Harmonic Anharmonic Splitting

Some systems can be decomposed into a harmonic (quadratic) part Ho(q,p) = p M p/2 + q Aq/2 and an anharmonic part H q,p) = U q). Then a splitting method can be formulated based on exact solution of the linear system together with kicks representing impulses defined by the anharmonic part. For a simple system consisting of a harmonic oscillator Ho q,p) = -I- such a method can 

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A harmonic-oscillator level with a degenerate vibration excited consists of several state of varying symmetry. (Anharmonicity splits the degenerate harmonic-oscillator levels into closely spaced levels of different symmetry.) If two harmonic-oscillator levels have states whose symmetries are such that an IR transition is allowed between them, then a transition is allowed between the harmonic-oscillator levels. Which of the following methane vibrational transitions are allowed (a) (0000)->(0300) (b) (0000)- (0020) (c) (1010)—>(0112). 

In the following equations it will appear to be suitable to split the H-bond bridge Hamiltonian (14) into a harmonic part H° and an anharmonic perturbation VAnh, according to... 

HF/DZ frequencies by 10-20% while inclusion of polarization functions into a split valence or DZ basis set reduces the deviation to 10-15% The MP2/DZ + P frequencies agree with the measured ones within 5-10% °. The largest discrepancies between calculated harmonic (co,) and experimentally observed frequencies (v,) are found for the stretching motions, for which anharmonic effects are considerable. 

Regardingthe intensities, the transition dipole moment for a generic fundamental transition (Eq. 10.27) can be split into a doubly harmonic term (i.e., depending only on and co) and an anharmonic shift (depending also on and K),... 

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