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New protocol for Fermi energy determination based on Newtons minimization method

Flaviano José dos Santos requested to merge flavianojs/q-e:develop into develop

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

Bi2Ge2Te5

Examples for M-P smearing: Bi2Ge2Te5, Ca18Si24

Bi2Ge2Te5_M-P Ca18Si24_M-P

Edited by Flaviano José dos Santos

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