The flexible nature of exchange, correlation and Hartree physics: resolving "delocalization" errors in a 'correlation free' density functional

Abstract

By exploiting freedoms in the definitions of 'correlation', 'exchange' and 'Hartree' physics in ensemble systems we better generalise the notion of 'exact exchange' (EXX) to systems with fractional occupations functions of the frontier orbitals, arising in the dissociation limit of some molecules. We introduce the Linear EXX ("LEXX") theory whose pair distribution and energy are explicitly \emph{piecewise linear} in the occupations $f_i^{\sigma }$. {\hi}We provide explicit expressions for these functions for frontier $s$ and $p$ shells. Used in an optimised effective potential (OEP) approach it yields energies bounded by the piecewise linear 'ensemble EXX' (EEXX) energy and standard fractional optimised EXX energy: $E^{EEXX}\le E^{LEXX}\le E^{EXX}$. Analysis of the LEXX explains the success of standard OEP methods for diatoms at large spacing, and why they can fail when both spins are allowed to be non-integer so that "ghost" Hartree interactions appear between \emph{opposite} spin electrons in the usual formula. The energy $E^{LEXX}$ contains a cancellation term for the spin ghost case. It is evaluated for H, Li and Na fractional ions with clear derivative discontinuities for all cases. The $p$-shell form reproduces accurate correlation-free energies of B-F and Al-Cl. We further test LEXX plus correlation energy calculations on fractional ions of C and F and again shows both derivative discontinuities and good agreement with exact results.

References in corpus (7)

• O(N) methods in electronic structure calculations
• The discontinuous nature of the exchange-correlation functional -- critical for strongly correlated systems
• Exchange and Correlation in Open Systems of Fluctuating Electron Number
• Correlation potentials for molecular bond dissociation within the self-consistent random phase approximation
• Linear density response function within the time-dependent exact-exchange approximation
• Beyond the RPA on the cheap: improved correlation energies with the efficient "Radial Exchange Hole" kernel
• Correlation energies beyond the random-phase approximation: ISTLS applied to spherical atoms and ions

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