Global analytical potential hypersurfaces for large amplitude nuclear motion and reactions in methane. I. Formulation of the potentials and adjustment of parameters to ab initio data and experimental constraints

Analytical representations of the global potential energy surface of XYn mo lecules are developed and applied to model the potential surface of methane in the electronic ground state. The generic analytical representation allo ws for a compact, robust, and flexible description of potentials fur XYn sy stems irrespective of the specific nature of the atomic interactions. The f unctions are global in that structures near several minima of the potential hypersurface as well as saddle points and dissociation limits are well des cribed. Clusters of atoms Y-n can be represented as well by this type of fu nction. Care is taken to implement conditions resulting from the symmetric group S-n and to construct positive definite bilinear forms of special func tional forms of certain coordinates (such as bond lengths and bond angles), in order to avoid artifacts in exceptional ranges of the potential hypersu rface. These special functional forms include intrinsic, symmetry allowed c ouplings between coordinates such as bending and stretching. We include lin ear potential terms in bond angle coordinates, which result in effectively quadratic potential terms for highly symmetric structures. True logical mul tidimensional 01-switching functions S-sw(r) of bond lengths r are used to interpolate between limiting ranges in the hypersurface. The particular for m S-sw(r) similar to exp(-(r(sw)/r)(nsw)) allows us to describe the potenti al as a multipole expansion representation in the lirlit of large r(ix). In the application to methane, first the representations are fitted to data f rom high level ab initio calculations using multireference configuration in teraction techniques. Additional conditions which help to improve the descr iption of experimental data are considered during the fit. Typically, these conditions involve some parameters or parameter groups and refer to the eq uilibrium geometry and harmonic force field. Other constraints apply to the energies of dissociation channels. We describe the model potentials METPOT 1 to METPOT 4 in the present work. (C) 1998 American Institute of Physics. [S0021-9606(98)01045-9].