A simple ‘range extender’ for basis set extrapolation methods for MP2 and coupled cluster correlation energies

We discuss the interrelations between various basis set extrapolation formulas and show that for the nZaPa and aug-cc-pVnZ basis set formulas, for n=4--6 their behavior closely resembles the Petersson (L+a)^{-3} formula with a shift a specific to the basis set family and level of theory. This is functionally equivalent to the Pansini-Varandas extrapolation for large L. This naturally leads to a simple way to extend these extrapolations to n=7 and higher. The formula is validated by comparison with newly optimized extrapolation factors for the AV{6,7}Z basis set pairs and literature values for {6,7}ZaPa. For L\geq5, the CCSD extrapolations of both the Schwenke and Varandas type are functionally equivalent to E(L)=E_\infty+A.(L-0.30)^{-3}, i.e., E(\infty)=E(L)+[E(L)-E(L-1)]/([(L-0.30)/(L-1.30)]^3-1)