Quantum monodromy in the spectrum of H2O and other systems: new insight into the level structure of quasi-linear molecules

The concept of quantum monodromy is introduced to give insight into the energy levels of systems with cylindrically symmetrical potential energy barriers. The K structure of bending progressions of bent molecules and the pendular states of dipolar molecules in strong electric ® elds are taken as molecular examples. Results are given for a two-dimensional champagne bottle model, for six computed bending progressions for water taken from the compilation of Partridge and Schwenke and for the quantal spherical pendulum. Sharp changes in the energy level patterns around the barrier energy are related to changes in the forms of the relevant classical trajectories. Analytical insight into the mathematical origin of the monodromy are also given.