pengwann.occupations.fermi_dirac

occupations.fermi_dirac(eigenvalues, mu, sigma)

The Fermi-Dirac occupation function.

Parameters:

eigenvaluesndarray of float

The Kohn-Sham eigenvalues.

mufloat

The Fermi level.

sigmafloat

The smearing width (= kT for some electronic temperature T).

Returns:

occupation_matrixndarray of float

The occupation matrix.

Notes

The Fermi-Dirac occupation function is defined as

\[f_{nk} = \left(\exp\left[\frac{\epsilon_{nk} - \mu}{\sigma}\right] + 1\right) ^{-1}.\]