[CP2K-user] [CP2K:18664] Calculation of the static dielectric constant of a 3D periodic water system

[Nathalie Smith]

Dear CP2K users,

I am having trouble with a problem that I have seen sporadically in this 
forum, but didn't really find an answer to.

I am trying to calculate the static dielectric constant of water using the 
variance of the total dipole moment of the system, like shown in several 
papers and CP2K tutorials (e.g. 
https://www.cp2k.org/exercises:2014_ethz_mmm:monte_carlo_ice or 
https://www.cp2k.org/exercises:2018_uzh_acpc2:mol_sol). Currently, I am 
tyring to reproduce the MD simulation shown in the last link, just for 
longer simulation times (in the nanosecond scale) and in the NVT instead of 
the NVE ensemble. Therefore, I use the TIP3/Fw water model, PBCs in all 
directions, the spme method to deal with electrostatic interactions, and 
the berry phase formula for the calculation of the dipole moments. You can 
see all the parameters in the attached input file.

When I got the file with the dipole moments, I used the linux terminal 
command „cat filename.dat | grep Debye > newfilename.dat“ to extract the 
dipole moments in Debye, removed the „MM DIPOLE [BERRY PHASE](Debye)|“ 
section and used a python skript to calculate the static dielectric 
constant from it (also attached to this message). The problem: The value I 
get is way too low, around 15 and not around 80 as I would expect. In other 
simulations that I set up (using SPC/E water and a larger cell), the 
problem was even worse and I got a value around 8. 

I checked my units and formulas several times and I honestly don’t think 
they are the reason I get wrong values. From what I have seen in the CP2K 
forum, this is a rather common problem; e.g. here 
https://lists.cp2k.org/archives/cp2k-user/2020-March/013043.html someone 
only got the right result after calculating the total dipole moment by 
themselves (which is something I could do for most MM methods, but not 
quite as easily for QM methods I guess, which I want to use later on. I 
know I could calculate molecular dipole moments using maximally localized 
Wannier centers, but this seems to be computationally more expensive). 

So my question is: Is there something wrong with my calculations that I 
don’t see? Or is it a problem with the CP2K dipole moments (e.g. wrong 
unit, or wrong values altogether)? I am convinced that CP2K can be used for 
the calculation of static dielectric constants using the variance of the 
total dipole moment because it was already used for this purpose in the 
literature (e.g. https://pubs.acs.org/doi/10.1021/jp4103355; please note 
that I am aware of the differences between their and my calculations (MC 
instead of MD, ice instead of water, DFT instead of a MM water model etc.)).

Thanks in advance for anyone who reads my question, and to anyone who also 
gives an answer.

Best wishes,

Nathalie Smith

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