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

[fy...@gmail.com]

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





-------------- next part --------------
An HTML attachment was scrubbed...
URL: <https://lists.cp2k.org/archives/cp2k-user/attachments/20201203/7d4dd9c1/attachment.htm>