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Subsystem functionals and the missing ingredient of confinement physics in density functionals

Hao, Feng H.; Armiento, Rickard; Mattsson, Ann E.

The subsystem functional scheme is a promising approach recently proposed for constructing exchange-correlation density functionals. In this scheme, the physics in each part of real materials is described by mapping to a characteristic model system. The "confinement physics," an essential physical ingredient that has been left out in present functionals, is studied by employing the harmonic-oscillator (HO) gas model. By performing the potential→density and the density→exchange energy per particle mappings based on two model systems characterizing the physics in the interior (uniform electron-gas model) and surface regions (Airy gas model) of materials for the HO gases, we show that the confinement physics emerges when only the lowest subband of the HO gas is occupied by electrons. We examine the approximations of the exchange energy by several state-of-the-art functionals for the HO gas, and none of them produces adequate accuracy in the confinement dominated cases. A generic functional that incorporates the description of the confinement physics is needed. © 2010 The American Physical Society.