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Meta-generalized gradient approximation: Explanation of a realistic nonempirical density functional

2004; American Institute of Physics; Volume: 120; Issue: 15 Linguagem: Inglês

10.1063/1.1665298

1520-9032

John P. Perdew, Jianmin Tao, Viktor N. Staroverov, Gustavo E. Scuseria,

nanoparticles nucleation surface interactions

Tao, Perdew, Staroverov, and Scuseria (TPSS) have constructed a nonempirical meta-generalized gradient approximation (meta-GGA) [Phys. Rev. Lett. 91, 146401 (2003)] for the exchange-correlation energy, imposing exact constraints relevant to the paradigm densities of condensed matter physics and quantum chemistry. Results of their extensive tests on molecules, solids, and solid surfaces are encouraging, suggesting that this density functional achieves uniform accuracy for diverse properties and systems. In the present work, this functional is explained and details of its construction are presented. In particular, the functional is constructed to yield accurate energies under uniform coordinate scaling to the low-density or strong-interaction limit. Its nonlocality is displayed by plotting the factor F(xc) that gives the enhancement relative to the local density approximation for exchange. We also discuss an apparently harmless order-of-limits problem in the meta-GGA. The performance of this functional is investigated for exchange and correlation energies and shell-removal energies of atoms and ions. Non-self-consistent molecular atomization energies and bond lengths of the TPSS meta-GGA, calculated with GGA orbitals and densities, agree well with those calculated self-consistently. We suggest that satisfaction of additional exact constraints on higher rungs of a ladder of density functional approximations can lead to further progress.