Effective basis set extrapolations for CCSDT, CCSDT(Q), and CCSDTQ correlation energies

It is well established that extrapolating the coupled-cluster single double triple [CCSD and (T)] correlation energies using empirically motivated extrapolation exponents can accelerate the basis set convergence. Here, we consider the extrapolation of coupled-cluster expansion terms beyond the CCSD(T) level to the complete basis set (CBS) limit. We obtain reference CCSDT-CCSD(T) [T₃-(T)], CCSDT(Q)-CCSDT [(Q)], and CCSDTQ-CCSDT(Q) [T₄-(Q)] contributions from cc-pV{5,6}Z extrapolations for a diverse set of 16 first- and second-row systems. We use these basis-set limit results to fit extrapolation exponents in conjunction with the cc-pV{D,T}Z, cc-pV{T,Q}Z, and cc-pV{Q,5}Z basis set pairs. The optimal extrapolation exponents result in noticeable improvements in performance (relative to α = 3.0) in conjunction with the cc-pV{T,Q}Z basis set pair; however, smaller improvements are obtained for the other basis sets. These results confirm that the basis sets and basis set extrapolations used for obtaining post-CCSD(T) components in composite thermochemical theories such as Weizmann-4 and HEAT are sufficiently close to the CBS limit for attaining sub-kJ/mole accuracy. The fitted extrapolation exponents demonstrate that the T₃-(T) correlation component converges more slowly to the CBS limit than the (Q) and T₄ terms. A systematic investigation of the effect of diffuse functions shows that it diminishes (i) in the order T₃-(T) > (Q) > T₄-(Q) and (ii) with the size of the basis set. Importantly, we find that diffuse functions tend to systematically reduce the T₃-(T) contribution but systematically increases the (Q) contribution. Thus, the use of the cc-pVnZ basis sets benefits from a certain degree of error cancellation between these two components.