On the Ratio L 12 /L 21 For n = 2 Eigenvalue Problems: An Empirical Constraint For The Calculation of Force Constants (Extended L Matrix Approximation)

The variation of the ratio L 12 /L 21 (where L ij refers to the element of the L matrix) as a function of the mass coupling term T=G 12 /|G| 1/2 has been studied for molecules of the type XY 4 (Td), XY 3 (D 3h ) and XY 2 C 2v ) using the exact force field data. In the case of the XY 4 and XY 3 type molecules, the ratio L 12 /L 21 is nearly independent of the mass coupling and in the case of the XY 2 type, it shows a nearly linear dependence on T. The force constants have been evaluated using an empirically determined constraint for L 12 /L 21 . The values are generally in good agreement with the exact ones. In all cases except VCl 4 the exact interaction term of the F matrix is in agreement with the sign rule of Müller et al.