[Wien] Non-self consistent energy (not just W2k)

[Laurence Marks]

To answer my own question, both Vasp and Wien2k use the Harris functional (
https://en.wikipedia.org/wiki/Harris_functional) which is not variational,
bounded by (e.g. Doi 10.1088/0953-8984/1/41/007)
(rho_in-rho_true)*(rho_true-rho_out) where rho_in is before the SCF
mapping, rho_out is after (i.e. lapw2) and rho_true is the fixed-point
solution. This compares to the KS functional which is variational and
bounded by (rho_true-rho_out)**2. The literature indicates that the Harris
functional energy is in general closer (for non-converged SCF) to the
energy than the KS energy when the density is not converged. (This follows
because rho_out is often quite bad.)

When the density is converged the KS functional and the Harris functional
give the same energy.


On Mon, Jan 31, 2022 at 8:23 AM Laurence Marks <laurence.marks at gmail.com>
wrote:

> In Wien2k the total energy is calculated in part from the current density,
> in part from the density of the orbitals that solve the KS equation. As
> such it is not a true variational energy except when the density is
> converged. [1]
>
> For other dft codes (not wavefunction codes [2]), is it the same, e.g.
> Vasp, QE, ab-init? Responses welcome, either via the list of directly.
>
> [1] There are technically ways one could calculate some form of
> variational energy, but it would require extra steps and to my knowledge
> has never looked useful so is not in the code.
> [2] In wavefunction codes where one varies the occupancy the energy is
> typically variational I think.
>
> --
> Professor Laurence Marks
> Department of Materials Science and Engineering
> Northwestern University
> www.numis.northwestern.edu
> "Research is to see what everybody else has seen, and to think what nobody
> else has thought" Albert Szent-Györgyi
>


-- 
Professor Laurence Marks
Department of Materials Science and Engineering
Northwestern University
www.numis.northwestern.edu
"Research is to see what everybody else has seen, and to think what nobody
else has thought" Albert Szent-Györgyi
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