pyPRISM.closure.MartynovSarkisov module¶
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class
pyPRISM.closure.MartynovSarkisov.MS(apply_hard_core=False)[source]¶ Bases:
pyPRISM.closure.MartynovSarkisov.MartynovSarkisovAlias of MartynovSarkisov
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class
pyPRISM.closure.MartynovSarkisov.MartynovSarkisov(apply_hard_core=False)[source]¶ Bases:
pyPRISM.closure.AtomicClosure.AtomicClosureMartynovSarkisov closure
Mathematial Definition
\[c_{\alpha,\beta}(r) = \left(\exp\left(\sqrt{\gamma_{\alpha,\beta}(r) - U_{\alpha,\beta}(r) - 0.5}\right) - 1.0 \right) - 1.0 - \gamma_{\alpha,\beta}(r)\]\[\gamma_{\alpha,\beta}(r) = h_{\alpha,\beta}(r) - c_{\alpha,\beta}(r)\]Variables Definitions
- \(h_{\alpha,\beta}(r)\)
- Total correlation function value at distance \(r\) between sites \(\alpha\) and \(\beta\).
- \(c_{\alpha,\beta}(r)\)
- 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 Martynov-Sarkisov (MS) closure is described as a generalization of the HyperNettedChain closure. See the references below for derivation and usage examples.
The change of variables is necessary in order to use potentials with hard cores in the computational setting. Written in the standard form, this closure diverges with divergent potentials, which makes it impossible to numerically solve.
The MS closure has been shown to be very accurate for hard-sphere spherical molecules and for high-density hard-core polymer systems.
References
- Martynov, G.A.; Sarkisov, G.N.; Mol. Phys. 49. 1495 (1983) [link]
- Yethiraj, A.; Schweizer, K.S.; J. Chem. Phys. 97. 1455 (1992) [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.MartynovSarkisov() # ** finish populating system object ** PRISM = sys.createPRISM() PRISM.solve()