A systematic study on the basis set dependence of the Hartree-Fock, MP2 and CIS harmonic force fields and vibrational frequencies of formaldehyde in comparison with the experimental results

Abstract

The aim of this work was to find the limits of the vibrational frequency calculations by ab initio methods, in the framework of the harmonic frequency model and so find the possibility of eliminating the scaling of force constants. Therefore the efficiency of the different ab initio methods and basis sets were investigated from the point of view of vibrational frequency calculations. The applied methods were the Hartree-Fock (HF), the Møller-Plessett second-order perturbation (MP2) and the configuration interaction with first excited states (CIS). Sixteen different basis sets were applied from STO-3G to 6–311 + G ∗∗. The model molecule was formaldehyde. Equilibrium configurations and energies, vibrational frequencies and thermodynamic properties were calculated for all 48 cases. The results were compared to the harmonized experimental geometric parameters and the harmonized measured frequencies. According to the comparison the results of the MP2 method were found to be preferable. For good agreements the application of polarization functions, at least on the heavy atoms, is essential. Therefore the MP2/4-31G ∗ is the smallest basis set resulting in reasonable harmonic frequencies without any scaling. The increase in the number of Gaussian functions replacing a Slater-type orbital, the subsequent splitting of the valence orbitals and the addition of polarization functions on the hydrogens improve the agreement. The influence of the diffuse functions is not very large but excluding the CH stretching modes they improve the calculated frequency values in comparison with the harmonized experimental ones. In the case of the CH stretching modes the calculations with the basis set containing only polarization functions yield the best results. The minimal deviations from the harmonized frequencies are in the magnitude of 1 %, and for some normal modes they are smaller than 1 %.