[CP2K-user] [CP2K:19924] Understanding GAPW gradient implementation: why many terms are not calculated?

[zc62]

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.

[image: 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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