The Construction and Fitting of Molecular Potential Energy Surfaces and Their Use in Vibration-rotation Calculations zy B. T. SUTCLIFFE zyxw Department of Chemistry, University zyxwvu of York, Heslington, York YO1 5DD, England J. TENNYSON Department of Physics and Astronomy, University College London, Cower Street, London WCIE 6BT, England Abstract The state-of-the-art in non-empirical calculations of potential energy surfaces for small molecules is discussed, as is the present position with respect to the analytic fitting of such surfaces. The results of some nonempirical vibration-rotation calculations performed zyxw on such analytic surfaces are presented and compared with experimental results. An attempt is made to assess the extent to which present methods of electronic structure calculation and present analytic fitting methods are adequate to produce surfaces for the interpretation of high-resolution spectral data. Introduction In the past decade computational quantum chemistry has developed, as com- puters have developed, to the position where it is possible, almost as a matter of routine, to obtain very accurate and extensive potential energy surfaces from electronic structure calculations for systems consisting of 3 or zyx 4 nuclei and up to about 10 electrons. There have also been parallel developments in the rather less accurate calculation of such surfaces for larger systems with more nuclei and more electrons. It is, however, the first sort of calculation on which interest will be centered in this paper, for it is these calculations that offer the best basis for nonempirical calculations of whole-molecule wave functions; that is, calculations of not only electronic structure but of nuclear motion behavior too. The interest in such calculations lies not only in the role that they play in interpreting the rotation-vibration spectra of molecules, but also in the role that they might play in understanding chemical reactions. Thus, if one could find methods of dealing with very highly excited vibration and rotational states, where the molecule is on the verge of dissociation, then one would be ap- proaching from below the elusive region of chemical reaction, which is ap- proached from above by scattering and collision theory. The work described in this article represents only a modest step toward the International Journal of Quantum Chemistry: Quantum Chemistry Symposium 20,507-520 (1986) zy 0 1986 by John Wiley zyxwvuts & Sons, Inc. CCC 0360-8832/86/010507- I4$04.00