fits module

Various approximate fits to the UEG or OCP

fits.classical_ocp(system, beta)
Evaluate the classical excess energy using the parametrised fit given by
    1. Hansen PRA 8, 6 1973.
Parameters:
  • system (class) – System being studied.
  • beta (float) – Inverse Temperature.
Returns:

U_xc – Excess internal energy for classical OCP.
Return type:

float
fits.ksdt(rs, zeta, t)

Fit to RPIMC data of Brown et al (Phys. Rev. Lett. 110, 146405 (2013)) from Karasiev, Sjostrom, Dufty and Trickey, PRL 112, 076403. Please cite these guys.

The KSDT fit is given as:

\[f_{\mathrm{xc}}^{\zeta}(r_s, t) = -\frac{1}{r_s}\frac{\omega_{\zeta}a(t) + b_{\zeta}(t)r_s^{1/2} + c_{\zeta}(t)r_s}{1+d_{\zeta}(t)r_s^{1/2} + e_{\zeta}(t)r_s}\]
Parameters:
  • rs (float) – Density desired.
  • zeta (int) – Spin polarisation.
  • t (float) – Reduced temperature (\(T/T_F\))
Returns:

f_xc – Exchange-correlation free energy per-particle.
Return type:

float
fits.pdw(rs, t, zeta)
Perrot, Dharma-wardana (Phys. Rev. A 30, 2619 (1984).)fit to RPA
correlation free energy of unpolarised UEG.
Parameters:
  • rs (float) – Density Parameter.
  • zeta (int) – Spin polarisation.
Returns:

f_c – Correlation free energy energy.
Return type:

float
fits.vwn_rpa(rs, zeta)
Vosko Wilk Nusair fit to RPA correlation energy of UEG. Can. J. Phys.

58, 1200 (1980).

Currently unpolarised only.

Parameters:
  • rs (float) – Density Parameter.
  • zeta (int) – Spin polarisation.
Returns:

ec – Correlation energy.
Return type:

float