Assessment of CCSD(T)-F12 Approximations and Basis Sets for Harmonic Vibrational Frequencies Jan M. L. Martin* and Manoj K. Kesharwani Department of Organic Chemistry, Weizmann Institute of Science, 76100 Reh̲ ovot, Israel * S Supporting Information ABSTRACT: We consider basis set convergence and the effect of various approximations to CCSD(T)-F12 for a representative sample of harmonic frequencies (the HFREQ2014 set). CCSD(T*)(F12*)/cc-pVDZ-F12 offers a particularly favorable compromise between accuracy and computational cost: its RMSD <3 cm -1 from the valence CCSD(T) limit is actually less than the remaining discrepancy with the experimental value at the valence CCSD(T) limit (about 5 cm -1 RMSD). CCSD(T)-F12a and CCSD(T)-F12b appear to benefit from error compensation between CCSD and (T). ■ INTRODUCTION The importance of vibrational spectra in chemistry, biochem- istry, and chemical biophysics hardly requires elaboration. In recent years, CCSD(T) 1 anharmonic force fields have proven a powerful predictive spectroscopic tool. 2,3 Basis set convergence of CCSD(T) vibrational frequencies is fairly slow, 4-7 and hence, such force fields are computationally very expensive beyond very small molecules, although this is somewhat mitigated by the recent availability of CCSD(T) analytical second derivatives 8 in a parallel implementation. 9 One recent approach has been to combine CCSD(T) harmonic frequencies with a DFT anharmonic force field. 10,11 Another tack has been to carry out pointwise basis set extrapolations, as seen, e.g., in the work of Huang et al. 12-14 and in ref 15. Yet another tactic would be to speed up basis set convergence of the CCSD(T) part by means of explicitly correlated (F12) approaches: 16,17 for many applications, these offer quintuple-zeta or better results with triple-ζ sized basis sets, or more generally a gain by 2-3 “zeta steps.” Huang et al. 14 compared extrapolation and F12 techniques for quartic force fields of H 2 O, N 2 H + , NH 2 + , and C 2 H 2 and concluded that F12 is competitive and in some cases necessary. Rauhut et al. 18 carried out comparative CCSD(T) and CCSD(T)-F12{a,b} basis set convergence studies for harmonic frequencies of H 2 O, HCN, CO 2 ,C 2 H 2 , and H 2 CO, as well as compared conven- tional and explicitly correlated anharmonic frequencies with the aug-cc-pVTZ basis set 19 for the above molecules plus H 2 O 2 , CH 2 NH, and C 2 H 2 O: they conclude that the “two zeta gain rule” applies here as well and unreservedly advocate for explicitly correlated methods. Since, however, the full CCSD-F12 approach is both algebraically and computationally very involved, 20 and no practical implementation of CCSD(T)-F12 without any approximations is available, one now needs to pay heed not only to the choice of the basis sets but also to the choice of the specific approximation made. Werner and co-workers proposed 21,22 the CCSD-F12a and CCSD-F12b approximations, which they implemented in the popular MOLPRO package: 23 more recently, Hä ttig et al. proposed 24 the CCSD(F12*) approximation (a.k.a., CCSD- F12c) which offers CCSD(F12) 25,26 quality at a cost comparable to that of CCSD-F12b. It should be noted here that the CCSD-F12b approximation includes a subset of terms from CCSD(F12*) and CCSD-F12a likewise from CCSD- F12b; thus, CCSD-F12a, CCSD-F12b, and CCSD(F12*) can be considered a hierarchy of increasingly rigorous approx- imations to CCSD-F12. In the present work, we will consider basis set convergence of harmonic frequencies using different approximations to CCSD- (T)-F12 for a medium-sized benchmark set of small molecules (HFREQ2014) selected and expanded from our earlier HFREQ27 set. 27 We will show that CCSD(T*)(F12*)/cc- pVTZ-F12 and especially CCSD(T*)(F12*)/cc-pVDZ-F12 offer particularly cost-effective means of calculating reliable vibrational spectra. ■ COMPUTATIONAL DETAILS Most calculations were carried out using MOLPRO 2012.1 23 running on the Faculty of Chemistry HPC cluster at the Weizmann Institute of Science. Some additional calculations were performed using Turbomole 6.5 28 running on the same platform. In most calculations, we employed the cc-pVnZ-F12 correlation consistent basis sets (n = D,T,Q) optimized for F12 calculations 29 and the auxiliary basis sets 30 and CABS Received: February 27, 2014 Published: April 8, 2014 Article pubs.acs.org/JCTC © 2014 American Chemical Society 2085 dx.doi.org/10.1021/ct500174q | J. Chem. Theory Comput. 2014, 10, 2085-2090