The density functional for the exchange-correlation energy of a many-electron system is a well-defined object that must be approximated in practice. An optimal approximation should be computationally tractable and yet accurate for atoms and molecules on the one hand and for solids and surfaces on the other, and thus also for molecules on surfaces. It should also be constructed without empiricism, since such a construction is a strong test of our understanding of the exact functional. We can now say that we understand much of the semi-locality of the exact functional, which manifests in the equilibrium properties of sp-bonded systems, but not its nonlocality, which manifests when electrons are shared over stretched bonds. The most successful nonlocal functionals are global, local, or range-separated hybrids, with one or more empirical parameters. Moreover, those that have only one empirical parameter always violate exact constraints. We will discuss what may need to be known to construct accurate, constraint-satisfying hybrid functionals without empiricism.

What do we know about density functional construction, and what don't we know?

243rd National Meeting (2012)

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