Scale-free-modeling (harmonic) vibrational frequencies: Assessing accuracy and cost-effectiveness by CBS extrapolation

Abstract

Empirical scaling of calculated vibrational harmonic frequencies is a popular approach used in the field of molecular sciences. A nonempirical scheme that aims at reducing their basis set error is suggested here. Nearly as cost-effective as the scaled Kohn–Sham density functional theory (KS DFT), it consists of splitting the frequencies into Hartree–Fock and electron correlation contributions, followed by their extrapolation to the complete basis set (CBS) limit. Since the former converges exponentially, the overall cost may actually equal that of CBS extrapolation of the correlation part. Despite shifts in the molecular geometry during vibration, reasons are advanced to justify the approach, with extrapolation from the first two steps of the basis set ladder being effective in accelerating convergence. As benchmark data, a set of harmonic frequencies and zero-point energies for 15 molecules is employed at the second-order Moller–Plesset and coupled-cluster single double triple [CCSD(T)] levels of theory. The results outperform the optimized KS DFT scaled values. As a second test set, equilibrium structures and harmonic frequencies were computed for H2O2, CH2NH, C2H2O, and the trans-isomer of 1,2-C2H2F2. The results are also encouraging, particularly when improved for excess correlation at the CCSD(T)/V DZ level via the focal-point approach. In extreme cases, CBS extrapolation is done from two double- ζ calculations: one canonical and the other using explicit correlation theory. As a further case study, benzene is considered. While the CCSD(T) results show the smallest deviation from the best estimates, the MP2 results also attain good quality: When improved for excess correlation, they show 6–10 cm−1 errors relative to the best data, only slightly outperformed at the CCSD(T)/CBS level. Tentative results for the fundamental frequencies are also presented.