sarkas.potentials.egs
Content
sarkas.potentials.egs#
Module for handling Exact Gradient corrected Screened (EGS) Potential.
Potential#
The exact-gradient screened (EGS) potential introduces new parameters that can be easily calculated from initial inputs. Density gradient corrections to the free energy functional lead to the first parameter, \(\nu\),
where \(\lambda\) is a correction factor; \(\lambda = 1/9\) for the true gradient corrected Thomas-Fermi model and \(\lambda = 1\) for the traditional von Weissaecker model, \(\mathcal I_{-1/2}[\eta_0]\) is the Fermi Integral of order \(-1/2\), and \(\Lambda_e\) is the de Broglie wavelength of the electrons.
In the case \(\nu < 1\) the EGS potential takes the form
with
where the parameter \(b\) arises from exchange-correlation contributions, see below.n On the other hand \(\nu > 1\), the pair potential has the form
with
Neglect of exchange-correlational effects leads to \(b = 1\) otherwise
where \(k_{\textrm{F}}\) is the Fermi wavenumber and \(\Theta = (\beta E_{\textrm{F}})^{-1}\) is the electron degeneracy parameter` calculated from the Fermi energy.
Force Error#
The EGS potential is always smaller than pure Yukawa. Therefore the force error is chosen to be the same as Yukawa’s
This overestimates it, but it doesn’t matter.
Potential Attributes#
The elements of sarkas.potentials.core.Potential.pot_matrix
are
if sarkas.core.Parameters.nu
less than 1:
pot_matrix[0] = q_iq_j/4pi eps0
pot_matrix[1] = nu
pot_matrix[2] = 1 + alpha
pot_matrix[3] = 1 - alpha
pot_matrix[4] = 1.0 / lambda_minus
pot_matrix[5] = 1.0 / lambda_plus
else
pot_matrix[0] = q_iq_j/4pi eps0
pot_matrix[1] = nu
pot_matrix[2] = 1.0
pot_matrix[3] = alpha prime
pot_matrix[4] = 1.0 / gamma_minus
pot_matrix[5] = 1.0 / gamma_plus
Functions
|
Print potential specific parameters in a user-friendly way. |
|
Assign potential dependent simulation's parameters. |