Positivity constraints and information-theoretical kinetic energy functionals

Recently several variants of a new orbital-free density functional for the total Ne-electron kinetic energy (KE) have been proposed. These are based on a systematically constructed (Ne − 1)-electron conditional probability function and Monte Carlo evaluation of the associated conditional expectation of the KE operator in the case of the homogeneous electron gas. Because the resulting functionals depend on n ln n (n = the electron number density), they have been interpreted as being the leading term in a Shannon information power expression for the non–von Weizsäcker part of the total KE. We show that these functionals violate known positivity constraints, are inconsistent with known results for the correlation energy of the homogeneous electron gas, and that the Shannon information power interpretation also violates known constraints. We consider both the full KE and Kohn-Sham cases. Possible corrections and extensions are considered, including an apparently new form for parametrization.