pyPRISM.closure.MeanSphericalApproximation module¶
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class
pyPRISM.closure.MeanSphericalApproximation.MSA(apply_hard_core=False)[source]¶ Bases:
pyPRISM.closure.MeanSphericalApproximation.MeanSphericalApproximationAlias of MeanSphericalApproximation
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class
pyPRISM.closure.MeanSphericalApproximation.MeanSphericalApproximation(apply_hard_core=False)[source]¶ Bases:
pyPRISM.closure.AtomicClosure.AtomicClosureMean Spherical Approximation closure
Mathematial Definition
\[c_{\alpha,\beta}(r) = -U_{\alpha,\beta}(r)\]Variables Definitions
- \(c_{\alpha,\beta}(r)\)
- Direct correlation function value at distance \(r\) between sites \(\alpha\) and \(\beta\).
- \(U_{\alpha,\beta}(r)\)
- Interaction potential value at distance \(r\) between sites \(\alpha\) and \(\beta\).
Description
The Mean Spherical Approximation (MSA) closure assumes an interaction potential that contains a hard-core interaction and a tail interaction. See Reference [1] for a derivation and discussion of this closure.
The MSA does a good job of describing the properties of the square-well fluid, and allows for the analytical solution of the PRISM/RISM equations for some systems. The MSA closure reduces to the PercusYevick closure if the tail is ignored.
References
- Hansen, J.P.; McDonald, I.R.; Theory of Simple Liquids; Chapter 4, Section 4; 4th Edition (2013), Elsevier [link]
Example
import pyPRISM sys = pyPRISM.System(['A','B']) sys.closure['A','A'] = pyPRISM.closure.PercusYevick() sys.closure['A','B'] = pyPRISM.closure.PercusYevick() sys.closure['B','B'] = pyPRISM.closure.MeanSphericalApproximation() # ** finish populating system object ** PRISM = sys.createPRISM() PRISM.solve()