Calculation of internal valence force constants for XY 3Z ( C3v) molecules

Abstract

In this paper, a pure vibrational force field [K. Kuczera and R. Czerminski, J. Mol. Struct., 105 (1983) 269; K. Kuczera, J. Mol. Struct., 160 (1987) 159] is calculated for XY 3Z ( C 3v) molecules from the most reliable empirical and ab initio force constants in symmetry coordinates available in the literature. The molecules studied include the monohalomethanes H 3CZ and trihalomethanes HCY 3 (Z and Y = F, Cl, Br and I). This method allows us to reduce the 16 F R dependent constants to 12 F∗ R independent constants, the same as the number of F S ° independent symmetry force constants. This can be explained by the fulfillment of four relationships between the F∗ R values obtained from the sum rule in Kuczera's treatment. It is thus possible to assign numerical values for bending, bending-bending and bending-stretching force constants. The above-mentioned relationships can also be obtained from the interactions among the displacement coordinates associated with each force constant. In addition, we study the behaviour of the force constants as a function of the bond lengths, obtaining some empirical relations. We also analyze the effect of replacing the central atom by Si, Ge and Sn in the case of H 3CZ molecules.