[CP2K-user] [CP2K:14389] how does CP2K construct electron density in real-space FFT mesh point? Is the Gaussian product a periodic Gaussian product?

[Fangyong Yan]

Dear Thomas,

Thanks for your explanation! Yes, periodicity has to be kept for condensed
phase calculations.

Best,

Fangyong

On Mon, Dec 14, 2020 at 5:12 AM Thomas Kühne <tku... at gmail.com> wrote:

> Dear Fangyong,
>
> within the GPW scheme, the orbitals are described by contracted Gaussian
> functions,
> whereas electron density is expanded in plane-waves. You are right that
> the extent of
> the Gaussian functions is finite, which is controlled by eps values that
> are eventually
> related to EPS_DEFAULT. You are also right wrt to the plane-waves, whose
> truncation
> is controlled by CUTOFF. However, contrary to the cutoff of conventional
> PW codes,
> the latter differs by a factor of 4, which due to the fact that the
> density is the sum of the
> orbitals squared combined with the application of the Shannon-Nyquist
> sampling theorem.
> Lastly, within the GAPW approach, the Gaussian functions are indeed also
> periodic
> Gaussians.
>
> Best,
> Thomas
>
> Am 08.12.2020 um 06:22 schrieb Fangyong Yan <fyya... at gmail.com>:
>
> Hi, Professor Hutter,
>
> I read your paper, and I think when you calculate the electron density
> based on periodic Gaussian, you need to truncate the periodic Gaussian
> because it is an infinite series, but it decays fast since the
> periodic Gaussian is a localized basis set. Am I understanding correctly?
>
> For electron density represented by planewaves, it also has the same
> problem, it is an infinite series, and has to be truncated, which is the
> planewave cutoff.
>
> Another question, in the Gaussian augmented planewave method, the atomic
> hard and soft electron density, they are atom-based electron density, and
> are represented by Gaussian functions, they are also periodic Gaussian, in
> order to fulfill the periodicity, am I correct? Thanks!
>
> Fangyong
>
>
>
>
> On Fri, Dec 4, 2020 at 9:49 AM Fangyong Yan <fyya... at gmail.com> wrote:
>
>> Dear Professor Hutter,
>>
>> I will read the paper. Thanks!
>>
>> Fangyong
>>
>> On Fri, Dec 4, 2020 at 4:37 AM <hut... at chem.uzh.ch> wrote:
>>
>>> Hi
>>>
>>> yes, it is periodic Gaussians. For details of the calculation
>>> read the publications:
>>>
>>>  Lippert, G; Hutter, J; Parrinello, M.
>>>  MOLECULAR PHYSICS, 92 (3), 477-487 (1997).
>>>  A hybrid Gaussian and plane wave density functional scheme.
>>>  https://doi.org/10.1080/002689797170220
>>>
>>>  VandeVondele, J; Krack, M; Mohamed, F; Parrinello, M; Chassaing, T;
>>>  Hutter, J. COMPUTER PHYSICS COMMUNICATIONS, 167 (2), 103-128 (2005).
>>>  QUICKSTEP: Fast and accurate density functional calculations using a
>>>  mixed Gaussian and plane waves approach.
>>>  https://doi.org/10.1016/j.cpc.2004.12.014
>>>
>>> --------------------------------------------------------------
>>> Juerg Hutter                         Phone : ++41 44 635 4491
>>> Institut für Chemie C                FAX   : ++41 44 635 6838
>>> Universität Zürich                   E-mail: hut... at chem.uzh.ch
>>> Winterthurerstrasse 190
>>> CH-8057 Zürich, Switzerland
>>> ---------------------------------------------------------------
>>>
>>> -----cp... at googlegroups.com wrote: -----
>>> To: "cp2k" <cp... at googlegroups.com>
>>> From: "fy... at gmail.com"
>>> Sent by: cp... at googlegroups.com
>>> Date: 12/04/2020 08:42AM
>>> Subject: [CP2K:14345] how does CP2K construct electron density in
>>> real-space FFT mesh point? Is the Gaussian product a periodic Gaussian
>>> product?
>>>
>>> Hi,
>>>
>>> The electron density in real-space FFT mesh point is defined as:
>>>
>>> n(Ri) = summation of m, n {P_mn * Gaussian_mn(Ri),
>>>
>>> Ri is the grid point, m and n are the index for the Gaussian basis set,
>>> P_mn is the density matrix, Gaussian_mn(Ri) is the product of Gaussian
>>> basis set m and Gaussian basis set n,
>>>
>>> my question is:
>>> 1)
>>> is Gaussian_mn(Ri) a periodic Gaussian? (Product Gaussian is also a
>>> Gaussian).
>>> That is,
>>>
>>> Gaussian_mn(Ri) = Gaussian_mn(Ri+L_unitcell), where L_unitcell is the
>>> length for the unit cell in either 1,2 or 3 dimension.
>>> 2) if it is the periodic Gaussian, and it should be in order to fulfill
>>> the periodicity of electron density, how do you do the calculation?
>>> Because the periodic Gaussian is actually an infinite series, that is,
>>> Gaussian(Ri) = summation of L (Gaussian(Ri+L), where L = n*L_unitcell,
>>> and n is an integer and span from minus infinite to positive infinite.
>>>
>>> Thanks!
>>>
>>> Fangyong
>>>
>>>
>>>
>>>
>>>
>>>
>>>   --
>>>  You received this message because you are subscribed to the Google
>>> Groups "cp2k" group.
>>>  To unsubscribe from this group and stop receiving emails from it, send
>>> an email to cp... at googlegroups.com.
>>>  To view this discussion on the web visit
>>> https://groups.google.com/d/msgid/cp2k/e023de64-1040-49bd-a228-2aa4cf0732a5n%40googlegroups.com
>>> .
>>>
>>>
>>> --
>>> You received this message because you are subscribed to the Google
>>> Groups "cp2k" group.
>>> To unsubscribe from this group and stop receiving emails from it, send
>>> an email to cp... at googlegroups.com.
>>> To view this discussion on the web visit
>>> https://groups.google.com/d/msgid/cp2k/OFE157B452.F6F180E1-ONC1258634.0034CF74-C1258634.0034DAA2%40lotus.uzh.ch
>>> .
>>>
>>
> --
> You received this message because you are subscribed to the Google Groups
> "cp2k" group.
> To unsubscribe from this group and stop receiving emails from it, send an
> email to cp... at googlegroups.com.
> To view this discussion on the web visit
> https://groups.google.com/d/msgid/cp2k/CAJjmc%2BJyp%3DM1Wmu6TResTf%3Dw3oNkcZB%2B%2BPL10Z6aURJ_x%2BoKfg%40mail.gmail.com
> <https://groups.google.com/d/msgid/cp2k/CAJjmc%2BJyp%3DM1Wmu6TResTf%3Dw3oNkcZB%2B%2BPL10Z6aURJ_x%2BoKfg%40mail.gmail.com?utm_medium=email&utm_source=footer>
> .
>
>
>
>
> ==============================
> Thomas D. Kühne
> Dynamics of Condensed Matter
> Chair of Theoretical Chemistry
> University of Paderborn
> Warburger Str. 100
> D-33098 Paderborn
> Germany
> tdku... at mail.upb.de
> +49/(0)5251/60-5726
>
> --
> You received this message because you are subscribed to the Google Groups
> "cp2k" group.
> To unsubscribe from this group and stop receiving emails from it, send an
> email to cp... at googlegroups.com.
> To view this discussion on the web visit
> https://groups.google.com/d/msgid/cp2k/83C07016-CE0A-4E58-9D3B-DDD18511A546%40gmail.com
> <https://groups.google.com/d/msgid/cp2k/83C07016-CE0A-4E58-9D3B-DDD18511A546%40gmail.com?utm_medium=email&utm_source=footer>
> .
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <https://lists.cp2k.org/archives/cp2k-user/attachments/20201214/b25c32ac/attachment.htm>