Global hybrid exchange energy functional with correct asymptotic behavior of the corresponding potential

A Critical Evaluation of the Hybrid KS DFT Functionals Based on the KS Exchange-Correlation Potentials

We have developed a critical methodology for the evaluation of the quality of hybrid exchange-correlation (XC) density functional approximations (DFAs) based on very fundamental quantities, i.e., Kohn-Sham (KS) XC potentials, self-consistent electron densities, first ionization potentials (IPs), and total energies. Since the XC potentials, the primary objects in the current study, are not directly accessible for the hybrids, we calculate them by inverting the KS electron densities. Utilizing this methodology, we tested 155 hybrid DFAs available in the LIBXC library using FCI and CCSD(T) methods as a reference. We have found that a group of functionals produces very decent XC potentials, mainly those with a large mixture of Hartree-Fock exchange. Moreover, the value of IP strongly depends on the XC potential quality. On the other hand, we show that the XC energy is dominated by functional-driven error, which in some cases leads to substantial errors in electronic densities. The study shows new directions for constructing more accurate XC functionals within the KS-DFT framework.

Recommendation of Orbitals for G0W0 Calculations on Molecules and Crystals

The many-body GW approximation, especially the G₀W₀ method, has been widely used for condensed matter and molecules to calculate quasiparticle energies for ionization, electron attachment, and band gaps. Because G₀W₀ calculations are well-known to have a strong dependence on the orbitals, the goal of the present work is to provide guidance on the choice of density functional used to generate orbitals and to recommend a choice that gives the most broadly accurate results. We have systematically investigated the dependence of G₀W₀ calculations on the orbitals for 100 molecules and 8 crystals by considering orbitals obtained with a diverse set of Kohn-Sham (KS) and generalized KS (GKS) functionals (63 functionals plus Hartree-Fock). The percentage of Hartree-Fock exchange employed in density functionals has been found to have strong influence on the predicted molecular ionization energy and crystal fundamental band gaps (with optimum values between 40 and 56%), but to have less effect on predicting molecular electron affinities. The low cost of the Gaussian implementation, even with hybrid functionals in periodic calculations, the better performance of global hybrids as compared to range-separated hybrids of either than screened exchange or long-range-corrected type, and the relatively low cost of global-hybrid-functional periodic calculations using Gaussians means that one can employ global-hybrid functionals at a very reasonable cost and obtain more accurate band gaps of semiconductors than are obtained by the methods currently widely employed, namely local gradient approximations. We single out three global-hybrid functionals that give especially good results for both molecules (100 in the test set) and crystals (8 in the test set, for all of which our benchmark data are the proper band gap rather than an optical band gap uncorrected for exciton effects).

Density functionals with asymptotic-potential corrections are required for the simulation of spectroscopic properties of materials

Five effects of correction of the asymptotic potential error in density functionals are identified that significantly improve calculated properties of molecular excited states involving charge-transfer character. Newly developed materials-science computational methods are used to demonstrate how these effects manifest in materials spectroscopy. Connection is made considering chlorophyll-a as a paradigm for molecular spectroscopy, 22 iconic materials as paradigms for 3D materials spectroscopy, and the VN - defect in hexagonal boron nitride as an example of the spectroscopy of defects in 2D materials pertaining to nanophotonics. Defects can equally be thought of as being "molecular" and "materials" in nature and hence bridge the relms of molecular and materials spectroscopies. It is concluded that the density functional HSE06, currently considered as the standard for accurate calculations of materials spectroscopy, should be replaced, in most instances, by the computationally similar but asymptotically corrected CAM-B3LYP functional, with some specific functionals for materials-use only providing further improvements.