## Samuel B. Trickey

### University of Florida, United States

Department of Physics

**Monday, 29 ^{th} August 2022,16:00 s.t.**

The talk will be given in a hybrid mode.

You can either attend in physical presence:

TU Wien, Institute of Materials Chemistry,

Getreidemarkt 9, 1060 Vienna

Lehartrakt BC, Seminar Lehar01 (1^{st} floor)

Or you can join via Zoom:

https://tuwien.zoom.us/j/94187837328?pwd=cGN5Skl4Z3pJbGR1RXYrbzJpampadz09

#### Hardness, Band Gaps, and Derivative Discontinuities from a Simple Exchange-Correlation Functional

Density functional exchange-correlation approximations (“DFAs”) with complicated orbital dependence are much-used in the context of molecular systems. However, the computational cost of such DFAs is prohibitive for large-scale (high-throughput) studies of large molecules such as molecular magnets and spin cross-over complexes. The issue is that both the molecules and their condensed phases must be treated on an equal footing for predictive studies of molecular materials. Improvement of computationally simple DFAs therefore is motivated.

A widely-held view is that although Kohn-Sham calculations with a simple, affordable DFA such as a generalized gradient approximation (“GGA”) can deliver reasonable thermochemical property values, the same cannot be said of the interpretability of the KS eigenvalue spectra. The title “More realistic band gaps from meta-generalized gradient approximations: Only in a generalized Kohn-Sham scheme” [Phys. Rev. B 93, 205205 (2016)] is illustrative. In particular, for such DFAs, the DFT ionization potential theorem usually is violated, the HOMO-LUMO gap (or KS band gap) is a significant underestimate of the fundamental gap (*E _{gap} = I–A* with

*I*,

*A*the ionization potential and electron affinity), and the exchange potential far from a finite system or surface does not decay correctly.

One way to address the problem is to address the derivative discontinuity. The electronic energy as a function of the number of electrons for the positive ion (N

_{0}-1), neutral (N

_{0}), and negative ion (N

_{0}+1) is given by a pair of lines connecting those integer values. The resulting discontinuity in the exchange-correlation potential has important consequences for the calculation of molecular hardnesses and solid band gaps. It is omitted in most GGAs. Analysis of the exact theory allows one to infer the effects of current approximations on the HOMO and LUMO eigenvalues. Enforcement of proper asymptotic behavior of the exchange potential in construction of a better GGA leads to the seemingly peculiar result of going to a positive constant at arbitrarily large distance [J. Chem. Theory Comput. 15, 303 (2019)]. However, that constant enables approximate determination of the derivative discontinuity shift of the frontier orbital eigenvalues. Thereby we can determine

*I*and

*A*through a single ground-state calculation of the reference system, including cases for which A < 0 [J. Phys. Chem. A 124, 1334 (2020)]. Hence we have calculation of reasonably accurate hardnesses and band-gaps from a GGA that also gives good quality thermochemical results. I will present results that show the approach is generally as accurate as the results obtained from hybrid DFAs.

It is a pleasure to acknowledge and thank the collaborators in this work: Javier Carmona-Espíndola, Anaid Flores, José L. Gázquez, and Alberto Vela. Work supported by U.S. Dept. of Energy EFRC grant DE-SC0019330.