We report a global-hybrid approximation, MN15, to the exchange–correlation functional of Kohn–Sham theory with broadly accurate performance for both multi-reference and single-reference systems.

Kohn-Sham density functional theory is widely used for applications of electronic structure theory in chemistry, materials science, and condensed-matter physics, but the accuracy depends on the quality of the exchange-correlation functional. Here, we present a new local exchange-correlation functional called MN15-L that predicts accurate results for a broad range of molecular and solid-state properties including main-group bond energies, transition metal bond energies, reaction barrier heights, noncovalent interactions, atomic excitation energies, ionization potentials, electron affinities, total atomic energies, hydrocarbon thermochemistry, and lattice constants of solids. The MN15-L functional has the same mathematical form as a previous meta-nonseparable gradient approximation exchange-correlation functional, MN12-L, but it is improved because we optimized it against a larger database, designated 2015A, and included smoothness restraints; the optimization has a much better representation of transition metals. The mean unsigned error on 422 chemical energies is 2.32 kcal/mol, which is the best among all tested functionals, with or without nonlocal exchange. The MN15-L functional also provides good results for test sets that are outside the training set. A key issue is that the functional is local (no nonlocal exchange or nonlocal correlation), which makes it relatively economical for treating large and complex systems and solids. Another key advantage is that medium-range correlation energy is built in so that one does not need to add damped dispersion by molecular mechanics in order to predict accurate noncovalent binding energies. We believe that the MN15-L functional should be useful for a wide variety of applications in chemistry, physics, materials science, and molecular biology.

This article presents a perspective on Kohn-Sham density functional theory (KS-DFT) for electronic structure calculations in chemical physics. This theory is in widespread use for applications to both molecules and solids. We pay special attention to several aspects where there are both concerns and progress toward solutions. These include: 1. The treatment of open-shell and inherently multiconfigurational systems (the latter are often called multireference systems and are variously classified as having strong correlation, near-degeneracy correlation, or high static correlation; KS-DFT must treat these systems with broken-symmetry determinants). 2. The treatment of noncovalent interactions. 3. The choice between developing new functionals by parametrization, by theoretical constraints, or by a combination. 4. The ingredients of the exchange-correlation functionals used by KS-DFT, including spin densities, the magnitudes of their gradients, spin-specific kinetic energy densities, nonlocal exchange (Hartree-Fock exchange), nonlocal correlation, and subshell-dependent corrections (DFT+U). 5. The quest for a universal functional, where we summarize some of the success of the latest Minnesota functionals, namely MN15-L and MN15, which were obtained by optimization against diverse databases. 6. Time-dependent density functional theory, which is an extension of DFT to treat time-dependent problems and excited states. The review is a snapshot of a rapidly moving field, and-like Marcel Duchamp-we hope to convey progress in a stimulating way.