[Octopus-users] TDDFT at finite temperature

[Miguel Marques]

   Dear David, Piin-Ruey,

   I think the situation is not so trivial. It is true that one can make 
a quick and dirty generalization of the work of de Gironcoli, and that 
is what is implemented in octopus. However, to my knowledge there is no 
proper formulation of TDDFT with an electronic temperature. There are 
two "schools":

1) The electronic temperature should just be used to obtain the initial 
state for TDDFT, and the propagation should not change the occupations. 
This is what happens when you do time-propagation with octopus. It is 
also the "correct" way according to Hardy Gross, etc. (I asked them so 
years ago, that they may have changed opinion ;)) This amount, in my 
opinion, to disconnect the system from the reservoir when one starts the 
propagation. Note that this also leads to the incorrect static limit.

2) In my opinion, the "correct" way is to keep the system connected to 
the reservoir, i.e., the occupation numbers should change with time. 
However, in this case, one does not know how to change them. One could 
try an "adiabatic" procedure, i.e., calculating the expectation value of 
the Hamiltonian, and use these time-dependent "eigenvalues" to adjust 
the occupations. I think that what is implemented in the Sternheimer 
approach in octopus amounts to this (correct me if I am wrong). This, 
however, is not the whole story I think.

   On the other hand, changing occupation numbers in TD open a pandora 
box (see the recent work on TD density-matrix theory).

   I would be very glad if someone has some more insight on this 
problem, as it has been bugging me for several years now...

   miguel

P.S. Davis, the link you sent is no longer valid, so I could not check  
the paper ;((

On 01/24/2011 04:08 AM, David Strubbe wrote:
> Piin-Ruey,
>
> Regarding Sternheimer linear response with finite temperature: see
> Stefano de Gironcoli, Phys Rev B 51, 6773(R) (1995). This is static
> but Octopus implements the generalization to nonzero frequency.
>
> For Casida linear response with finite temperature, see the original
> Casida paper: ME Casida, "Time-dependent density functional response
> theory for molecules,"  in Recent Advances in Density Functional
> Methods, edited by DE Chong, vol. 1 of Recent Advances in
> Computational Chemistry, pp. 155-192 (World Scientific, Singapore),
> available at http://dcm.ujf-grenoble.fr/PERSONNEL/CT/casida/research/chong.ps
>
> David
>
> 2011/1/23 Pan Piin-Ruey<iealtamperodicooti_s at hotmail.com>
>> Dear octopus users,
>>
>>     I found that there is a variable in octopus that controls the electronic occupations (SmearingFunction = Fermi_dirac), and I want to learn more about it.
>>
>> Can someone give me theoretical information about how octopus combines finite temperature and TDDFT?
>>
>>
>>
>> P.S. I’m new to TDDFT; I have researched the topic using google for a while, but I couldn’t find the answer I want.
>>
>> (The information I found are mostly about non-equilibrium Green function, but not Time-propagation or Linear response at finite temperature. )
>>
>>
>>
>> Thanks a lot!
>>
>>
>>
>> Sincerely yours
>>
>>
>>
>> Piin-Ruey Pan
>>
>> Department of physics
>>
>> National Taiwan University
>>
>>
>>
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-- 
Dr. Miguel A. L. Marques
marques at tddft.org
http://www.tddft.org/bmg

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