Basis sets optimized for CCSDT(Q) calculations

Question

CCSDT(Q) and CCSDTQ calculations are extraordinarily expensive, both in terms of FLOP count and RAM capacity requirements, eg. CCSDTQ requires a computational effort that scales as ~$N^{10}$, where N is the number of (contracted) basis functions. Given that, it is easy to see why running CCSDTQ calculations with fewer basis functions would be advantageous.

The obvious way to reduce N is to use a smaller basis set. While there is some evidence [1,2] that the CCSDT(Q)-CCSDT and especially the CCSDTQ-CCSDT(Q) contributions converge to the basis set limit faster than lower complexity contributions, CCSDT(Q)/cc-pVDZ can still be extremely demanding.

The other alternative would be to create basis sets optimized specifically for the purpose of post-CCSD(T) (CCSDT, CCSDT(Q), ...) calculations, with fewer contracted basis functions per atom. One could really crank up the number of primitive gaussians per basis function, if required, and integral evaluation time would still be utterly negligible compared to the time spent in the CCSDT(Q) code. Something like a hypothetical "ANO-CCQ" basis set might make CSSDT(Q) calculations more feasible.

My question is:

Has anyone ever developed or seen a basis set specifically optimized for post-CCSD(T) calculations?

Answer 1

To the best of my knowledge, there have not been basis sets optimized for post-CCSD(T) calculations. Note that the cc-pVXZ have been optimized using CISD. One would expect these to be also close to optimum for CCSD and beyond. We have played with optimizing basis sets at the CCSD(T) level, but they offer marginal improvement compared to the standard cc-pVXZ, and we have never published this.

Now I guess you are asking for optimizing the accuracy vs. effort for composite methods involving high-level CC, such as the Wn methods, i.e. using different basis sets for each higher CC-excitation level. Fundamentally one would not expect that e.g. the Q-contributions would have a lower basis set requirements than the SD contributions, if different, probably the Q-contributions would have a larger basis set requirement. But the absolute Q-contribution is much smaller than the SD-contribution, and one can thus tolerate a much larger relative Q-error for the same absolute error, and this is the argument for using small(er) basis sets for the higher CC-excitation levels. Another reason is of course that high CC-excitation levels are only possible in small(er) basis sets....

One could try to establish the 'optimum' basis set size for each CCSDnnn(m) level, and also perform explicit basis set optimization. This could be done analogous to the cc-pVXZ by calculating the energy contribution at a given CCSDnnn(m) level as a function of the basis set composition and exponents. This is certainly doable, but not a trivial endeavour, with the risk that the answer is that e.g. the standard cc-pVXZ or ANO are close to optimum.

It is difficult to believe that basis sets smaller than DZP quality can be used for high-CC excitations, as one anticipates that a balance between radial and angular correlation will be important, and e.g. the ANO includes a large number of primitive functions that likely effectively saturates the exponent space.