Density-functional errors in ionization potential with increasing system size

Abstract

This work investigates the effects of molecular size on the accuracy of density-functional ionization potentials for a set of 28 hydrocarbons, including series of alkanes, alkenes, and oligoacenes. As the system size increases, delocalization error introduces a systematic underestimation of the ionization potential, which is rationalized by considering the fractional-charge behavior of the electronic energies. The computation of the ionization potential with many density-functional approximations is not size-extensive due to excessive delocalization of the incipient positive charge. While inclusion of exact exchange reduces the observed errors, system-specific tuning of long-range corrected functionals does not generally improve accuracy. These results emphasize that good performance of a functional for small molecules is not necessarily transferable to larger systems.

The Importance of Being Inconsistent

“…As the length of a long-chain hydrocarbon grows, the ionization potential collapses to the KS HOMO level with standard approximations, due to the incorrect delocalization of the hole over the entire molecule [WVIJ15]. This effect should not be present in HF-DFT, but that has yet to be tested.…”

Challenges for semilocal density functionals with asymptotically nonvanishing potentials

“…It became clear that these omitted features play a decisive role, e.g., in the description of charge transfer [20,30,31] and ionization [8,17,18,32,33]. Attempts have been made to model such features directly into semilocal xc potentials [34][35][36][37][38][39][40][41][42][43][44][45], partially also with an additional (nonlocal) eigenvalue dependence, e.g., as done by Gritsenko et al (GLLB) [46] and Kuisma et al [47].…”

Orbital nodal surfaces: Topological challenges for density functionals

“…This success is based on the favorable ratio of accuracy to computational cost that DFT offers, especially with semilocal approximations for the exchange-correlation (xc) energy E xc [n(r)]. However, while the low computational cost of semilocal functionals has very much contributed to the success of DFT because it enables access to large systems of practical relevance, the functional derivatives of typical semilocal functionals, i.e., their corresponding xc potentials, miss important features of the exact xc potential, in particular discontinuities [3,4] and step structures [5][6][7][8][9] that are relevant, e.g., in charge-transfer situations [10][11][12] and ionization processes [5,[13][14][15][16]. Many attempts have been made to incorporate some of the missing features into semilocal DFT [17][18][19][20][21][22][23][24][25][26][27].…”