Density functional theory is straying from the path toward the exact functional

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Science  06 Jan 2017:
Vol. 355, Issue 6320, pp. 49-52
DOI: 10.1126/science.aah5975

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Whither the density in DFT calculations?

The continuing development of density functional theory (DFT) has greatly expanded the size and complexity of molecules amenable to computationally tractable simulation. The conventional metric of success for new functionals has been the accuracy of their calculated energies. Medvedev et al. examined how well these functionals calculate electron density across a series of neutral and cationic atoms (see the Perspective by Hammes-Schiffer). Although historically the accuracies of energy and density have improved in tandem, certain recent functionals have sacrificed fidelity to the true density.

Science, this issue p. 49; see also p. 28


The theorems at the core of density functional theory (DFT) state that the energy of a many-electron system in its ground state is fully defined by its electron density distribution. This connection is made via the exact functional for the energy, which minimizes at the exact density. For years, DFT development focused on energies, implicitly assuming that functionals producing better energies become better approximations of the exact functional. We examined the other side of the coin: the energy-minimizing electron densities for atomic species, as produced by 128 historical and modern DFT functionals. We found that these densities became closer to the exact ones, reflecting theoretical advances, until the early 2000s, when this trend was reversed by unconstrained functionals sacrificing physical rigor for the flexibility of empirical fitting.

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