Hyper-netted chain: Difference between revisions

Revision as of 18:10, 26 June 2007

The hyper-netted chain (HNC) equation has a clear physical basis in the Kirkwood superposition approximation (Ref. 1). The hyper-netted chain approximation is obtained by omitting the elementary clusters, $E(r)$ , in the exact convolution equation for $g(r)$ . The hyper-netted chain approximation was developed almost simultaneously by various groups, namely: van Leeuwen, Groeneveld and de Boer, 1959 (Ref. 2). Morita and Hiroike, 1960 (Ref.s 3-8), Rushbrooke, 1960 (Ref. 9), Verlet, 1960 (Ref. 10), and Meeron, 1960 (Ref. 11). The HNC omits the bridge function, i.e. $B(r)=0$ , thus the cavity correlation function becomes

\ln y(r)=h(r)-c(r)\equiv \gamma (r)

The hyper-netted chain closure relationcan be written as

f\left[\gamma (r)\right]=e^{[-\beta \Phi (r)+\gamma (r)]}-\gamma (r)-1

or

c\left(r\right)=h(r)-\beta \Phi (r)-\ln {\rm {g}}(r)

or (Eq. 12 Ref. 1)

c\left(r\right)=g(r)-\omega (r)

where $\Phi (r)$ is the intermolecular pair potential. The hyper-netted chain approximation is well suited for long-range potentials, and in particular, Coulombic systems. For details of the numerical solution of the HNC for ionic systems (see Ref. 12).

References

@@ Line 4: / Line 4: @@
 the  [[cavity correlation function]] becomes
 :<math>\ln y (r) =  h(r)  -c(r) \equiv \gamma (r)</math>
-The  hyper-netted chain closure can be written as
+The  hyper-netted chain [[Closure relations | closure relation]]can be written as
 :<math>f \left[ \gamma (r) \right] = e^{[-\beta \Phi (r) + \gamma (r)]} - \gamma (r) -1</math>
 or

Hyper-netted chain: Difference between revisions

Revision as of 18:10, 26 June 2007

References

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