Effects of non-local exchange functionals in the density functional theories for the description of molecular vibrations

In this work, we present a systematic study on the effect of non-local Hartree-Fock (HF) exchange term of density functional methods on the vibrational description of polyatomic molecules. Working with three different functionals PBE0, B3LYP, and B2PLYP, we find that the standard deviations of errors with different amounts of HF exchange term in the functionals are well fitted with cubic polynomials. Sensitivity of the accuracy of vibrational frequencies with the HF exchange differs for different types of vibrations (e.g., high energy hydrogen stretching modes, stretching modes, bending modes, etc.). The wavenumbers decrease systematically with the increasing HF exchange in the functional as a result of the decrease in the geometric parameters at the equilibrium structures. The changes in harmonic wavenumbers are significant, and the anharmonic corrections are much less affected. The magnitudes of minimum errors with optimum values of the HF exchange terms differ from the default formulation.