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 XY3Z (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 H3CZ and trihalomethanes HCY3(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 H3CZ molecules.
Fernández-Liencres, M. P., Fernández Gómez, M., López González, J. J., & Rajamanickam, N. (1997). Calculation of internal valence force constants for XY3Z (C(3v)) molecules. Journal of Molecular Structure, 407(2–3), 101–116. https://doi.org/10.1016/S0022-2860(96)09738-4