In the literature, an F12 correction is reported as a single value, calculated at the CCSD(F12)/dawCV5Z level. This value was added as a final correction to the reported calculated IE (ionization energy).
I have my own calculated IE values for a range of basis sets (d-aug-cc-pwCVXZ where X=D,T,Q,5).
My question: How to apply an F12 correction from one basis set, to a basis set series?
Nowhere in the paper, nor in the Supplementary Material, does it show this formula, but I believe this is how their "F12 correction" is calculated:
$$\tag{1} E_{F_{12}-\textrm{correction} } = E_{\textrm{CCSD(F12)} } - E_{\textrm{CCSD} }. $$
If you add that energy to $E_{\textrm{CCSD} }$, you get $E_{\textrm{CCSD(F12)} }$.
Unfortunately they do not show any of the above three energies, and they only show the difference between the left-side energy for the neutral and charged species:
$$\tag{2} \Delta E_{F_{12}-\textrm{correction} } = \Delta E_{\textrm{CCSD(F12)} } - \Delta E_{\textrm{CCSD} }, $$
but again, adding the left-side ionization energy (or electron affinity) to the CCSD ionization energy (or electron affinity) will give you the corresponding CCSD(12) ionization energy (or electron affinity).
Turbomole is commercial software, but the Supplementary Material shows some calculations from the open-source Dalton software that can be compared, although only for closed shell systems like He, Be, Ne and ions, and you still have the problem (as described in the paper), that you'd be comparing calculations that used density-fitting, to calculations that did not.
Technically $E_{\textrm{CCSD(F12)} }$ and $E_{\textrm{CCSD} }$ were not entirely calculated using the same basis sets, since calculating $E_{\textrm{CCSD(F12)} }$ involved using auxiliary basis orbitals/geminals.
The quoted $\Delta E_{\textrm{CCSD(F12)} }/\textrm{d-aug-cc-pwCV5Z}$ energy can probably be added to the CCSD energy with any smaller basis set, but perhaps it would be ideal to calculate $\Delta E_{\textrm{CCSD(F12)} }$ individually for each X value in d-aug-cc-pwCVXZ. Since they didn't provide this data, unless you want to do F12 calculations, the easiest thing to do would be to use the following formula:
$$\tag{3} \Delta E_{F_{12}-\textrm{correction/d-aug-cc-pwCVXZ }} = \Delta E_{\textrm{CCSD(F12)/d-aug-cc-pwCV5Z } } - \Delta E_{\textrm{CCSD/d-aug-cc-pwCVXZ } }. $$
This won't work if X=100, because you would be adding a very big energy (the difference between an X=5 energy and a CBS estimate), to something that is already very close to the CBS limit. For this reason, using my Eq. 3 above may not work so well for lower values of X either, so ideally one would not "apply an F12 correction from one basis set, to a basis set series" but would rather calculate the F12 correction at each value of X.
The F12 methods are not add-ons to some other calculation. CCSD-F12 is a method in its own right. It cannot be calculated from a previous CCSD calculation.
