Counterpoise correction with Grimme D4

[Holger Sassnick]

Hello,

lately I have been trying to calculate the adsorption energy of water in the CAU-23 MOF with different XC functionals. To avoid the quite significant BSSE of CP2K's MOLOPT basis sets, I had to apply a counterpoise correction.

However, when using the Grimme D4 method the obtained values didn't really make sense as they resulted in a positive interaction energy (I have attached the corresponding input and output files). The  same calculation with the PBE functional or PBE + Grimme D3 gives a negative interaction energy (the absolute value is also significantly smaller).

I was wondering whether this is a bug in the code? Would it be possible that the ghost atoms are not properly treated by the interface to the DFTD4 library?

I would be very grateful for some feedback.

Thanks in advance and all the best,

Holger 

[Quentin Pessemesse]

Hi Holger,

Counterpoise correction is a correction to the electronic energy, you should reason only on the electronic energies. The dispersion energy of the isolated fragments has no physical meaning, and the D3/D4 empirical correctoin plays no part in the BSSE as it is added after the SCF, and only depends on the geometry.

Here, I think CP2k is giving dispersion correction to the ghost atoms, calculating both the error that comes from basis functions of fragment being used to build the density of fragment B (BSSE), and adding some dispersion energy of the fragments and total system as well.

Instead of :

BSSE = (EA − EA(B)) + (EB − E (A)B)

You get:

([E(elec)A + E(disp)A] - [E(elec)A(B) - E(disp)AB]) + ([E(elec)B + E(disp)B] - [E(elec)(A)B - E(disp)AB]) = BSSE + (E(disp)A + E(disp)B - 2*E(disp)AB)

Try to run the BSSE single point calculation without the empirical dispersion and substract it from the interaction energy you get with D3/D3 correction. If it does not fix the issue, maybe I'm mistaken and something else is wrong.

Hope this helped :)

Q.

[Quentin Pessemesse]

Also, the order of magnitude of your "BSSE-corrected" interaction energy looks like the order of magnitude of E(disp)AB, which would make sense if the ghost atoms are not treated as ghost by the empirical dispersion correction

[Holger Sassnick]

Hi Quentin,

Thank you for the help and the swift response. You are right, the dispersion interaction of "ghost" atoms is (wrongly) added which leads to these unreasonable values. As far as I understand, I can just manually sum up the energy contributions of the fragments, replacing  the dispersion interaction energy with the one from the fragment without ghost atoms. Taking those total energy and calculating the interaction energy and BSSE-corrected total energy leads then to values similar to PBE or PBE-D3.

I think it would be also great if the implementation in CP2K could take care of ghost atoms and calculate all the fragment energies correctly as is done for the Grimme-D3 and other van der Waals corrections.

Have a great start to the week.

All the best,

Holger 

[Jürg Hutter]

Hi

thank you for bringing this to our attention. I have opened a bug report
on the CP2K github page.
https://github.com/cp2k/cp2k/issues
[CP2K:21126] Counterpoise correction with Grimme D4

regards
JH

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Sent: Monday, February 10, 2025 7:19 AM
To: cp2k
Subject: [CP2K:21130] Re: Counterpoise correction with Grimme D4

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[Holger Sassnick]

Hi Prof Hutter,

thank you for transferring the issue to the github repository. I was also wondering whether it would be reasonable and feasible to design a larger MOLOPT basis set with negligible BSSE. In this context I am also thinking about the training of MLPs, e.g. in this publication (https://pubs.acs.org/doi/10.1021/jacs.4c15287) trajectories were re-calculated with VASP for the training to ensure accurate results.

Fox example, in FHI-Aims the "tight" basis set parameters have hardly any BSSE. I know that the code uses a different localized basis set, so maybe this kind of accuracy cannot be reached with GTOs? I would be happy to hear your opinion on this matter.

All the best,

Holger

[Jürg Hutter]

Hi

the MOLOPT basis sets are optimized to perform for a wide range of
systems (molecules, solutes, solids, open structures), while keeping a
small number of functions for performance reasons.
BSSE is of similar size as for comparable size Gaussian basis sets.
For MD calclulation we tested and confirm that BSSE is typically
a constant shift on energies and does not affect dynamics.
If you want to have smaller/no BSSE you have to increase the
number of functions and e.g. include the atomic ground
state functions in the Basis (as in FHI-AIMS). There is the danger
that these near complete basis sets will perform poorly in dense
systems due to bad condition numbers.

regards
JH

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Sent: Thursday, February 13, 2025 11:14 AM
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Subject: Re: [CP2K:21142] Re: Counterpoise correction with Grimme D4

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[Holger Sassnick]

Hi Prof Hutter,

Thank you for the reply and insights. Unfortunately, I fear that the constant BSSE would still bias the sampling if the "binding energy" is part of the acceptance criteria to insert/delete a molecule in a MC scheme.

In FHI-Aims, (from my experience) even the larger basis sets seem to perform satisfactorily on molecular as well as dense systems. Do you think it would be worth a try to design, e.g., a QZVPP basis set to push the boundaries a bit?

I am not sure if that would be large enough to keep the BSSE on an acceptable level.

All the best,

Holger

[Jürg Hutter]

Hi
What type of system and BSSE values are you interested in? There is
a discussion on BSSE for Molopt basis sets in the original paper.
Results are for small molecule dimers.
See
J. Chem. Phys. 127, 114105 (2007) https://doi.org/10.1063/1.2770708
Section III D, Table VI
Molopt basis sets outperform normal Gaussian basis sets. However,
I don't know how the numerical basis sets look for these systems.

regards
JH

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Sent: Thursday, February 20, 2025 7:54 AM
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Subject: Re: [CP2K:21177] Re: Counterpoise correction with Grimme D4

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[Holger Sassnick]

Hi Prof Hutter,

in principle metalorganic frameworks with water adsorbed in the pores (like the attached input file of the initial post). The BSSE here is around 0.05 eV for one water molecule in the MOF. I am planning to train MLPs on the total energies that are in turn used in Monte Carlo simulations and the binding energy (MOF/H2O - MOF - H2O) is plugged into the criteria to accept or reject a deletion/insertion move. So I think I really need to ensure that the BSSE is very low in order to not bias the MC simulations.

Taking that into account, I see two options:

* Remove the BSSE via the Counterpoise correction on the whole training set. This would mean a multitude of calculations for each training point.

* Move to a plane-wave code.

I very much like CP2K since it is a very efficient code with extensive functionality. Thus, I was wondering whether it would be possible to have a basis set with negligible BSSE in CP2K.

All the best,

Holger

[Quentin Pessemesse]

Maybe I can add something: in my opinion going from DZVP/TZVP to QZVPP will greatly increase the computational cost of your calculation, especially on a large system, compared to adding counterpoise correction (which is just 2 single points). In addition to the pure scaling in BS size, you could also run into convergence issues which will be harder to solve compared to running counterpoise correction. 

Le 23 févr. 2025 à 11:03, Holger Sassnick <holger....@gmail.com> a écrit :

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[Jürg Hutter]

Hi

I assume that BSSE error is for the replacement of a single water within
the solvated MOF. BSSE in water systems are rather difficult to avoid
(see in the book of Koch & Holthausen pp 222/223).

I assume you can get decent results using the original Molopt basis sets
(in BASIS_MOLOPT - not sr types). Adding difuse sp functions would
then go to the limit. However, this will cost CPU time.

Another idea (empirical) would be to follow the work of Grimme on the -3c
methods. There BSSE for small basis sets is corrected using a pair potential.
You would have to get the parameters (Basis set and functional dependent)
yourself.
For applying it, see examples in the tests folder, e.g.
cp2k/tests/QS/regtest-hf-3c/*.inp

regards
JH

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Sent: Sunday, February 23, 2025 10:10 AM
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Subject: Re: [CP2K:21199] Re: Counterpoise correction with Grimme D4

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[Holger Sassnick]

Hi,

thank you for the valuable advice, I will read myself into the topic and check out the different approaches.

All the best,

Holger