We present a general nonlinear inverse method utilizing discrete experimental data to extract inter- and intramolecular potential energy surfaces. The inverse method is formulated in terms of perturbation expansions of the experimental data upon the functional variations of the underlying potential energy surface--a functional sensitivity analysis approach. A distinction is drawn between the inverse method and the conventional parameter fitting procedure in that the former treats the potential energy surfaces as continuous functions of the internuclear coordinates, whereas the latter is based on restricted forms with a small number of parameters. The possible numerical instability of molecular nonlinear inverse problems is examined in detail using singular function expansion analysis and is overcome using the Tikhonov regularization method, which incorporates the a priori smooth properties of the sought-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 physically acceptable potential energy surfaces for a variety of problems--either spectroscopic or colloisional and one-dimensional or multidimensional. An example employing actual laboratory data has been successfully inverted. Application of the method to small polyatomic systems of current interest and improvement of the method by including higher-order sensitivity densities are also discussed.
All Science Journal Classification (ASJC) codes
- Physical and Theoretical Chemistry