#
APS March Meeting 2014

## Volume 59, Number 1

##
Monday–Friday, March 3–7, 2014;
Denver, Colorado

### Session G1: Recent Advances in Density Functional Theory III

11:15 AM–2:15 PM,
Tuesday, March 4, 2014

Room: 103/105

Sponsoring
Units:
DCP DCOMP

Chair: John P. Perdew, Temple University

Abstract ID: BAPS.2014.MAR.G1.5

### Abstract: G1.00005 : Hybrid Density Functionals Tuned towards Fulfillment of Fundamental DFT Conditions

12:27 PM–1:03 PM

Preview Abstract
Abstract

####
Author:

Matthias Scheffler

(Fritz-Haber-Institut der Max-Planck-Gesellschaft, Berlin-Dahlem, Germany)

Hybrid exchange-correlation functionals (XC), e.g. PBE0 and HSE, have
significantly improved the theoretical description of molecules and solids.
Their degree of exact-exchange admixture ($\alpha )$ is in principle a
functional of the electron density, but the functional form is not known. In
this talk, I will discuss \textit{fundamental conditions} of exact density-functional theory (DFT) that
enable us to find the optimal choice of $\alpha $ for ground-state
calculations. In particular, I will discuss the fact that the highest
occupied Kohn-Sham level of an $N$-electron system ($\varepsilon
_{\mathrm{HOMO}}(N))$ should be constant for fractional particle numbers
between $N$ and \textit{N-1 }[1,2] and equals the ionization potential (IP) [3, 4], as given
by the total-energy difference. In practice, we realize this in three
different ways. XC($\alpha )$ will be optimized (opt-XC) until it $(i)$ fulfills
the condition: $\varepsilon_{\mathrm{HOMO}}(N) = \varepsilon
_{\mathrm{HOMO}}$(\textit{N-1/2}) or the Kohn-Sham HOMO agrees with the ionization
potential computed in a more sophisticated approach $\varepsilon
_{\mathrm{HOMO}}(N) =$ IP such as \textit{(ii)} the
$G_{\mathrm{0}}W_{\mathrm{0}}$@opt-XC method [5,6] or \textit{(iii)} CCSD(T) or full CI
[6].
Using such an opt-XC is essential for describing electron transfer between
(organic) molecules, as exemplified by the TTF/TCNQ dimer [5]. It also yields
vertical ionization energies of the G2 test set of quantum chemistry with a
mean absolute percentage error of only $\approx $3{\%}. Furthermore, our
approach removes the starting-point uncertainty of \textit{GW} calculations [5] and
thus bears some resemblance to the consistent starting point scheme [7] and
quasiparticle self-consistent \textit{GW} [8]. While our opt-XC approach yields large
$\alpha $ values for small molecules in the gas phase [5], we find that
$\alpha $ needs to be 0.25 or less for organic molecules adsorbed on metals
[9].
\\[4pt]
[1] J. P. Perdew et al., PRL 1982.\\[0pt]
[2] P. Mori-Sanchez et al., JCP 2006.\\[0pt]
[3] M. Levy et al., PRA 1984.\\[0pt]
[4] T. Stein et al., PRL 2010.\\[0pt]
[5] V. Atalla et al., PRB 2013.\\[0pt]
[6] N. A. Richter, et al., PRL 2013.\\[0pt]
[7] T. K\"{o}rzd\"{o}rfer, N. Marom, PRB 2012.\\[0pt]
[8] M. van Schilfgaarde et al., PRL 2006.\\[0pt]
[9] O. T. Hofmann et al., NJP 2013.

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2014.MAR.G1.5