Perturbation theory anharmonic vibrational spectroscop

The basic theory of vibration-rotation of polyatomic molecules has been worked out for many years, including the form of the vibration-rotation Hamiltonian, the quantum mechanical solution of certain anharmonic oscillators," and the relationship, in terms of perturbation theory,between experimental spectroscopic data and higher than quadratic terms in the potential function. Still, prediction of harmonic... 

Purely quantum studies of the fully coupled anharmonic (and sometimes nonrigid) rovibrational state densities have also been obtained with a variety of methods. The simplest to implement are spectroscopic perturbation theory based studies [121, 122, 124]. Related semiclassical perturbation treatments have been described by Miller and coworkers [172-174]. Vibrational self-consistent field (SCF) plus configuration interaction (Cl) calculations [175, 176] provide another useful alternative, for which interesting illustrative results have been presented by Christoffel and Bowman for the H + CO2 reaction [123] and by Isaacson for the H2 + OH reaction [121]. The MULTIMODE code provides a general procedure for implementing such SCF-CI calculations [177]. Numerous studies of the state densities for triatomic molecules have also been presented. 

Another manifestation of vibrational anharmonicity occurs in Fermi resonance [8]. When two vibrational states of the same overall symmetry are accidentally degenerate, they can become strongly mixed by the anharmonic coupling terms between them. Their energies may be repelled considerably (in the language of degenerate perturbation theory), and the intensities of the spectroscopic transitions to these levels may be redistributed by the mixing. 

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