Reproduced from:

M. M. Law, I. A. Atkinson and J. M. Hutson (eds.)

Rovibrational Bound States in Polyatomic Molecules

ISBN 0-9522736-6-7 © 1999, CCP6, Daresbury

This booklet was produced in connection with a CCP6 Workshop on ``Rovibrational Bound States in Polyatomic Molecules", which was held at the University of Aberdeen, Scotland on 11th - 14th April 1999. Each participant in the Workshop was invited to prepare a brief review of their field, with references to their own and related work. The articles should thus provide a good introduction to the field for workers outside it, and a useful update for those more directly involved.

The objective of the Workshop was to bring together the leading
specialists in the fields of rovibrational quantum calculation and
experimental spectroscopy to share ideas and expertise on the
challenging problems faced in dealing with wide-amplitude molecular
motion. Triatomic calculations are becoming routine (at least for
closed-shell systems), so this meeting focussed on tetraatomic and
larger molecules. The results of work in this field have not only
resolved difficult problems in the interpretation of high-resolution
molecular spectra but have also allowed the determination of accurate
potential energy surfaces (PESs) by fitting to such data. Conversely
the most rigorous tests of *ab initio* PESs depend on being able
to calculate accurate spectroscopic transitions based on the
potentials for comparison with experimental data.

In this volume, Handy reports on recent variational calculations on 3- and 4-atom systems (including in the former case systems with two or three coupled electronic surfaces) and discusses the major problem of representing the kinetic energy operator for molecules executing simultaneous rotation and vibration. This topic is also addressed in detail by Mladenovic, with applications to 4-atom systems. Full rovibrational variational calculations on 5-atom systems are even more computationally demanding and Tennyson and Xie report on progress towards significantly moderating this cost by taking advantage of the high symmetry of methane-like molecules. Van der Avoird and Wormer summarise recent investigations of the effects of internal motions in Van der Waals complexes with applications to Ar-CH and the water trimer. The computational cost of determining the (rotation-)vibration energy levels is dominated by the process of diagonalising (that is finding the eigenvalues of) the Hamiltonian matrix. Huang and Carrington compare several efficient iterative approaches to extracting the desired eigenvalues. This theme is continued later by Yu and Nyman who focus on spectral transformation and filter diagonalization methods. The `direct' method which also avoids the explicit storage and diagonalisation of very large Hamiltonian matrices is reviewed by Viel and Leforestier.

Given the severe technical challenges associated with exact
variational methods, there is wide scope for developing approximation
methods, especially for systems with more than four atoms. Halonen
describes a perturbation-resonance approach to describing
large-amplitude (intramolecular) vibrational motions using curvilinear
internal coordinates. The vibrational self-consistent field
approximation method is described by Carter and Bowman and then later
by Wright *et al.*; the former summarise results for molecular and
adsorbate systems with up to 18 (vibrational) degrees of freedom,
while the latter include discussion of lower-accuracy calculations on
a 3500-mode hydrated protein system. All the computational methods
discussed above are applied to finding excited vibrational energy levels.
If however only ground-state properties are required (such as rotational
constants or the zero-point energy) then a Diffusion Monte Carlo simulation
may be the most efficient method for large systems. This approach is described
by Clary with applications to highly non-rigid weakly-bound molecular clusters.

All the rovibrational energy level calculations discussed here depend
on the availability of a molecular potential energy
surface. Hutson discusses the current ``state of the art'' in determining
intermolecular potential energy surfaces from empirical data and
*ab initio* calculation. The tremendous progress in the understanding of
inter- and intra-molecular forces in the last decade has been the result
of combined advances in theory and experiment. Nesbitt describes recent
high-resolution infrared studies of Van der Waals clusters using supersonic
jet expansions and direct laser absorption whilst Callegari *et al.* summarise
work on the rovibrational spectroscopy of single molecules trapped
inside superfluid helium nanodroplets. Both these experimental papers
raise challenges to theoreticians, highlighting the value of workshops
such as these.

I hope that this booklet will bring some of the ideas and expertise gathered at this Workshop to a wider audience.

Although the Workshop's primary sponsor was CCP6, it also received support from the High Resolution Spectroscopy Group of the Royal Society of Chemistry and the Chemistry Department of the University of Aberdeen.

Mark M. Law

Aberdeen

April 1999

Tue Aug 17 18:54:52 BST 1999