Bending vibration angular momentum

The bending vibration of a linear ABC molecule may be treated as a two-dimensional isotropic harmonic oscillator. The v,l) basis set is particularly convenient, where v and l are respectively the vibrational and vibrational angular momentum quantum numbers. The allowed values of l are —v, —v + 2,. .. v. Since there are two quantum numbers, two pairs of creation, annihilation operators are needed to generate all basis states from the v = 0, 1=0) zero-point state. These are, following the notation of Cohen-Tannoudji, et al., (1977), a, ay and at,a9, where... 

CH-bend quanta, and ii the vibrational angular momentum. Each overtone transition can be characterized by the quantum number IV = + 5 In these studies they found... 

In the harmonic approximation any vibrational state is defined by three vibrational quantum numbers Vx, V2, V3 of the corresponding modes and by the vibrational angular momentum 1 of the bending mode the state is denoted by... 

The second type of quantum monodromy occurs in the computed bending-vibrational bands of LiCN/LiNC, in which the role of the isolated critical point is replaced by that of a finite folded region of the spectrum, where the vibrational states of the secondary isomer LiNC interpenetrate those of LiCN [9, 10]. The folded region is finite in this case, because the secondary minimum on the potential surface merges with the transition state as the angular momentum increases. However, the shape of the potential energy surface in HCN prevents any such angular momentum cut-off, so monodromy is forbidden [10]. 

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