In this article, we investigate the effect of different types of atomic orbitals in the basis set on molecular vibrations by systematically including diffuse functions and polarization functions of different angular momentum to compute the quartic potential energy surface. The resultant harmonic and anharmonic frequencies from VPT2 calculations are compared against the converged basis set results from cc-pVnZ, with \(n = 2\) , 3, 4, 5 and 6. With a case study on a set of three molecules (formic acid, ethylene and trans-diazene) that represent the most common vibrations in organic molecules, the present study shows that the variations in frequencies correlate with the bond-dissociation energies for the stretching modes, implying the effect of different atomic orbitals on bond strengths. The results suggest that basis sets without polarization functions produce large deviations, which often increase with the inclusion of diffuse functions. The polarization d orbitals on second-row elements are essential for vibrational frequencies, and p orbitals on H atoms provide a more balanced description. A set of f orbitals improves the results only for the MP2 method and the B2PLYP methods. The 6-311G(df,p) basis set, despite being small in size, gives a better description of anharmonic effects compared to larger basis sets. The effects of the atomic orbitals are consistent for electronic structure methods.
Graphical abstract
The effect of different atomic orbitals on molecular vibrations is studied by systematically adding diffuse and polarization functions to compute the quartic potential energy surface. The polarisation p functions on H atoms and d functions on the second row elements are essential for a balanced description.
