Ruth L. Jacobsen, Karl K. Irikura, Russell D. Johnson, and Raghu N. Kacker

            Determining molecular vibrational frequencies is critically important to solving problems in chemistry, physics, biology, and other fields. In computational quantum chemistry, harmonic and anharmonic methods based on modestly accurate electronic structure models are commonly used to estimate these frequencies. The anharmonic methods are expected to be more accurate than the harmonic ones, although they are significantly more expensive. In addition, to reproduce experimental frequencies with spectroscopic accuracy, both types of calculations need to be scaled with empirical factors. Since both types of calculations are adjusted empirically, is it worthwhile to use anharmonic methods to estimate these frequencies instead of harmonic methods, which are significantly cheaper?

            To answer this question, we compare the accuracy of harmonic and anharmonic (obtained using second-order vibrational perturbation theory) predictions from Hartree Fock theory, second-order perturbation theory, and density functional theory combined with 6-31G(d) and 6-31+G(d,p) basis sets. Comparisons of harmonic and anharmonic root-mean-square deviations obtained from differences between calculated and experimental frequencies show that scaled harmonic and scaled anharmonic predictions are most often equally reliable. The data used are from the NIST Computational Chemistry Comparison and Benchmark Database (CCCBDB),[1] which includes more than 3939 independent vibrations for 358 molecules.

[1] R. D. Johnson III, NIST Computational Chemistry Comparison and Benchmark Database, Release 15b; NIST Standard Reference Database Number 101, August 2011.