pyPRISM.potential.WeeksChandlerAndersen module¶
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class
pyPRISM.potential.WeeksChandlerAndersen.WeeksChandlerAndersen(epsilon, sigma=None)[source]¶ Bases:
pyPRISM.potential.LennardJones.LennardJonesPurely repulsive Weeks-Chandler-Andersen potential
Mathematical Definition
\[ \begin{align}\begin{aligned}U_{\alpha,\beta}(r) = \begin{cases} 4\epsilon_{\alpha,\beta}\left[\left(\frac{\sigma_{\alpha,\beta}}{r}\right)^{12.0} - \left(\frac{\sigma_{\alpha,\beta}}{r}\right)^{6.0}\right] + \epsilon_{\alpha,\beta} & r<r_{cut}\\ 0.0 & r \geq r_{cut} \end{cases}\end{aligned}\end{align} \]\[r_{cut} = 2^{1/6}\sigma_{\alpha,\beta}\]Variable Definitions
- \(\epsilon_{\alpha,\beta}\)
- Strength of repulsion between sites \(\alpha\) and \(\beta\).
- \(\sigma_{\alpha,\beta}\)
- Length scale of interaction between sites \(\alpha\) and \(\beta\).
- \(r\)
- Distance between sites.
- \(r_{cut}\)
- Cutoff distance where the value of the potential goes to zero.
Description
The Weeks-Chandler-Andersen potential for purely repulsive interactions. This potential is equivalent to the Lennard-Jones potential cut and shifted at the minimum of the potential, which occurs at \(r=2^{1/6}\sigma\).Example
import pyPRISM #Define a PRISM system and set the A-B interaction potential sys = pyPRISM.System(['A','B'],kT=1.0) sys.domain = pyPRISM.Domain(dr=0.1,length=1024) sys.potential['A','B'] = pyPRISM.potential.WeeksChandlerAndersen(epsilon=1.0,sigma=1.0)
Warning
If sigma is specified such that it does not fall on the solution grid of the
Domainobject specified inSystem, then the sigma will effectively be rounded. A warning should be emitted during the construction of aPRISMobject if this occurs.