[Pw_forum] How does PWSCF deal with charged solids?

[Paolo Giannozzi]

On Jan 4, 2007, at 18:22 , xqhu at duke.edu wrote:

> Recently, I have been working on some charged solids (like diamond).
> I think the Makov-Payne correction only is used for isolated  
> molecules.
> So I just wonder how PWSCF deals with charged solids?

by (implicitly) adding a neutralizing background, i.e. calculating the
G=0 energy terms as for a neutral system

> I calculated diamond with one more electron per unit cell through
> PWSCF. Is the total energy correct?

it depends on what you mean by "correct". The total energy of a
charged system is infinite for an infinite system. The calculated
energy should ideally give information on the energy required to
add or remove 1 electron to the system, not 10^23 electrons.

For an isolated system, the calculated energy will eventually
converge, for larger and larger supercells, to the energy of the
charged system, but the convergence is exceedingly slow.
The Makov-Payne correction does a decent job in this case.
More refined (and expensive) approaches use a modified
Coulomb interaction and enlarged supercells to solve the
Poisson equation.

For a true crystal, there isn't much one can do: you cannot
(for instance) calculate the ionization potential or the electronic
affinity by just making the difference between the calculated
total energies for different charge states.

A case in which energies for charged systems can be useful
(with some care) is the relative stability of charge states for
defects in semiconductors. For instance:
   E_f(-) = E(crystal:defect+e) - E(crystal) - E(defect) - \mu
   E_f(0) = E(crystal:defect) - E(crystal) - E(defect)
where \mu is the energy of an electron from an electron reservoir,
i.e. the Fermi energy of the crystal, inside the gap. A comparison
of various charge states yields the relative stability with respect to
the position of the Fermi energy (something that depends on the
impurities that are present in the semiconductor).

Paolo
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Paolo Giannozzi, Democritos and University of Udine, Italy