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axeljr7

Member

Registered: 2023-07-31

Posts: 18

a question about the code

Dear all,
Can anyone help me in the source code, population.f90 file line 4971 and 4972, what these variables mean:

fdens(gridatm(ipt)%x,gridatm(ipt)%y,gridatm(ipt)%z)
gridatm(ipt)%value
beckeweigrid(ipt)

I guess/expect some of them should be the unit cell volume and one of them should be QM electron density but I have no clue about exact meanings and would be super thankful for some hints.
Thanks in advance,
AxA

sobereva

Tian Lu (Multiwfn developer)

From: Beijing

Registered: 2017-09-11

Posts: 1,775

Website

Re: a question about the code

fdens is the function used to evaluate electron density for a given Cartesian coordinate.
gridatm(ipt)%x/y/z records X,Y,Z coordinate of integration point ipt
gridatm(ipt)%value records function value at integration point ipt
beckeweigrid(ipt) records weight of point ipt

They are not directly relevant to cell volume.

If you are not familiar with Becke's multi-center integration algorithm, please check its original paper J. Chem. Phys. 88, 2547. It is standard algorithm to integrate exchange-correlation functional in quantum chemistry codes.

axeljr7

Member

Registered: 2023-07-31

Posts: 18

Re: a question about the code

fdens is the function used to evaluate electron density for a given Cartesian coordinate.
gridatm(ipt)%x/y/z records X,Y,Z coordinate of integration point ipt
gridatm(ipt)%value records function value at integration point ipt
beckeweigrid(ipt) records weight of point ipt

They are not directly relevant to cell volume.

If you are not familiar with Becke's multi-center integration algorithm, please check its original paper J. Chem. Phys. 88, 2547. It is standard algorithm to integrate exchange-correlation functional in quantum chemistry codes.

many thanks, Prof. Lu for the hints. So, I am wondering, what's the difference between fdens and gridatm(ipt)%value as both give the electron density (here they are multiplied together).
And in the mentioned code, the fdens, gridatm(ipt)%value, and beckeweigrid(ipt) are all multiplied together. I would be thankful if you comment what is the idea behind it?

sobereva

Tian Lu (Multiwfn developer)

From: Beijing

Registered: 2017-09-11

Posts: 1,775

Website

Re: a question about the code

I made a mistake. gridatm(ipt)%value is single-center integration weight of point ipt. It is essentially combined from radial weight (second Gauss-Chebyshev) and angular weight of Lebedev method.

The final weight of a integration point is combined of single-center integration weight and Becke's atom weight.

It is strongly adviced to check "subroutine intfunc_silent(ifunc,intval)" in otherfunc.f90, it is a minimal code to integrate a specific real space function over the whole space, it is useful for you to understand the implementation of the integration.

I also have a blog article to detailedly describe the Becke's multi-center integration algorithm://www.umsyar.com/69, but it was written in Chinese.

axeljr7

Member

Registered: 2023-07-31

Posts: 18

Re: a question about the code

I made a mistake. gridatm(ipt)%value is single-center integration weight of point ipt. It is essentially combined from radial weight (second Gauss-Chebyshev) and angular weight of Lebedev method.

The final weight of a integration point is combined of single-center integration weight and Becke's atom weight.

It is strongly adviced to check "subroutine intfunc_silent(ifunc,intval)" in otherfunc.f90, it is a minimal code to integrate a specific real space function over the whole space, it is useful for you to understand the implementation of the integration.

I also have a blog article to detailedly describe the Becke's multi-center integration algorithm://www.umsyar.com/69, but it was written in Chinese.

Thank you very much for the great details, your prompt support, and the great work
Best,
AxA