Analysis of the FASSST rotational spectrum of NCNCS in view of quantum monodromy

Quantum monodromy has a strong impact on the ro-vibrational energy levels of chain molecules whose bending potential energy function has the form of the bottom of a champagne bottle (i.e. with a hump or punt) around the linear configuration. NCNCS, cyanogen iso-thiocyanate, is a particularly good example of such a molecule and clearly exhibits a distinctive monodromy-induced dislocation of the energy level pattern at the bending-rotation energy at the top of the potential energy hump. Indeed, NCNCS [B. P. Winnewisser et al., Phys. Rev. Lett. 2005, 95, 243002] and the water molecule [N. F. Zobov et al., Chem. Phys. Lett. 2005, 414, 193-197] were the first two molecules for which experimental confirmation of quantum monodromy was obtained. We used the fast scan sub-millimetre spectroscopic technique (FASSST) to extend the measurements and spectral analysis to pure rotational transitions (end-over-end) in bending vibrational states lying well above the monodromy point. The analysis of 9204 lines assigned to 7 vibrational states, presented here, shows that the topological properties of the bending potential function are mapped onto every aspect of the ro-vibrational energy levels involving excitation of the quasi-linear bending vibration. In order to model the large amplitude dynamics of such a molecular system, and also to achieve some insight beyond satisfactory parameters for reproducing the spectrum, we used the generalized semi-rigid bender (GSRB) Hamiltonian, which is described in some detail. This Hamiltonian provides a good description of the energy levels over the seven bending states observed, coming close to experimental accuracy. Due to high J values of the measured rotational transitions (J</= 116), the least squares fitting procedure was applied not directly to the measured frequencies, but to effective constants derived from fitting the transition frequencies to a set of polynomials in J(J + 1) yielding effective B(eff) and D(eff) constants. The GSRB wave functions are used to show that the expectation values of any quantity which varies with the large amplitude bending coordinate will also have monodromy-induced dislocations. This includes the electric dipole moment components. High level ab initio calculations not only provided the molecular equilibrium structure of NCNCS, but also the electric dipole moment components mu(a) and mu(b) as functions of the large-amplitude bending coordinate. Calculated expectation values of these quantities for individual ro-vibrational levels show the now recognizable monodromy pattern. Finally, a generalization of the quasi-linear parameter gamma(0) is suggested.

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