Reply to ‘‘Comment on ‘Modified weighted-density-functional theory of nonuniform classical liquids’ ’’

Abstract

Using an identity due to Percus [J. K. Percus, in The Equilibrium Theory of Classical Fluids, edited by H. L. Frisch and J. L. Lebowitz (Benjamin, New York, 1964)] implying a connection between the theories of nonuniform and uniform liquids, Kim and Jones [Soon-Chul Kim and Gerald L. Jones, preceding paper, Phys. Rev. A 41, 2222 (1990)] demonstrate that the modified weighteddensity approximation for nonuniform liquids corresponds to the hypernetted-chain (HNC) approximation for uniform liquids. We point out that the Ramakrishnan-Yussouff density-functional theoryin its simplest formulationalso implies the HNC approximation, a feature of the theory previously observed

Self-consistent theory of freezing of the classical one-component plasma

“…But if we now use co 3) as given in Ref. [13], and take into account the fact that the average densities of the solid and the liquid are constrained to be equal in isochoric melting, we see that FcV for the MWDA must vanish. A similar conclusion can be drawn for all higher contributions to F« WDA , so that for an isochoric transition the MWDA is operationally equivalent to the original RY theory, truncated at second order.…”

“…Here, we present results obtained using two different approximations, namely, ^3 ) (r,r')< •MfOAG^Aflr-r'l), (13) which has been introduced by Iyetomi and Ichimaru [17], and 4 3) (r,r')=f(rMr'M|r-r'|), (14) introduced by Barrat, Hansen, and Pastore [20]. In (13), h(r)=g(r) -1; in (14), the more general function t(r) can be unambiguously determined by using the exact relation (10) between cd 2) and cd 3) . In both cases, we include contributions from 100 shells in the reciprocal-lattice summation of Eq.…”

“…1). With approximation (13), on the other hand, convergence of the double summation in Eq. (l 1) is somewhat slower, though ultimately guaranteed by the Gaussian factors.…”

“…(l 1) is somewhat slower, though ultimately guaranteed by the Gaussian factors. It is known [8,17] that for larger values of its arguments, approximation (13) itself is quite inaccurate, and for this reason we follow Barrat [8] by including only the (1,1,1) and (1,1,2) sets in order to provide a comparison. Figure 1 illustrates the dependence of F, F id , and F ex on the localization parameter a with approximations (13) and (14) used for ck 3) .…”

“…The self-consistency requirement in the determination of p also guarantees that in general there are contributions from all higher orders in the functional expansion included in the MWDA functional. Indeed, it can be shown for the MWDA that, provided Ai^O, the third-order contribution to the MWDA functional is nonzero and extensive [13]. However, this result no longer holds for an isochoric transition.…”