The ability of Kohn−Sham density functional theory (KS-DFT) to accurately predict various types of electronic excitation energies with (necessarily approximate) exchangecorrelation functionals faces several challenges. Chief among these is that valence excitations are usually inherently multiconfigurational and therefore best treated by functionals with local exchange, whereas Rydberg and charge-transfer excitations are often better treated with nonlocal exchange. The question arises regarding whether one can optimize a functional such that all three kinds of excitations (valence, Rydberg, and charge transfer, including long-range charge transfer) are treated in a balanced and accurate way. The goal of the present work is to try to answer that question and then to optimize a functional with the best possible balanced behavior. Of the variety of functional types available, we choose to use a range-separated hybrid meta functional for the following reasons: (i) Range separation allows the percentage of Hartree−Fock (HF) exchange to change with interelectronic separation, and therefore, one can have 100% HF exchange at large interelectronic separations, which gives good performance for long-range charge-transfer excitations, while the range separation allows one to simultaneously have smaller values of HF exchange at small and intermediate interelectronic separations, giving good performance for valence and Rydberg excitations. (ii) Meta functionals allow one to obtain better accuracy with high HF exchange than is possible with functionals whose local part depends only on spin densities and their gradients. This work starts with the range-separated hybrid meta functional M11 and reoptimizes it (with strong smoothness restraints) against electronic excitation energies and ground-state properties to obtain a new functional called revM11 that gives good performance for all three types of electronic excitations and at the same time gives very good predictions across the board for ground-state properties.

Screened-exchange hybrid density functionals are especially recommended for solid-state systems because they combine the advantages of hybrid functionals with the correct physics and lower computational cost associated with the attenuation of Hartree–Fock exchange at long range. We present a screened-exchange hybrid functional, M06-SX, that combines the functional form of the local revM06-L functional with a percentage of short-range nonlocal Hartree–Fock exchange. The M06-SX functional gives good results not only for a large set of training data but also for several databases quite different from the training data. The mean unsigned error (MUE) of the M06-SX functional is 2.85 kcal/mol for 418 atomic and molecular energies (AME418) in Minnesota Database 2019, which is better than all five other screened-exchange hybrid functionals tested in this work. The M06-SX functional also gives especially good results for semiconductor band gaps, molecular dissociation energies, noncovalent interactions, barrier heights, and electronic excitation energies excluding long-range charge transfer excitations. For the LC18 lattice constants database, the M06-SX functional gives an MUE of only 0.034 Å. Therefore, the M06-SX functional is well suited for studying molecular chemistry as well as solid-state physics.

The way to improve Kohn–Sham density functional theory is to improve the exchange–correlation functionals, and functionals have been successively improved by adding new ingredients, especially local spin density gradients, nonlocal Hartree–Fock exchange, and local meta terms based on kinetic energy density. Here, we present a new kind of functional obtained by adding rung-3.5 terms to a functional including local gradients, local meta terms, and range-separated Hartree–Fock exchange. A rung-3.5 term has short-range nonlocality designed to account for nondynamic correlation; we add two kinds of rung-3.5 terms, one kind modeled on position-dependent Hartree–Fock exchange and another modeled on the spin density at a point interacting with the opposite-spin exchange hole at the same point. Optimization of the functional yields broad accuracy for both ground states and excited states with especially significant improvement for systems with strong correlation.