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

Abstract

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. In the same way, we efficiently construct orbital-averaged exchange and correlation potentials for hybrid and kinetic-energy-density-dependent functionals. We also show how the Kohn-Sham inversion approach can be used to compute functional derivatives of explicit density functionals and to approximate functional derivatives of orbital-dependent functionals.

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

“…The latter task can be simplified using the techniques developed by us recently. 72,92 The most important message of this work is that instead of tackling the complicated OEP integral equation one can obtain its solution almost exactly by constructing a model potential (DCEP). The DCEP works so well because the DCEP and OEP equations are formally identical to the first order of perturbation of the KS Hamiltonian.…”

“…Our approach synthesizes some old 36,69,70 and recent 71,72 ideas, and advances them significantly. Because the exact-exchange OEP is by far the best-studied and the most important effective potential, we focus our exposition on the exact-exchange functional as the prototype of all orbitaldependent approximations.…”

Improved method for generating exchange-correlation potentials from electronic wave functions

“…Figures 1 and 2 highlight a common feature of all RKS and mRKS potentials: they are smooth and have no spurious oscillations that plague optimized effective potential methods 11,[54][55][56][57] and KS inversion techniques that fit potentials to Gaussian-basis-set densities. 19,24,34,58,59 This is because Eqs. (11) and (19) contain only terms that are well-behaved in any reasonable basis set.…”

Perspective: Fifty years of density-functional theory in chemical physics

“…A simple reorganization of the HF equations is all that is required. [206][207][208] Thus, post-Hartree-Fock implementations of EXX-based functionals like B05, B13, or PSTS are conceivable at essentially no cost beyond HF itself (plus, perhaps, an additional HFS computation to correct for basisset artifacts 207,208 ). Post-Hartree-Fock DFT is not new.…”