Bc. Hathorn et Ra. Marcus, Estimation of vibrational frequencies and vibrational densities of states in isotopically substituted nonlinear triatomic molecules, J PHYS CH A, 105(23), 2001, pp. 5586-5589
For use in unimolecular reactions, a simple method is introduced for obtain
ing the unknown vibration frequencies: of the many asymmetric isotopomers o
f a molecule from those of the symmetric ones. The method is illustrated fo
r a triatomic molecule XYZ, ozone. It is based on the neglect of a single G
;matrix element in the GF expression for XYZ, yielding for it a block-facto
red expression of the XYX type for the frequencies of all the isotopomers X
YZ. It agrees with available data to the accuracy needed, a few cm(-1). The
first-order perturbation vanishes. (The zeroth-order case is not a symmetr
ic molecule since it contains all three masses.) PL Simple second-order per
turbation result for-the GF matrix using data for one asymmetric isotopomer
then provides agreement to about 1 cm(-1). The virtues of the method are i
ts simplicity, transparency, and,novelty, though normally one would use muc
h more general methods such as ASYM 20 or 40. The method itself is not rest
ricted to triatomic molecules.