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