Derivative discontinuity with localized Hartree-Fock potential

Abstract

The localized Hartree-Fock potential has proven to be a computationally efficient alternative to the optimized effective potential, preserving the numerical accuracy of the latter and respecting the exact properties of being self-interaction free and having the correct $-1/r$ asymptotics. In this paper we extend the localized Hartree-Fock potential to fractional particle numbers and observe that it yields derivative discontinuities in the energy as required by the exact theory. The discontinuities are numerically close to those of the computationally more demanding Hartree-Fock method. Our potential enjoys a "direct-energy" property, whereby the energy of the system is given by the sum of the single-particle eigenvalues multiplied by the corresponding occupation numbers. The discontinuities $c_{\uparrow }$ and $c_{\downarrow }$ of the spin-components of the potential at integer particle numbers $N_{\uparrow }$ and $N_{\downarrow }$ satisfy the condition $c_{\uparrow }{N}_{\uparrow }+c_{\downarrow }{N}_{\downarrow }=0$. Thus, joining the family of effective potentials which support a derivative discontinuity, but being considerably easier to implement, the localized Hartree-Fock potential becomes a powerful tool in the broad area of applications in which the fundamental gap is an issue.

11 pages, 6 figures

References in corpus (4)

• Piecewise Linearity of Approximate Density Functionals Revisited: Implications for Frontier Orbital Energies
• Accurate and efficient approximation to the optimized effective potential for exchange
• Ground-State Energy as a Simple Sum of Orbital Energies in Kohn-Sham Theory: A Shift in Perspective through a Shift in Potential
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Cited by in corpus (4)

• Exact "exact exchange" potential of two- and one-dimensional electron gases beyond the asymptotic limit
• On Augmented Kohn-Sham Potential for Energy as a Simple Sum of Orbital Energies
• Quasi-low-dimensional electron gas with one populated band as a testing ground for time-dependent density-functional theory
• Exchange kernel $f_x^h(q,\omega )$ of electron liquid from the variational principle of McLachlan