pengwann.occupations.cold

occupations.cold(eigenvalues, mu, sigma)

The Marzari-Vanderbilt (cold) occupation function.

Parameters:

eigenvaluesndarray of float

The Kohn-Sham eigenvalues.

mufloat

The Fermi level.

sigmafloat

The smearing width.

Returns:

occupation_matrixndarray of float

The occupation matrix.

Notes

The Marzari-Vanderbilt occupation function is defined as [1]

\[f_{nk} = \frac{1}{2}\left[\sqrt{\frac{2}{\pi}}\exp\left[-x^{2} - \sqrt{2}x - 1/2\right] + 1 - \mathrm{erf}\left(x + \frac{1}{\sqrt{2}}\right)\right],\]

where \(x = \frac{\epsilon_{nk} - \mu}{\sigma}\).

References

[1]

Nicola Marzari, David Vanderbilt, Alessandro De Vita, and M. C. Payne. Thermal contraction and disordering of the Al(110) surface. Phys. Rev. Lett., 82:3296–3299, Apr 1999. URL: https://link.aps.org/doi/10.1103/PhysRevLett.82.3296, doi:10.1103/PhysRevLett.82.3296.