v_s^N(r)$ as $N$ passes through an integer. We further show that, for all the cases considered, the inner orbital energies and the non-interacting kinetic energy are nearly piecewise linear functions of $N$. This leads us to propose a simple approximation of the KS potential $v_s^N(r)$ at any fractional electron number $N$ which uses only quantities of the systems with the adjacent integer electron numbers.

References in corpus (12)

• Localization and delocalization errors in density functional theory and implications for band-gap prediction
• The discontinuous nature of the exchange-correlation functional -- critical for strongly correlated systems
• Full optimization of Jastrow-Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules
• Undoing static correlation: Long-range charge transfer in time-dependent density functional theory
• Partition Density Functional Theory
• Piecewise Linearity of Approximate Density Functionals Revisited: Implications for Frontier Orbital Energies
• Study of the discontinuity of the exchange-correlation potential in an exactly soluble case
• The flexible nature of exchange, correlation and Hartree physics: resolving "delocalization" errors in a 'correlation free' density functional
• Zero-variance zero-bias quantum Monte Carlo estimators of the spherically and system-averaged pair density
• Optimized Unrestricted Kohn-Sham Potentials from Ab Initio Spin Densities
• Degeneracy and size consistency in electronic density functional theory
• Frozen density embedding with non-integer subsystems' particle numbers

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