Monodromy of the LiNC/NCLi molecule

Using the potential surface of Essers, Tennyson, and Wormer in [Chem. Phys. Lett. 89 (1982) 223], we show that the system of bending vibrational states of the isomerizing molecule LiNC/NCLi has monodromy. On the basis of a deformed spherical pendulum model, we explain dynamical and geometric reasons of this phenomenon and of its absence in the similar system HCN/CNH. 2003 Elsevier B.V. All rights reserved. Monodromy is an interesting property of certain quantum systems whose levels cannot be labeled globally by one set of quantum numbers. More precisely, even though such systems have no obvious subsystems, each with its own set of quantum numbers, quantized energy cannot be expressed as one smooth function of any quantum numbers. Dynamical meaning of this phenomenon can be uncovered [1,2] by analyzing monodromy of the corresponding classical analogue. For the details of the classical theory see [3] and references therein. * Corresponding author. E-mail addresses: [email protected] (M. Joyeux), [email protected] (D.A. Sadovski ı), j.tennyson@ ucl.ac.uk (J. Tennyson). 0009-2614/$ see front matter 2003 Elsevier B.V. All rights reserv doi:10.1016/j.cplett.2003.10.099 Monodromy is not uncommon. It has been found in several fundamental atomic and molecular systems, notably the perturbed hydrogen atom [4], Stark effect in rotating dipolar molecules [5], rotating quasi-linear triatomic molecules [6], systems with coupled angular momenta [7], and H2 [8]. Floppy triatomic molecules with linear equilibrium configuration(s) form another set of candidate systems with monodromy [9]. In this Letter, we describe monodromy of LiNC/NCLi. We compare this system to HCN/CNH, which we have analyzed recently in [10]. Our study of LiNC/NCLi uses the two-dimensional potential [14] which gives the energy of the LiNC configurations as function of the bending angle c and Li–NC stretch distance R for the length r of the N–C bond fixed at 2.186 bohr. We assume approximate separability of the two degrees of freedom corresponding to overall