A b i n i t i o force field for the planar vibrations of benzene

A theoretical force field for in-plane vibrations of benzene has been determined from ab initio calculations at both the Hartree–Fock level with 4-21G, 6-31G, and 6-31G* basis sets and the MP2 level with 4-21G and 6-31G basis sets. The average error of the calculated frequencies at the MP2 level is between 2% and 3%. The reliability of the force field and vibrational frequency predictions of the calculations are analyzed. All diagonal stretching force constants obtained at the MP2 level are in quantitative agreement with Ozkabak–Goodman experimental force field, while the diagonal force constants involving ring deformation and CH rock are somewhat overestimated by the theory. Most of the off-diagonal force constants agree with the Ozkabak–Goodman results in sign but there are some significant quantitative differences in magnitude. Comparisons are made with other force fields, including results obtained by scaling ab initio calculations or introducing modified Hamiltonians. A simple extrapolation method for introducing correlation corrections into Hartree–Fock force constants gives excellent results for benzene.