LOCAL ENERGY AND CHEMICAL-POTENTIAL EQUATIONS AND THE EXCHANGE-CORRELATION POTENTIAL

Local energy and chemical potential equations are considered in some d etail in relation to low-order density matrices. Some asymptotic prope rties can be extracted in exact form. The spatial derivative of the ch emical potential equation referred to above yields the external force, defined as the (negative of the) gradient of the potential energy of the nuclear framework. This quantity, by utilizing the differential vi rial theorem, can be expressed as a sum of three terms: (i) a Laplacia n contribution known explicitly in terms of the ground-state electron density; (ii) a kinetic part derivable from the ''near-diagonal'' beha viour of the first-order density matrix; and (iii) a term from electro n-electron interactions, that involves the electronic pair correlation function. Following the work of Holas and March, this allows the exch ange-correlation potential of density functional theory to be expresse d in terms of low-order density matrices. Finally, scaling of electron -electron interactions is briefly considered, as well as the adiabatic connection formula in density functional theory. Such scaling argumen ts lead to a kinetic correction to the Harbola-Sahni form of the excha nge-only potential.