Is it possible to make segmented contracted basis sets for correlated calculations?

The segmented contracted basis sets are usually handled well by the QM programs than generally contracted basis sets, as the primitives are not repeated. The correlation consistent basis sets (cc-PVnZ) are all generally contracted, and optimized for electron correlation calculations such as CCSD.

Would it be possible to make segmented contracted basis sets that performed well for CCSD and other correlation methods? I have been told by my lecturer that in correlated calculations, the HF calculation is the fast step, so there is no real benefit to using segmented contraction. However, I am still curious as to whether it is possible, and if not then why?

However, as you (or your lecturer) said, segmented basis sets are much less beneficial for correlated calculations than SCF theory, since whereas SCF is usually dominated by the cost of forming the Fock matrix (i.e. calculating the two-electron integrals), in correlated calculations the cost of forming the integrals is often small compared to the post-HF calculation itself. For instance, the traditional AO $$\to$$ MO integral transform has a $$\mathcal{O}(N^5)$$ computational cost, while CCSD has an iterative $$\mathcal{O}(N^6)$$ computational cost.