A new method is suggested
for calculating the ratios of harmonic frequencies for certain types of molecules
and their isotopic forms by making use of Coriolis coupling constants. The
method applies to cases where there are two distinct degenerate vibrations with
the same species. The anharmonicity constants for these vibrations can then be
evaluated.
A study of the variation of the vibrational potential energy contribution with interbond angles in XY 3 pyramidal molecules confirms the observation previously made for XY 2 bend symmetric systems that the actual equilibrium configuration lies in the premises of minimum F bend and zero y stretch-bend * An analysis of the variation of the vibrational potential energy with geometry in simple molecules can be of fundamental interest and a mathematical formalism for this purpose has been developed recently [1]. The plots of various contributions to the potential energy V with semi interbond angle 9 in XY 2 bend symmetric systems seem to suggest that the actual equilibrium configuration lies in the premises of minimum for ^bend and zero for F bend _ stretch . Extension of the analysis to XY 3 pyramidal systems is discussed below.XY 3 pyramidal molecules belong to the C 3v point group, have the vibrational representation T = + 2E, and contributions to the potential energy come from stretching, bending, and different mutual interactions between the two. The recipe for plotting the potential energy contributions as a function of the semi interbond angle 9 is almost the same as given in the earlier work [1] except that here one has to deal with two vibrational species viz., A : and E, both of order two (as against one vibrational species of order two and one vibrational species of order one viz., A : and B ! in XY 2 bend symmetric systems).Fortunately, there are a few XY 3 pyramidal molecules in the literature for which the interbond angles are uniquely fixed and the normal and isotopic frequencies have been exactly determined [2], Moreover, these happen to be hydrides where the isotopic fre-1050
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