#### Degree

Master of Science

#### Program

Chemistry

#### Supervisor

Prof. Viktor N. Staroverov

#### Abstract

Density-functional theory (DFT) is the most widely used method of modern computational chemistry. All practical implementations of DFT rely on approximations to the unknown exchange-correlation functional. These approximations may be devised in terms of energy functionals or effective potentials. In this thesis, several approximations of the latter type are presented.

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). We show that 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 an orbital-specific 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 obtain, for the first time, 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.

Motivated by the absence of an efficient practical method for computing the exact- exchange optimized effective potential (OEP) we devised the Kohn–Sham exchange-correlation potential corresponding to a Hartree–Fock electron density. This potential is almost indistinguishable from the OEP and, when used as an approximation to the OEP, is vastly better than all existing models. Using our method one can obtain unambiguous, nearly exact OEPs for any finite one-electron basis set at the same low cost as the Krieger–Li–Iafrate and Becke–Johnson potentials. For all practical purposes, this solves the long-standing problem of black-box construction of OEPs in exact-exchange calculations.

#### Recommended Citation

Kananenka, Alexei, "Approximation of Exchange-Correlation Potentials for Orbital-Dependent Functionals" (2013). *Electronic Thesis and Dissertation Repository*. 1610.

https://ir.lib.uwo.ca/etd/1610