Calculation of the Force Field for the Benzene Molecule by the Density Functional Method in the Dependent Natural Coordinates

The B3LYP method with the 6-311 + G** basic set is used to calculate normal vibrations of the benzene molecule and its two isotopes. An algorithm for calculating the force field in the dependent coordinates is described. An autoscaling method in the dependent natural coordinates is suggested. Scaling factors are calculated for four groups of natural coordinates. Their use provided good agreement between the calculated and experimental frequencies of plane and non-plane vibrations of the benzene molecule. The force field in the benzene molecule is calculated in the dependent natural coordinates. The problem of choosing the force field in the dependent coordinates is discussed.