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The convergence of undamped, inverse power series asymptotic van der Waals expansions for the hydrogen molecule is tested. The role of this kind of expansion in the description of global potential energy surfaces for strongly bound molecules is discussed. The single-bond breaking dissociation channel of the water molecule is shown to display the same behaviour. It is suggested that such expansions do not provide a good starting point for this problem as they only become reliable when the interaction energy is very small. [ABSTRACT FROM AUTHOR]

This paper presents an overview of R-matrix theory of electron scattering by diatomic and polyatomic molecules. The paper commences with a detailed discussion of the fixed-nuclei approximation which in recent years has been used as the basis of the most accurate ab initio calculations. This discussion includes an overview of the computer codes which enable electron collisions with both diatomic and polyatomic molecules to be calculated. Nuclear motion including rotational and vibrational excitation and dissociation is then discussed. In non-resonant energy regions, or when the scattered electron energy is not close to thresholds, the adiabatic-nuclei approximation can be successfully used. However, when these conditions are not applicable, non-adiabatic R-matrix theory must be used and a detailed discussion of this theory is given. Finally, recent applications of the theory to treat electron scattering by polyatomic molecules are reviewed and a detailed comparison of R-matrix calculations and experimental measurements for water is presented. [ABSTRACT FROM AUTHOR]

Relative equilibria of molecules are classical trajectories corresponding to steady rotations about stationary axes during which the shape of the molecule does not change. They can be used to explain and predict features of quantum spectra at high values of the total angular momentum J in much the same way that absolute equilibria are used at low J. This paper gives a classification of the symmetry types of relative equilibria of AB[sub 2] molecules and computes the relative equilibria bifurcation diagrams and normal mode frequencies for D[sub 2] H[sup +] and H[sub 2] D[sup +] . These are then fed into a harmonic quantization procedure to produce a number of predictions concerning the structures of energy level clusters and their rearrangements as J increases. In particular the formation of doublet pairs is predicted for H[sub 2] D[sup +] from J 26. [ABSTRACT FROM AUTHOR]

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 fields 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. [ABSTRACT FROM AUTHOR]