# [Octopus-users] TDDFT at finite temperature

David Strubbe dstrubbe at berkeley.edu
Mon Jan 24 23:12:13 WET 2011

```Sorry, that link used to work. I put the PostScript up at
http://civet.berkeley.edu/~dstrubbe/casida.ps
It is not about temperature per se, but gives equations for arbitrary
occupations.

David

On Mon, Jan 24, 2011 at 1:43 AM, Miguel Marques <marques at teor.fis.uc.pt>wrote:

>  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 P.S. Davis, the link you sent is no longer valid, so I could not check  the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
>>>
>>> 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
>>>
>>>
>>>
>>> _______________________________________________
>>> Octopus-users mailing list
>>> Octopus-users at tddft.org
>>> http://www.tddft.org/mailman/listinfo/octopus-users
>>>
>>>  _______________________________________________
>> Octopus-users mailing list
>> Octopus-users at tddft.org
>> http://www.tddft.org/mailman/listinfo/octopus-users
>>
>>
>
> --
> Dr. Miguel A. L. Marques
> marques at tddft.org
> http://www.tddft.org/bmg
>
> Laboratoire de Physique de la Matière Condensée et Nanostructures
> (LPMCN) - Université Lyon I
> Bâtiment Brillouin, Domaine scientifique de la DOUA
> 69622 Villeurbanne Cedex
> Tel +33 (0)4 72448187
> Fax +33 (0)4 72432648
>
>
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>
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