sarkas.potentials.lennardjones
Content
sarkas.potentials.lennardjones#
Module for handling Lennard-Jones interaction.
Potential#
The generalized Lennard-Jones potential is defined as
\[U_{\mu\nu}(r) = k \epsilon_{\mu\nu} \left [ \left ( \frac{\sigma_{\mu\nu}}{r}\right )^m -
\left ( \frac{\sigma_{\mu\nu}}{r}\right )^n \right ],\]
where
\[k = \frac{n}{m-n} \left ( \frac{n}{m} \right )^{\frac{m}{n-m}}.\]
In the case of multispecies liquids we use the Lorentz-Berthelot mixing rules
\[\epsilon_{12} = \sqrt{\epsilon_{11} \epsilon_{22}}, \quad \sigma_{12} = \frac{\sigma_{11} + \sigma_{22}}{2}.\]
Force Error#
The force error for the LJ potential is given by
\[\Delta F = \frac{k\epsilon}{ \sqrt{2\pi n}} \left [ \frac{m^2 \sigma^{2m}}{2m - 1} \frac{1}{r_c^{2m -1}}
+ \frac{n^2 \sigma^{2n}}{2n - 1} \frac{1}{r_c^{2n -1}} \
-\frac{2 m n \sigma^{m + n}}{m + n - 1} \frac{1}{r_c^{m + n -1}} \
\right ]^{1/2}\]
which we approximate with the first term only
\[\Delta F \approx \frac{k\epsilon} {\sqrt{2\pi n} }
\left [ \frac{m^2 \sigma^{2m}}{2m - 1} \frac{1}{r_c^{2m -1}} \right ]^{1/2}\]
Potential Attributes#
The elements of the sarkas.potentials.core.Potential.pot_matrix are:
pot_matrix[0] = epsilon_12 * lj_constant
pot_matrix[1] = sigmas
pot_matrix[2] = highest power
pot_matrix[3] = lowest power
pot_matrix[4] = short-range cutoff
Functions
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Print potential specific parameters in a user-friendly way. |
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Assign potential dependent simulation's parameters. |