Verlet modified: Difference between revisions
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in terms of the [[cavity correlation function]], is (Eq. 3) | in terms of the [[cavity correlation function]], is (Eq. 3) | ||
:<math>y(r) = \gamma (r) - A \frac{1}{2} \gamma^2(r) \left[ \frac{1}{1+ B \gamma(r) /2} \right]</math> | :<math>\ln y(r) = \gamma (r) - A \frac{1}{2} \gamma^2(r) \left[ \frac{1}{1+ B \gamma(r) /2} \right]</math> | ||
where several sets of values are tried for ''A'' and ''B'' (Note, when ''A=0'' the [[HNC| hyper-netted chain]] is recovered). | where several sets of values are tried for ''A'' and ''B'' (Note, when ''A=0'' the [[HNC| hyper-netted chain]] is recovered). | ||
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by minimising the difference between the pressures obtained via the [[Pressure equation | virial]] and [[Compressibility equation | compressibility]] routes: | by minimising the difference between the pressures obtained via the [[Pressure equation | virial]] and [[Compressibility equation | compressibility]] routes: | ||
:<math>y(r) = \gamma (r) - A \frac{1}{2} \gamma^2(r) \left[ \frac{1+ \lambda \gamma(r)}{1+ \mu \gamma(r)} \right]</math> | :<math>\ln y(r) = \gamma (r) - A \frac{1}{2} \gamma^2(r) \left[ \frac{1+ \lambda \gamma(r)}{1+ \mu \gamma(r)} \right]</math> | ||
with <math>A= 0.80</math>, <math>\lambda= 0.03496</math> and <math>\mu = 0.6586</math>. | with <math>A= 0.80</math>, <math>\lambda= 0.03496</math> and <math>\mu = 0.6586</math>. | ||
Revision as of 17:00, 1 September 2015
The Verlet modified (1980) (Ref. 1) closure relation for hard sphere fluids, in terms of the cavity correlation function, is (Eq. 3)
where several sets of values are tried for A and B (Note, when A=0 the hyper-netted chain is recovered). Later (Ref. 2) Verlet used a Padé (2/1) approximant (Eq. 6) fitted to obtain the best hard sphere results by minimising the difference between the pressures obtained via the virial and compressibility routes:
with , and .