Relativistic Four-Component DFT Calculations of Vibrational Frequencies

We investigate the effect of relativity on harmonic vibrational frequencies. Density functional theory (DFT) calculations using the four-component Dirac-Coulomb Hamiltonian have been performed for 15 hydrides (H₂X, X = O, S, Se, Te, Po; XH₃, X = N, P, As, Sb, Bi; and XH₄, X = C, Si, Ge, Sn, Pb) as well as for HC≡CPbH₃. The vibrational frequencies have been calculated using finite differences of the molecular energy with respect to geometrical distortions of the nuclei. The influences of the choice of basis set, exchange-correlation functional, and step length for the numerical differentiation on the calculated harmonic vibrational frequencies have been tested, and the method has been found to be numerically robust. Relativistic effects are noticeable for the heavier congeners H₂Te and H₂Po, SbH₃ and BiH₃, and SnH₄ and PbH₄ and are much more pronounced for the vibrational modes with higher frequencies. Spin-orbit effects constitute a very small fraction of the total relativistic effects, except for H₂Te and H₂Po. For HC≡CPbH₃ we find that only the frequencies of the modes with large contributions from Pb displacements are significantly affected by relativity.