# Is this approximate equivalence table between Pople's basis sets and Jensen's DFT attuned polarization consistent basis sets (pcseg-n) correct?

I have some calculations results I runned previously using Pople's basis sets, mostly 6-311+G(d), under Gaussian09. These days I read some texts on Frank Jensen's family of polarization consistent, segmented basis sets, optimized for DFT (pcseg-0, pcseg-1, pcseg-2, pcseg-3, pcseg-4 and the respective augmented versions). Now I'm thinking about trying to reproduce my results using Jensen's basis set family and Gamess-US.

Said that, I'm not sure about the correspondence between the two sets. I understand in Pople's basis sets, for light elements (first 3 periods of the periodic table) it's common to see people using double zeta(DZ) 3-21G for rough calculations, and either double zeta 6-31G or triple zeta(TZ) 6-311G for more precise work. Both 6-31G and 6-311G can have up to two polarization functions (or none) and up to two diffuse functions (or none) associated, resulting in 2x3x3 = 12 combinations between them (not counting heavier elements, that would require f polarization orbitals). In the table 5 of Nagy, Balazs, and Frank Jensen. “Basis Sets in Quantum Chemistry.” Reviews in Computational Chemistry (2017): 93–150. Print., they group together 3-21G and pcseg-0; 6-31G(d), cc-pVDZ and pcseg-1; and 6-311G(2df), cc-pVTZ and pcseg-2. So I assume each basis set inside these 3 groups to be equivalent (but not sure). As pcseg-2 is the only triple zeta option, despite already falling in the range of f-polarized basis, I suppose that, to map these 12 Pople's basis into the respective Jensen's basis, I need some combination between pcseg-0, pcseg-1, pcseg-2, aug-pcseg-0, aug-pcseg-1 and aug-pcseg-2 over H and heavier atoms (6x6 = 36 possibilities). For me it's not trivial to choose which of the 36 Jensen's possibilities in this range best match the 12 Pople's ones not explicitly cited on the paper. My guess at the closest mapping between the 2 sets is as follow:

Type    POPLE's         DUNNING     JENSEN'S CLOSEST
DZ      3-21G                       pcseg-0 on all atoms?
DZ      6-31G                       ?
DZP     6-31G(d)        cc-PVDZ     pcseg-0 on H, pcseg-1 on heavier?
DZP     6-31+G(d)                   pcseg-0 on H, aug-pcseg-1 on heavier?
DZP     6-31G(d,p)                  pcseg-1 on H, pcseg-1 on heavier?
DZP     6-31+G(d,p)                 pcseg-1 on H, aug-pcseg-1 on heavier?
DZP     6-31++G(d,p)                aug-pcseg-1 on H, aug-pcseg-1 on heavier?
TZ      6-311G                      ?
TZ      6-311+G                     ?
TZP     6-311+G(d)                  pcseg-0 on H, aug-pcseg-2 on heavier?
TZP     6-311G(d,p)                 pcseg-1 on H, pcseg-2 on heavier?
TZP     6-311+G(d,p)                pcseg-1 on H, aug-pcseg-2 on heavier?
TZP     6-311++G(d,p)               aug-pcseg-1 on H, aug-pcseg-2 on heavier?
TZP     6-311G(2df)     cc-PVTZ     pcseg-2 on all


Is my reasoning sound and the proposed equivalence table correct, or did I get it all wrong? If wrong, could somebody please give the correct mapping from Pople's traditional basis sets to Jensen's optimized ones?

• My personal opinion is that Pople-basis sets should have left serious calculations ten years ago. That being said, I would ignore the previously used basis set and simply pick the basis based on the standard criterion: what is the best basis set that I can afford for the calculation that I want to do? If this does not meet publication-level accuracy, obtain more computational resources. I also would not mix basis sets, the risk for errors due to internal BSSE is too large. – TAR86 Mar 29 at 17:32
• @ksousa, since this question went 1 month with no upvotes and no answers, yet within 24 hours on Matter Modeling SE you got an answer from Frank Jensen himself (the inventor of the Jensen basis set you're trying to come up with), and this seems to have happened to you 3 times now, could you help us by writing an answer describing your experience, here? materials.meta.stackexchange.com/q/1/5 – user1271772 May 7 at 5:02
• Thank you @user1271772, I'll write it. If somebody else happens to stumble in the same problem and find this question, please don't use my attemped table. I got it mostly wrong. The correct table was given here. – ksousa May 7 at 22:51