[DFTB-Plus-User] Electronic temperature

[Reinaldo Pis Diez]

Dear Bálint,

Thank you very much for your answer pointing out the importance of 
paying attention to the Mermin free energy when the electronic 
temperature is not zero and occupation numbers are non-integers.

Following your advice, I've compared the total energy and the Mermin 
free energy for those hard_to_converge cases I mentioned in my 
former mail. I've noted that the difference between them is a few 
tenths of eV for, say, 20-50 K. I guess this is a good result but 
now a new question arises: Can the difference between the total 
energy and the Mermin free energy be taken as a measure of the 
reliability of the results? In other words, can I state that the 
smaller the difference between the total energy and the Mermin free 
energy, the more reliable the result?

Thanks again.

Best regards,

Reinaldo

On 09/03/2012 03:35 AM, Bálint Aradi wrote:
> Dear Reinaldo,
>
>> However, a new system under study is becoming really hard to converge.
>> I'm able to achieve convergence with small electronic temperatures but
>> at the cost of having some non-integer occupation numbers. If the
>> temperature is decreased a little, then no convergence is achieved at
>> all. Thus, my question is: what limiting values are accepted for
>> non-integer occupation numbers when electron smearing or electron
>> temperature is used for scf? That is, is a distribution like 0.70-0.30,
>> for example, acceptable or not?
>   The short answer would be: depends on your system, but basically
> everything is allowed. In theory, in DFT you could even make the
> occupation numbers part of the optimization process and optimize them to
> yield the lowest possible energy. Of course, no one really does that...
>
>   In metallic systems or more general in systems with degenerate or
> nearly degenerate levels, you would naturally have non-integer
> occupancies. It wouldn't be even physical to have only integer ones, as
> through that (provided your system converges at all), you would pick out
> some of those degenerated orbitals and occupy them, while the others of
> them you would leave unoccupied. But that would create a sort of
> symmetry breaking, by treating theoretically equivalent orbitals
> differently.
>
>   It is important, however, that when temperature causes non-integer
> occupations, it is the free energy, which is the relevant energy, not
> the total energy any more. You'll see, that in those cases the two
> quantities differ somewhat.
>
>    Best regards,
>
>     Bálint
>
>
>
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