[Wien] temperature dependent DFT (band, ...) calculations

Sat Apr 18 21:07:58 CEST 2020

Regarding the question of temperature effects, let me add some
remarks about electronic temperature.

Under diverse circumstances (e.g. laser heating) it is possible
for the electrons and phonons to have very different temperatures
for experimentally meaningfully long times.   Of course it also is
possible for the two populations to be at equilibrium at a temperature
that is high with respect to some important criterion.

In either case, finite-temperature or free-energy DFT can
be important for calculation.  Free energy DFT has been known since
Mermin's paper in 1965. Superficially, the computation looks like a
ground-state Kohn-Sham equation with non-integer Fermi-Dirac 
approximations.
Often that superficial resemblance has led people to implement calculations
by taking an ordinary ground state XC functional, e.g. PBE, and stuffing in
a finite-T density.  For comparatively low electronic temperatures, up to
several thousand Kelvin (i.e. about 0.75 eV) perhaps, that is reasonably
OK for equations of state, conductivity, etc.  Above that it is
not OK (despite some expert opinion to the contrary) and one
should use exchange-correlation free energy density functional 
approximations.

Our group has worked very intensely on this problem. Details are in

"Status of free-energy representations for the homogeneous electron gas"
V.V. Karasiev, S.B. Trickey, and J.W. Dufty, Phys. Rev. B 99, 195134 (2019)

"Nonempirical Semi-local Free-Energy Density Functional for Matter Under 
Extreme Conditions:
V.V. Karasiev, J.W. Dufty, and S.B. Trickey, Phys. Rev. Lett. 120, 
076401 (2018)

"Importance of Finite-temperature Exchange-correlation for Warm Dense 
Matter Calculations"
V.V. Karasiev, L. Calder\'in, and S.B. Trickey, Phys. Rev. E 93, 063207 
(2016)

"Accurate Homogeneous Electron Gas Exchange-correlation Free Energy for 
Local Spin-density Calculations"
V.V. Karasiev, T. Sjostrom, J. Dufty, and S.B. Trickey, Phys. Rev. Lett. 
112, 076403 (2014)

"Innovations in Finite-Temperature Density Functionals"
V.V. Karasiev, T. Sjostrom, D.Chakraborty, J.W. Dufty, F.E. Harris, K. 
Runge, and S.B. Trickey, in "Frontiers and Challenges in Warm Dense 
Matter", F. Graziani et al. eds., (Springer, Heidelberg, 2014) 61-85.

References to the other literature are in our papers. All of them are 
downloadable from  www.qtp.ufl.edu/ofdft

Also, some time ago Andreas G\"orling and colleagues at Erlangen worked 
out finite-T exact exchange and gave examples
   M. Greiner, P. Carrier, and A. G\"orling
   Phys. Rev. B 81, 155119 [12 pp] (2010)
and more recently Andreas and his student Trushin have applied it to 
topological phase transitions
    Egor Trushin and Andreas G\"orling
    Phys. Rev. Lett. 120, 146401 [5 pp] (2018)

Perhaps this will be helpful.

Peace, Sam

On 4/18/2020 11:42 AM, Peter Blaha wrote:
> [External Email]
>
> If you are lucky, yes, but in general, the answer is NO !!!
>
> The lattice parameter is only a "mean value", and is a "prerequisite"
> for a finit temp calculation.
>
> But think about: what means "Termperature"  ?
>
> It vibrations, which are excited more or less with T. The atoms move
> around heavily and this can be even anisotropic.
> And one measures basically an average of a certain quantity while the
> atoms are vibrating around.
>
> Calculating phonons gives you entropy and free energies;
> Doing properties with temperature dependent average displacements gives
> you properties at finite T.
>
> One example: Physical Review B, 98 (2018), S. 235205.
>
>
> Am 18.04.2020 um 15:33 schrieb Dr. K. C. Bhamu:
>> Dear Experts,
>>
>> Could you please confirm that if I have temperature dependent lattice
>> parameters, from DFT calculation, then whatever properties like band,
>> phonon, elastic, ... , I compute will be considered as temperature
>> dependent ?
>> Yes, ionic positions should be relaxed what I know.
>> My own answer would be yes for this query but I need a confirmation.
>>
>> It would be a help from computational resources point of view. I do not
>> want to test the calculation and see the the difference as system is
>> more computational time demanding.
>>
>> Thank you very much.
>>
>> Regards
>> Bhamu
>>
>>
>>
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> Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
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-- 
   Samuel B. Trickey
   QTP, Depts. of Physics and Chemistry
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