INVERSION OF EXPERIMENTAL-DATA TO EXTRACT INTERMOLECULAR AND INTRAMOLECULAR POTENTIALS

We present a general nonlinear inverse method utilizing discrete exper imental data to extract inter- and intramolecular potential energy sur faces. The inverse method is formulated in terms of perturbation expan sions of the experimental data upon the functional variations of the u nderlying potential energy surface-a functional sensitivity analysis a pproach. A distinction is drawn between the inverse method and the con ventional parameter fitting procedure in that the former treats the po tential energy surfaces as continuous functions of the internuclear co ordinates, whereas the latter is based on restricted forms with a smal l number of parameters. The possible numerical instability of molecula r nonlinear inverse problems is examined in detail using singular func tion expansion analysis and is overcome using the Tikhonov regularizat ion method, which incorporates the a priori smooth properties of the s ought-after potential energy surfaces. Numerical studies show that the iterative inversion procedure based on this inverse method is generic , efficient, and stable and is capable of accurately rendering physica lly acceptable potential energy surfaces for a variety of problems-eit her spectroscopic or collosional and one-dimensional or multidimension al. An example employing actual laboratory data has been successfully inverted. Application of the method to small polyatomic systems of cur rent interest and improvement of the method by including higher-order sensitivity densities are also discussed.