New protocol for Fermi energy determination based on Newtons minimization method
This Merge Request is meant to correct a long-standing problem on the Fermi energy determination of insulators when M-P and cold smearings are used (see issue 81). The problem arises because the M-P and cold occupation functions are non-monotonic, which can make the Fermi energy not uniquely defined. This solution implements a numerical protocol based on the Newton's minimization algorithm applied to
[N(mu) - N0]^2
where N(mu)
is the number of electrons for a given chemical potential mu
and N0
is expected number of electrons. The initial guess for this method is obtained from a prospection using the bisection root-finding method with the Gaussian broadening.
Example for cold smearing: Bi2Ge2Te5
Examples for M-P smearing: Bi2Ge2Te5, Ca18Si24
Edited by Flaviano José dos Santos