Generalized average local ionization energy and its representations in terms of Dyson and energy orbitals.

Ryabinkin and Staroverov [J. Chem. Phys.

Origin of the step structure of molecular exchange-correlation potentials.

The exact exchange-correlation potential of a stretched heteronuclear diatomic molecule exhibits a localized upshift in the region around the more electronegative atom; by this device the Kohn-Sham scheme ensures that the molecule dissociates into neutral atoms. Baerends and co-workers showed earlier that the upshift originates in the response part of the exchange-correlation potential. We describe a reliable numerical method for constructing the response potential of a given many-electron system and report accurate plots of this quantity.

Reduction of Electronic Wave Functions to Kohn-Sham Effective Potentials.

A method for calculating the Kohn-Sham exchange-correlation potential v(XC)(r) from a given electronic wave function is devised and implemented. It requires on input one- and two-electron reduced density matrices and involves construction of the generalized Fock matrix. The method is free from numerical limitations and basis-set artifacts of conventional schemes for constructing v(XC)(r) in which the potential is recovered from a given electron density, and is simpler than various many-body techniques.

Hierarchy of model Kohn-Sham potentials for orbital-dependent functionals: a practical alternative to the optimized effective potential method.

We describe a method for constructing a hierarchy of model potentials approximating the functional derivative of a given orbital-dependent exchange-correlation functional with respect to electron density. Each model is derived by assuming a particular relationship between the self-consistent solutions of Kohn-Sham (KS) and generalized Kohn-Sham (GKS) equations for the same functional. In the KS scheme, the functional is differentiated with respect to density, in the GKS scheme--with respect to orbitals.

Apparent violation of the sum rule for exchange-correlation charges by generalized gradient approximations.

The exchange-correlation potential of Kohn-Sham density-functional theory, vXC(r), can be thought of as an electrostatic potential produced by the static charge distribution qXC(r) = -(1∕4π)∇(2)vXC(r). The total exchange-correlation charge, QXC = ∫qXC(r) dr, determines the rate of the asymptotic decay of vXC(r). If QXC ≠ 0, the potential falls off as QXC∕r; if QXC = 0, the decay is faster than coulombic.

Efficient construction of exchange and correlation potentials by inverting the Kohn-Sham equations.

Given a set of canonical Kohn-Sham orbitals, orbital energies, and an external potential for a many-electron system, one can invert the Kohn-Sham equations in a single step to obtain the corresponding exchange-correlation potential, vXC(r). For orbitals and orbital energies that are solutions of the Kohn-Sham equations with a multiplicative vXC(r) this procedure recovers vXC(r) (in the basis set limit), but for eigenfunctions of a non-multiplicative one-electron operator it produces an orbital-averaged potential. In particular, substitution of Hartree-Fock orbitals and eigenvalues into the Kohn-Sham inversion formula is a fast way to compute the Slater potential.