Extremal properties of the Harris-Foulkes functional and an improved screening calculation for the electron gas

In this paper we demonstrate that the extremal properties of the Harris-Foulkes energy functional in combination with the exact form for the exchange and correlation energy functional are qualitatively the same as those using the local-density approximation for the latter functional. Foremost among these properties is that the Harris-Foulkes functional does not have a local maximum at the exact ground-state charge density. The extremal properties are shown to depend on whether the static local-field-correction function G(q;ω=0) is greater or less than unity. Our results are based on an improved and very accurate expression for G(q;ω=0), which we present in this paper. This expression satisfies the exact asymptotic results for the short- and long-wavelength limits as determined in terms of some exact frequency moments of the density-density correlation function. One of the major ingredients of this G(q;0) is the quantum-Monte-Carlo results of Ceperley and Alder for the correlation energy in the paramagnetic state of the uniform electron gas. Although the present G(q;0) has some similarities with the Utsumi-Ichimaru G(q), it differs from the latter in a fundamental way. For comparison, the consequences of using the latter G(q) in the context of the present work are indicated. Further, we discuss a number of issues of a general nature pertinent to the practical application of the Harris-Foulkes functional. As G(q;0) involves momentum moments of the momentum distribution function of the interacting electron gas, we also present a model for this function, along with some very accurate interpolation expressions for a number of the coefficients both in this and in G(q;0). Consequences of the use of various local-field-correction functions on the static screening properties of interacting electron gas in the paramagnetic phase are also discussed.