Monodromy in the water molecule
نویسندگان
چکیده
The change in the energy level structure of a bent molecule as it starts to sample linear geometries has been discussed in terms of monodromy found in simple two-dimensional model problems. Infrared spectra of hot (T 3000 K) water are analysed for transitions involving states with high bending excitation which can sample linear HOH geometries. One hundred and thirty four new experimental energy levels are determined for bending states with 5 6 v269 including band origins for 7m2, 8m2 and 9m2. Plots of those levels with J = Ka show the characteristic rearrangement of energy levels predicted for a system displaying quantum monodromy. Quantum monodromy for water occurs about the m2 = 7, J = 0 level. The barrier to linearity in H2 O is estimated to lie at 11114 ± 5 cm . 2005 Elsevier B.V. All rights reserved.
منابع مشابه
Monodromy problem for the degenerate critical points
For the polynomial planar vector fields with a hyperbolic or nilpotent critical point at the origin, the monodromy problem has been solved, but for the strongly degenerate critical points this problem is still open. When the critical point is monodromic, the stability problem or the center- focus problem is an open problem too. In this paper we will consider the polynomial planar vector fields ...
متن کاملMonodromy in the spectrum of a rigid symmetric top molecule in an electric field
We show that for rigid symmetric top molecules in electric fields the phenomenon of monodromy arises naturally as a ‘‘defect’’ in the lattice of quantum states in the energy-momentum diagram. This makes it impossible to use either the total angular momentum or a pendular quantum number to label the states globally. The monodromy is created or destroyed by classical Hamiltonian Hopf bifurcations...
متن کاملCO2 molecule as a quantum realization of the 1:1:2 resonant swing-spring with monodromy.
We consider the wide class of systems modeled by an integrable approximation to the 3 degrees of freedom elastic pendulum with 1:1:2 resonance, or the swing-spring. This approximation has monodromy which prohibits the existence of global action-angle variables and complicates the dynamics. We study the quantum swing-spring formed by bending and symmetric stretching vibrations of the CO2 molecul...
متن کاملFractional bidromy in the vibrational spectrum of HOCl.
We introduce the notion of fractional bidromy which is the combination of fractional monodromy and bidromy, two recent generalizations of Hamiltonian monodromy. We consider the vibrational spectrum of the HOCl molecule which is used as an illustrative example to show the presence of nontrivial fractional bidromy. To our knowledge, this is the first example of a molecular system where such a gen...
متن کاملMonodromy 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 righ...
متن کامل