[QE-users] epsilon.x and hybrids

Timrov Iurii iurii.timrov at epfl.ch
Wed Apr 8 20:15:36 CEST 2020 

Dear All,


> Do I remember correctly that epsilon.x also does not take into account the nonlocal pseudopotential contribution?


Correct


> ...there used to be an option in the  turbo_davidson.x and turbo_lanczos.x codes, namely no_hxc=.true.,  which permits an independent-electron calculation.


Correct. By default, the matrix element of the dipole operator is computed (in reciprocal space) via the matrix element of the commutator that Paolo mentioned [H,x] (see Eq.(14) in S. Baroni and R. Resta, Phys. Rev. B 33, 7017 (1986)): but in this case there is a kinetic term and the part coming from the non-local part of a pseudopotential. In epsilon.x, only the kinetic term is present, while in TDDFT codes both terms are present (the second term was implement long ago in the Phonon code to compute the dielectric tensor). But still, in the case of hybrid functionals, in [H,x] there is another term which is missing - the commutator with another non-local potential which is EXX. Stefano Baroni and I developed a way how to compute this missing term several years ago: I implemented it in QE and it worked well, but I never had time to release it and publish some paper about it. But there is a workaround for finite systems: the matrix element of the dipole operator can be computed in real space based on the observation that the charge density of the finite system decays fast outside the finite system, and hence the non-periodicity problem of the dipole operator is no longer a problem. But this trick in real space is not gonna work for periodic systems, because the charge density if non-zero in the whole simulation cell. Thus, the only way to overcome this problem is to implement the missing term for hybrids in [H,x].


Greetings,

Iurii


--
Dr. Iurii Timrov
Postdoctoral Researcher
STI - IMX - THEOS and NCCR - MARVEL
Swiss Federal Institute of Technology Lausanne (EPFL)
CH-1015 Lausanne, Switzerland
+41 21 69 34 881
http://people.epfl.ch/265334
________________________________
From: users <users-bounces at lists.quantum-espresso.org> on behalf of Giuseppe Mattioli <giuseppe.mattioli at ism.cnr.it>
Sent: Wednesday, April 8, 2020 7:42:35 PM
To: Quantum ESPRESSO users Forum
Subject: Re: [QE-users] epsilon.x and hybrids


Dear all
I don't want to raise the confusion level, so please correct me if I'm
wrong... If you want to calculate a heavily approximate absorption
spectrum of a (large and non-symmetrical) periodic system after a
ground state hybrid calculation, there used to be an option in the
turbo_davidson.x and turbo_lanczos.x codes, namely no_hxc=.true.,
which permits an independent-electron calculation. At least, hybrid
functionals and Gamma ground states should be properly treated by such
codes, resulting in an absorption spectrum compatible with those
obtained by using epsilon.x, which, AFAIK, calculates
<occupied|r|virtual> contributions to the absorption spectrum.
However, I don't know how much this kind of calculation is expensive
for large supercells. Of course if you are not interested in
absorption, then my suggestion is nonsense...
HTH
Giuseppe

Quoting Lorenzo Paulatto <paulatz at gmail.com>:

> Also, epsilon.x cannot use symmetry-reduced grids, which would be a
> huge wast of time with hybrids, but you can use open_grid.x after
> the pw.x calculation too obtain the full grid and work around this
> problem.
>
> cheers
>
> On 4/8/20 6:38 PM, Paolo Giannozzi wrote:
>> I think epsilon.x assumes that the dipole element of x can be
>> computed using [H,x]=p\hbar/m. The exchange potential is nonlocal,
>> so its commutator with x will yield an additional term that is not
>> accounted for. Not sure how important it is in practice. Do I
>> remember correctly that epsilon.x also does not take into account
>> the nonlocal pseudopotential contribution?
>>
>> Paolo
>>
>> On Wed, Apr 8, 2020 at 4:29 PM Manu Hegde <mhegde at sfu.ca
>> <mailto:mhegde at sfu.ca>> wrote:
>>
>>    Hi Michal,
>>    Yes, it is possible.I did use both supercell and hybrid
>>    calculations. It did work.
>>    Manu
>>
>>    On Wed, Apr 8, 2020 at 10:08 AM Michal Krompiec
>>    <michal.krompiec at gmail.com <mailto:michal.krompiec at gmail.com>> wrote:
>>
>>        Hello,
>>        Is it possible to use epsilon.x on results of a calculation with a
>>        hybrid functional (supercell, gamma point only)?
>>
>>        Thanks,
>>
>>        Michal Krompiec
>>        Merck KGaA
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>>
>> --
>> Paolo Giannozzi, Dip. Scienze Matematiche Informatiche e Fisiche,
>> Univ. Udine, via delle Scienze 208, 33100 Udine, Italy
>> Phone +39-0432-558216, fax +39-0432-558222
>>
>>
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>
> --
> Lorenzo Paulatto - Paris
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GIUSEPPE MATTIOLI
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