Tightening the Screws: The Importance of Tight d Functions in Coupled-Cluster Calculations up to the CCSDT(Q) Level

It is well established that the basis set convergence of the correlation consistent (cc-pVnZ) basis sets depends on the presence of high-exponent "tight" d functions in the basis set for second-row atoms. The effect has been linked to low-lying 3d virtual orbitals approaching the valence shell. However, since most of this effect is captured at the self-consistent field level, the effect of tight d functions in high-level coupled-cluster calculations has not been extensively studied. Here, we construct an extensive data set of 45 second-row species to examine the effect of tight d functions in CCSD, CCSD(T), CCSDT, and CCSDT(Q) calculations in conjunction with basis sets of up to sextuple-ζ quality. The selected set of molecules covers the gamut from systems where the tight d functions play a relatively minor role (e.g., SiH, SH, SiF, PF₃, HOCl, Cl₂, and C₂Cl₂) to challenging systems containing a central second-row atom bonded to many oxygen or fluorine atoms (e.g., PF₅, SF₆, SO₃, ClO₃, and HClO₄) and systems containing many second-row atoms (e.g., P₄, S₄, CCl₄, and C₂Cl₆). In conjunction with the cc-pVDZ basis set, we find chemically significant contributions to the total atomization energies (TAEs) of up to ∼2 kcal/mol at the CCSD level, ∼1 kcal/mol at the (T) level, and contributions of up to ∼0.1 kcal/mol for the post-CCSD(T) components. The effects of the tight d functions are diminished with the size of the basis set; however, they are still chemically significant at the CCSD and (T) levels. For example, with the cc-pVTZ basis set, we obtain contributions to the TAEs of up to ∼1.5 and ∼0.3 kcal/mol at the CCSD and (T) levels, respectively, and with the cc-pVQZ basis set, we obtain contributions of up to ∼1.0 and ∼0.2 kcal/mol at the CCSD and (T) levels, respectively. We also find that a simple natural bond orbital population analysis of the 3d orbitals of the second-row atom provides a useful a priori indicator of the magnitude of the effect of tight d functions on post-CCSD(T) contribution to the TAEs in oxide and fluoride systems. These results are particularly important in the context of high-level composite ab initio methods capable of confident benchmark accuracy in thermochemical predictions.