Effect of ensemble generalization on the highest-occupied Kohn-Sham eigenvalue

Abstract

There are several approximations to the exchange-correlation functional in density-functional theory that accurately predict total energy-related properties of many-electron systems, such as binding energies, bond lengths, and crystal structures. Other approximations are designed to describe potential-related processes, such as charge transfer and photoemission. However, the development of a functional which can serve the two purposes simultaneously is a long-standing challenge. Trying to address it, we employ in the current work the ensemble generalization procedure proposed in Phys. Rev. Lett. 110, 126403 (2013). Focusing on the prediction of the ionization potential via the highest occupied Kohn-Sham eigenvalue, we examine a variety of exchange-correlation approximations: the local spin-density approximation, semi-local generalized gradient approximations, and global and local hybrid functionals. Results for a test set of 26 diatomic molecules and single atoms are presented. We find that the aforementioned ensemble generalization systematically improves the prediction of the ionization potential, for various systems and exchange-correlation functionals, without compromising the accuracy of total energy-related properties. We specifically examine hybrid functionals. These depend on a parameter controlling the ratio of semi-local to non-local functional components. The ionization potential obtained with ensemble-generalized functionals is found to depend only weakly on the parameter value, contrary to common experience with non-generalized hybrids, thus eliminating one aspect of the so-called 'parameter dilemma' of hybrid functionals.

The Importance of Being Inconsistent

“…But HF-DFT sidesteps the issue, by using a better density without studying the potential. An ensemble generalization is one of many other approaches to this problem [KSKK15].…”

Enforcing the linear behavior of the total energy with hybrid functionals: Implications for charge transfer, interaction energies, and the random-phase approximation

“…They either aim to correct for those terms in the total energy that are nonlinear in the density (i.e., the Hartree and XC energy) [62,65], or introduce an ensemble generalization of the Kohn-Sham reference system [63,[66][67][68][69], or add a penalty functional to the KS Hamiltonian [64,[70][71][72][73], or use the DFT+U approach [74]. These approaches do not change the total energy (and for applications more importantly the total energy differences) at integer charges and simultaneously restore the straight line property.…”

Approximations to the exact exchange potential: KLI versus semilocal

“…The KLI approximation to OEP, which has also been used for functionals other than EXX (e.g., self-interaction corrected [18][19][20][21] or MGGA [22][23][24] functionals) is an interesting alternative to the OEP since it avoids the numerical difficulties of EXX-OEP (very recent works are Refs. [25][26][27][28][29][30][31][32][33] in the case of EXX and Refs. 23 and 24 for MGGAs).…”