Forces not equivariant upon molecule rotation

[Harry Richardson]

Hi I am running some energy+force calculation of a single benzene molecule using WB97X-D (benzene.inp). 

In order to test the equivariance of the force calculations I have rotated the molecule by 180 degrees around the vector [0.5,0.5,0.5] via the file rotation.ipynb. 

I then calculate the forces for both (forces_0, forces_180) and use the file equi_checker.ipynb to rotate the forces back to the original space and compare them. 

When I do this the forces do not appear equivariant at all, in fact the magnitude of the difference in forces is of the order of the forces themselves i.e. converting force to ev/A: 

sum absolute difference 270 deg rotation: 1.651721858651293 eV/A sum absolute difference 180 deg rotation: 1.5320346141088304 eV/A sum absolute difference 90 deg rotation: 0.6562673988482665 eV/A

and this is when the total absolute forces themselves are ~1.55ev/A

Does anyone have any ideas or can see any issues with my input / outputs forces? I have tried tightening convergence and trying different potentials, none seemed to make much difference?

Thank you for any help anyone can provide

[Jürg Hutter]

Hi

the periodic Hamiltonian with plane wave basis sets (as partly used in CP2K or in PW codes) is not
rotationally and translationally (only up to quantas of grid spacings) invariant.

The variation in energy/forces depends on several factors, but exact invariance will only be achieved
for infinite box size and infinite PW cutoff.

regards
JH

________________________________________
From: cp...@googlegroups.com <cp...@googlegroups.com> on behalf of Harry Richardson <harrysgr...@gmail.com>
Sent: Monday, June 16, 2025 1:07 PM
To: cp2k
Subject: [CP2K:21545] Forces not equivariant upon molecule rotation

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[Harry Richardson]

Hi Jürg

Thanks for your reply, I understand there will be limitations to the invariance, i.e. not perfectly invariant, but if you glance at the forces they do not really seem invariant at all, as in lots of forces are in opposite directions etc, do you think I could have set up the input file incorrectly or something as I could not see any mistakes? 

Thanks 

Harry