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-zeta 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, Cl-2, 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., P-4, S-4, 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 similar to 2 kcal/mol at the CCSD level, similar to 1 kcal/mol at the (T) level, and contributions of up to similar 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 similar to 1.5 and similar to 0.3 kcal/mol at the CCSD and (T) levels, respectively, and with the cc-pVQZ basis set, we obtain contributions of up to similar to 1.0 and similar to 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.

Automated summary

The tight d functions have a significant chemical contribution to the total atomization energies in high-level coupled-cluster calculations, particularly at the CCSD and (T) levels. The study of 45 second-row species demonstrates the important influence of tight d functions on the 3d orbitals and total atomization energies of second-row atoms. Additionally, a simple natural bond orbital population analysis of the 3d orbitals provides a useful predictor for the impact of tight d functions on the post-CCSD(T) contribution to the total atomization energies.