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[Nicola Marzari <marzari@mit.edu>]

jzwanzig@dal.ca wrote:
> Dear Colleagues, 
>
> even having read the paper by Verstraete and Gonze I'm a little unclear on 
> the interplay between tsmear, tphysel, and occopt. For example, with occopt = 
> 7 and tphysel = 300 K, should the energy be variational in tsmear? That is, 
> am I to expect monotonic behavior in the energy with increasing (or 
> decreasing) tsmear? I kind of hope not as I don't get that, at least for bulk 
> zinc. Is the idea to increase both the kpt mesh and repeatedly vary tsmear, 
> looking for stability (as opposed to a minimum or a maximum)? thanks for your 
> help,
>
> Joe Zwanziger



Dear Joe,


for a tsmear corresponding to fermi-dirac, or gaussian, and a
tphysel set to 0, the total free energy (not sure how abinit calls
it) is quadratic in tsmear (and with a negative coefficient),
*provided you have an infinite mesh of k-points*.

If the smearing is methfessel-paxton, or marzari-vanderbilt,
the free energy will be quartic or cubic, respectively.

Most importantly, if the mesh of k-points is not infinite, the
free energy calculated at small tmsear will have a large statistical
sampling error (going either way, up or down), while the free energy
calculated at large tmsear will have a small sampling error.

If tphysel is different from 0 - I don't know
(haven't look at the Verstraete/Gonze in a long time) but I would
suspect the same identical comments would apply
(but note that 300K is really almost zero, in practice).

Another source of information is Chap 4 of
http://quasiamore.mit.edu/phd ; it is fairly complete, but does not
address the Verstraete and Gonze developments (it was written in '96).

                        nicola


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Prof Nicola Marzari   Department of Materials Science and Engineering
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