DFT-theory (Pedagogical lectures)

31 video lectures on Density Functional Theory.

The physical meaning of orbitals and orbital energies in DFT and TDDFT

Evert Jan Baerends

Theoretical Chemistry,Vrije Universiteit, Amsterdam, The Netherlands

Video Recording

Abstract

We will first review many wrong statements in the literature on the nature and the (lack of) physical meaning of Kohn-Sham orbitals.
Next the nature of the occupied KS orbitals, and their advantages over Hartree-Fock orbitals are highlighted.
Then we address orbital energies. Exact KS orbitals have many virtues:

1. the orbital energies of the occupied orbitals are close to ionization potentials (an order of magnitude better agreement than the Koopmans’ type agreement in Hartee-Fock) [1];
2. virtual orbital energies are realistic: occupied-unoccupied orbital energy differencies are very close to excitation energies. There is no “gap problem” in DFT! [2,3]
3. the KS virtual orbitals are typically bound states and have good (valence type) shapes (not unphysically diffuse like the Hartree-Fock virtuals); excitations can be described in most cases as simple single orbital-to-orbital transitions [2,3].

Unfortunately, orbital energies in the common LDA and GGA calculations are very wrong: they are typically 5 eV (more than 100 kcal/mol) higher than the exact Kohn-Sham orbital energies, an error that would be completely unacceptable in total energies. We will first analyze where this error comes from - it is not due to wrong asymptotic behavior of LDA/GGA potentials, or to a “self-interaction error” but it is caused by erroneous density dependence of the standard Exc[ρ] functionals, hence a wrong derivative (= potential). We will demonstrate that approximate potentials can be formulated that have similar good properties for ionization and excitation energies as the exact KS potential [4].

Understanding time-dependent density-functional theory (TD-DFT)

Mark E. Casida

Professeur, chimie théorique, Laboratoire de Chimie Inorganique REdox (CIRE),
Département de Chimie Moléculare (DCM, UMR CNRS/UGA 5250), Institut de Chimie Moléculaire  de Grenoble(ICMG, FR-2607),
Université Grenoble Alpes, 301 rue de la Chimie, CS 40700, 38058 Grenoble
Cedex 9, FRANCE.

Video Recording

Abstract

Ordinary density-functional theory (DFT) is restricted to calculating the static electronic energy and density of the electronic ground state. Time-dependent (TD) DFT is a parallel formalism which
allows us to extend the power of DFT to treat time-dependent perturbations. Time-dependent response theory then allows us to calculate absorption spectra from TD-DFT and hence to treat excited states. This formalism is explained at the level of a Masters student, first by setting the stage with a reminder of simple wave function theory for excited states as well as some more advanced ab initio quantum chemistry ideas, and then by focusing on TD-DFT. Some illustrative examples are also presented ^1,2 . We also direct the interested reader to highly-cited review articles, including our own ^3,4 .