[CP2K-user] [CP2K:19928] Understanding GAPW gradient implementation: why many terms are not calculated?

[Jürg Hutter]

Hi

you are having most of term correct. The 1-center terms only depend on
the atomic positions through the coefficients C'. The derivatives wrt the local functions are in fact zero. You can best see that by inspecting their dependencies
on the molecular geometry.

If you wish you can download the thesis of Gerald Lippert from this link (expires in
early March).

https://filesender.switch.ch/filesender2/?s=download&token=7549a87c-9cad-44b0-9138-45a53c6f796a

It is in German but has all the formulas in great detail. To compare to the current
implementation in CP2K you have to set the two compensation charges
(hard and soft) equal. This simplifies the formulas slightly.

regards
JH

________________________________________
From: cp2k at googlegroups.com <cp2k at googlegroups.com> on behalf of zc62 <chenzh1993 at gmail.com>
Sent: Friday, February 16, 2024 10:51 PM
To: cp2k
Subject: [CP2K:19924] Understanding GAPW gradient implementation: why many terms are not calculated?

Hi,

Recently I have been trying to derive GAPW nuclear coordinate gradients (somehow they are not presented in the 1999 and 2000 GAPW papers) and compare with the actual implementation, but there are a few places I could not understand.

[截屏2024-02-16 下午3.35.17.png]
Above shows what I have derived for Hartree and Exc (without density matrix derivative terms). However, the actual implementation does not have any 1c terms implemented. To be specific, they are:

1. C' derivatives. C' is calculated from the projection, and the overlap between the projector at A and basis at B certainly will change.
2. For the compensation density (rho0), the integral of g_A^lm gradient with V_H is calculated in qs_rho0_ggrid.F on the global grid, but the corresponding local grid integral is not calculated (if I did not miss it).
3. All the local grid integrals involve the gradient of basis functions are not calculated (at least not in hartree_local_methods.F).

According to my numerical tests, the analytic gradients do agree with numerical differentiations, but I do feel that I am unable to correctly understand why these terms should be zero. Can you help me develop a proper understanding for this?

Thanks!

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