Interpolating moving least-squares (IMLS) methods are an accurate and reliable way for generating hypersurfaces from sparse calculations of points. IMLS generalizes the mathematical underpinnings of the popular Modified Shepard method used in chemistry for fitting potential energy surfaces (PESs) but, unlike that method, does not require gradients or Hessians of the surface for an accurate fit. In past years, joint work at our two institutions has shown how IMLS could be used to automatically fit PESs by directing electronic structure methods to perform calculations at IMLS-selected geometries. More recently, we are engaged in three projects. First, we have used IMLS to produce a new H2CN surface for future dynamics studies. The equilibrium and transition state frequencies of the IMLS fit favorably compare to those of the ab initio force field determinations. Classical trajectory computed dissociation rates converge rapidly with the number of included ab initio points. Second, we have incorporated gradients as well as energies into the IMLS framework. Since many electronic structure methods can produce the vector gradients at the same computational cost as the scalar energy the cost of producing a multidimensional IMLS fit could be dramatically reduced by incorporating gradients. Since the function minimized in the least squares step is composed of information (energies and gradients) with different units that affect minimization, scaling is an issue for gradient incorporation. Several scaling methods are being pursued and their implications for IMLS will be discussed. Third, we are developing a sequence of general automatic PES generation codes for posting on our web site.a These codes include permutation symmetry for the common case where the PES represents a system with chemically identical atoms, e.g., HOOH. Proper treatment of permutation produces proper fits with the added benefit of more compact basis sets that improve time to solution. These codes are being tested on analytic PES libraries such as POTLIB.b In the near future, the call to the analytic PES routine will be replaced by electronic structure calls for automatic generation of new PESs. In addition, with entire PES libraries as test beds, new basis sets, coordinate systems, and sampling methods for IMLS can be more universally and rigorously tested.
a
http://www.chem.missouri.edu/Thompson/SciDAC/index.htm
b
http://comp.chem.umn.edu/potlib