The hidden kernel of molecular quasi-linearity: Quantum monodromy

Abstract

Chain molecules with one low-lying bending mode provide a set of model species for the exploration of quantum monodromy in quasi-linear molecules. Recent work on water [N.F. Zobov et al., Chem. Phys. Lett. 414 (2005) 193–197] and NCNCS [B.P. Winnewisser et al., Phys. Rev. Lett. 95 (2005) 243002.] have shown that the topology of the energy–momentum maps of such molecules follows closely the predictions based on the mathematical concept of non-trivial monodromy. From existing data and new calculations which extrapolate beyond the existing data for several species, we can now present the topological properties of the bending-rotation energy–momentum maps of a range of molecules, from rigidly linear to rigidly bent. The generalized semi-rigid bender (GSRB) Hamiltonian used for the extrapolations is reviewed, and the mathematical concepts required to define the monodromy perspective are presented. Furthermore, it is shown that the energy–momentum map for the end-over-end rotational energy, represented by the effective rotational constant B or B ¯ , has previously unremarked properties which, like the basic bending-rotation energy–momentum map, are robust across the whole set of molecules studied. The molecules discussed are OCCCS, NCCNO, HCNO, OCCCO, ClCNO and BrCNO, NCNCS, HCCNCO, NCNCO and NCSCN.