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

[hut... at chem.uzh.ch]

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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