Kinetic energy contribution to the exchange-correlation energy functional of the extended constrained-search theory

We present the kinetic energy contribution to the exchange-correlation energy functional of the extended constrained-search (ECS) theory by means of the generalized Bauer's relation. Due to the nature of the exchange-correlation energy functional being a function of the Bohr radius and e(2), three kinds of expressions for the kinetic energy contribution are obtained. These can be utilized as constraints in developing and/or evaluating the approximate form of the exchange-correlation energy functional of the ECS theory. Furthermore, by combining three expressions with the virial relation, we derive other useful relations that include not the kinetic energy contribution but only the exchange-correlation energy functional.