Derivation of Quantal HyperNetted Chain Equation from the KohnSham Theory
Abstract
A quantal hypernetted chain (HNC) equation for a quantum fluid, which was derived previously by extending Percus' functional expansion method to quantum systems, is shown to be obtained from the KohnSham scheme, which is a method of dealing with an inhomogeneous electron gas in the ground state. This quantal HNC approximation also provides an integral equation for the density distribution n(rU) induced by imposition of an arbitrary external potential U(r), which is valid in the case of almost constant density. By following the KohnSham scheme, the groundstate energy of an inhomogeneous electron (or neutral) fluid is represented, in terms of the quantal direct correlation function, in the nonlocal form whose gradient expansion involves all terms of type nabla^{2km}n(r)\cdotnabla^{m} n(r); this expression results in a new integral equation for n(rU) , which is applicable to the case of not necessarily almost constant density. In addition, it is shown that any integral equation for n(rU) in an inhomogeneous system can determine, also, the densitydensity response function χ_{Q} for the homogeneous system in a selfconsistent manner; this χ_{Q} is to be used again in the integral equation for n(rU) , which is described in terms of χ_{Q}. It should be emphasized that these two integral equations for n(rU) are applicable to both the charged and neutral fluids at zero or nonzero temperature.
 Publication:

Progress of Theoretical Physics
 Pub Date:
 January 1978
 DOI:
 10.1143/PTP.59.76
 Bibcode:
 1978PThPh..59...76C