# Is it good practise to mix double and triple zeta basis sets?

I need to compute extremely accurate single point energies using the coupled cluster method. The methods to be employed scale largely with the number of basis functions. A few basis functions may have a huge impact in the computational cost.

I planned assigning a 3ζ basis set to a central atom, and 2ζ for the surrounding atoms. I cannot compute everything at 3ζ.

Clearly, these small basis sets are intended for estimate the contribution of high excitation.

Are there any reason which prevent this mixture, or any argument supporting the usage of 2ζ for every atom?

It is perfectly fine, and actually quite common, to use big basis sets for the most important atoms (perhaps at the active site of the chemical reaction) and a smaller basis set for the surrounding hydrogen atoms (for example).

The only problem you might face would be, that this complicates the basis set extrapolation to get closer to the complete basis set limit. Such an extrapolation works best if you are, for example, extrapolating from 2Z & 3Z to infinity (not a mixed extrapolation such as 2Z/3Z & 3Z/4Z to infinity). In fact you won't be able to extrapolate because you likely won't be doing calculations with a 1Z basis set, and you won't be able to do a 3Z/4Z mix (because if you could do that, then you wouldn't need to mix 2Z into your 3Z calculation!).

I do want to point out that if you need to compute "extremely accurate single point energies" then even if you could use 3Z on the whole molecule, it would not likely even get you to 1 kcal/mol precision for energy differences. So as long as "extremely accurate" means in your context "+/- 10 kcal/mol for energy differences", you are doing everything just fine (and don't need a basis set extrapolation anyway). If you are aiming for better accuracy than that, you'll probably need a basis set extrapolation (meaning you want all atoms represented at 3Z level).

In the following reference a "mixed" basis set was used; in this paper TZP (3Z) is used for the atoms Fe, S, and Mo while SVP (2Z) is used for C, H, O, and N:

Li, Z.; Li, J.; Dattani, N. S.; Umrigar, C. J.; Chan, G. K. The electronic complexity of the ground-state of the FeMo cofactor of nitrogenase as relevant to quantum simulations. J. Chem. Phys. 2019, 150 (2), 024302. DOI: 10.1063/1.5063376.

Since the molecule is FeMoco (an iron-sulfur complex) it is likely that the Fe and S are very important (so they have a big basis set). It is also believed that the molybdenum (Mo) is important, because why else would a biological molecule have Mo in it, so it has a big basis set too. The rest have a small basis set.

• Thank you! I can compute the energy of these molecules up to something like CCSD(T)/aug-cc-pV5Z. The question is related to the tiny contribution of even higher excitations. Could you add a reference in which such mixing is done? Aug 22, 2019 at 3:28
• No, excuse me for the delay, I worked up to 2am tonight and from 7 to 18 today. I was completely out of time. Thank you very much for the reference. Aug 22, 2019 at 22:33
• I've corrected for def2-SVP, which is a double zeta basis set (i.e. split valence with polarisation functions). If 'extremely accurate' means +/- 10 kcal/mol for energy differences, then that is not accurate at all, and there wouldn't be any reason to run CC calculations. You'd get qualitatively better results with DFA. Aug 23, 2019 at 11:45
• @user1420303: How many spin orbitals (2x the number of spatial orbitals) do you have for the aug-cc-pV5Z calculation? If you can do CCSD(T)/aug-cc-pV5Z then with my program you might be able to do CCSDT(Q)/aug-cc-pVTZ (not with MRCC or other programs, but we are currently developing a powerful code that treats the matrices differently in RAM). Aug 25, 2019 at 23:51
• @user1420303: our software is currently being developed and is in the testing phase. We don't have any website yet unfortunately, we're just a small team but we are focused on HPC. If you can do CCSDT(2)_Q on NWChem, we can probably do CCSDT(Q) for you. This was already true for a system where we did CCSDTQ for 55 electrons. If we can do CCSDTQ for 55 electrons, we can do CCSDT(Q) for much more !! Aug 26, 2019 at 1:08