Extrapolation formula for basis set convergence

[Riccardo Pezzetta]

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

[Riccardo Pezzetta]

Sorry I wrote the wrong link for the article, the DOI is 10.1021/ct4002202

Riccardo Pezzetta

[Frederick Stein]

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]

Thank you for the answer.
Kind regards,

Riccardo Pezzetta