**C D Cooper and M S Child
**

Current highly successful effective Hamiltonian techniques for modeling Fermi and Darling-Dennison resonances etc rely on the strength of the underlying harmonic oscillator theory, which provides simple expressions both zeroth order energy expansions and intermode matrix elements. Such models can, however, never reproduce the near cusp-like variation in local level spacings arising from a potential barrier [1], nor the associated quantum monodromy [2], if angular momentum is included.
On the other hand our work on quantum monodromy provides detailed information on the quantum, classical and semiclassical dynamics for barrier containing models, such as the ˇchampagne bottle˘ [2,3] and ˇspherical pendulum˘ [2,4,5]. We have also devised a new approach to the accurate estimation of arbitrary matrix elements between the states of such systems [6]. Preliminary efforts towards combining these results, with a view to modeling the states of H2O at the barrier to linearity will be described.

**References**

1.R. N. Dixon, Trans. Far. Soc., 60, 1363 (1964)

2.M. S. Child, T. Weston and J. Tennyson, Mol. Phys., 96, 371 (1999)

3.M. S. Child, J. Phys. A, 31, 657 (1998)

4.M. P. Jacobson and M. S. Child, J. Chem. Phys., 114, 262 (2001)

5.M. P. Jacobson and M. S. Child, J. Phys. Chem. A, 105, 2834 (2001)

6.M. S. Child, M. P. Jacobson and C. D. Cooper, J. Phys. Chem. A, 105, 10791, (2001)