[CP2K-user] [CP2K:22225] Re: Extrapolation formula for basis set convergence

[Riccardo Pezzetta]

Thank you for the answer.
Kind regards,

Riccardo Pezzetta

Il giorno mercoledì 6 maggio 2026 alle 13:13:23 UTC+2 Frederick Stein ha 
scritto:

> Dear Riccardo,
> Both is possible. Keep in mind that it is an approximation anyways. The 
> correlation energies (without EXX) is described well by the given formula. 
> The other contributions (SCF, EXX) usually decay exponentially but for 
> simplicity, you may use the same formula as with RPA. As you can see, the 
> difference is quite small. Be aware that there is a variety of other 
> sources of errors (beyond-RPA corrections, vibrational corrections, 
> geometry, experimental errors, core corrections). From my experience, 
> higher order basis set corrections (X^-4-term) are roughly an order of 
> magnitude lower than the basis set correction itself, so are also at the 
> order of the deviation you observe between both results.
> Best,
> Frederick
>
> Riccardo Pezzetta schrieb am Mittwoch, 6. Mai 2026 um 12:42:16 UTC+2:
>
>> Sorry I wrote the wrong link for the article, the DOI is 10.1021/ct4002202
>>
>> Riccardo Pezzetta
>>
>> Il giorno mercoledì 6 maggio 2026 alle 12:37:59 UTC+2 Riccardo Pezzetta 
>> ha scritto:
>>
>>> Dear all,
>>> I am doing a calculation for the binding energy of the argon dimer with 
>>> RPA and I used as primary basis sets aug-cc-pVTZ and aug-cc-pVQZ. In the 
>>> CP2K maual I saw that I have to use the extrapolation formula E(X)=A+B/X^3 
>>> for correlation energies, but I don't know how to extrapolate the EXX 
>>> energy. In the article https://pubs.acs.org/journal/jctcce I saw that 
>>> they use the extrapolation formula for the cohesive energies instead of 
>>> correlation energies. So I tried to make the extrapolatoin in two ways:
>>> 1) I calculated the binding energy of the dimer with TZ and QZ basis 
>>> sets separately and made the cubic extrapolation with the resulting bonding 
>>> energies
>>> 2) I made the extrapolation with the cubic formula with absolute RPA and 
>>> EXX energies for the dimer and the atom separately and after that I 
>>> calculated the bonding energy with the extrapolated results.
>>> With the first method I get E bonding = -8.4 meV, with the second one I 
>>> get E bonding = -8.6 meV.
>>> Are these procedures correct? Since the results are similar can I deduce 
>>> that both methods are correct? In both cases the atom calculation has been 
>>> made with a ghost atom with the same geometry of the dimer in order to take 
>>> into account the basis set superposition error.
>>> Kind regards;
>>>
>>> Riccardo Pezzetta
>>
>>

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