Quasi-dimensional models applied to kinetic and exchange energy density functionals

Abstract We investigate the behavior of three-dimensional 3D exchange energy functional density-functional theory in anisotropic systems with two-dimensional 2D character and 1D character. The local density approximation (LDA), generalized gradient (GGA), meta-GGA behave as functions quantum well width. use infinite-barrier model (IBM) for well. In first section, we describe problem functional, second section introduce quasi-2D IBM system, third quasi-1D system. Using that an exact-exchange provides correct approach to true limit, want show limit can be considered a constraint on approximate functionals. For case also propose new obtained methods completely similar those limit.