On the theory of molecule vibrations

In this contribution we review the known solutions for three types of triatomic molecules (linear symmetric A B A, linear asymmetric A B C, bent symmetric A B A), paying special attention for all intermediate analytical calculation which is usually absent in literature. The intermediate analytical calculation is of fundamental importance because it allows see what kind of assumption was done in the process of deriving a final result. Besides, it helps to gain a better insight into our analytical solution obtained for a linear symmetric tetra-atomic molecule A B B A, which we also submit in this paper. For this molecule we have calculated vibration frequencies of five normal vibrations.