A systematic theoretical study of harmonic vibrational frequencies: The ammonium ion NH4+ and other simple molecules

Analytic gradient techniques have been used to predict the harmonic vibrational frequencies of HCN, H2CO, H2O, CH4 and NH4+ at several levels of molecular electronic structure theory. Basis sets of double zeta, double zeta plus polarization, and extended plus polarization quality have been used in conjunction with self-consistent-field and configuration interaction methods. For the four spectroscopically characterized molecules, comparison with theory is particularly appropriate because experimental harmonic frequencies are available. For the 16 vibrational frequencies thus considered, the DZ SCF level of theory yields average errors of 166 cm−1 or 8.0%. The DZ+P SCF results are of comparable accuracy, differing on the average from experiment by 176 cm−1 or 8.3%. With the extended basis set, the comparable SCF frequency errors are only slightly less. The explicit incorporation of correlation effects qualitatively improves the agreement between theoretical and experimental harmonic vibrational frequencies. The DZ CI frequencies differ on the average by only 44 cm−1 or 2.0%. Perhaps surprisingly, the use of larger basis sets in conjunction with CI including all singly and doubly excited configurations leads to larger average errors in the vibrational frequencies. For example, the DZ+P CI frequencies have average errors of 80 cm−1 or 3.5%. Thus it seems clear that higher excitations (probably unlinked clusters especially) have a significant effect (order of 50 cm−1) on the theoretical prediction of polyatomic vibrational frequencies. The apparent discrepancy between the theoretical and experimental equilibrium geometry of CH4 is resolved here, and shown to have been a simple consequence of basis set incompleteness. Finally, the gas phase NH4+ equilibrium bond distance is predicted to be 1.022 Å, or 0.01–0.02 Å shorter than found by Ibers and Stevenson for NH4+ in crystalline NH4Cl and NH4F.