[CP2K-user] [CP2K:14345] how does CP2K construct electron density in real-space FFT mesh point? Is the Gaussian product a periodic Gaussian product?

[Fangyong Yan]

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
>
>
>
>
>
>
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