Shepard interpolation

This type of weight was used in the first implementation of modified Shepard interpolation in the construction of PES. 

Shepard interpolation has been applied to several systems. Wu et al. have used it to construct the ground potential energy surface for the reaction CH4 -I- H -> CH3 -I- H2 [63]. Neural networks can be described as general, non-linear fitting functions that do not require any assumptions about the functional form of the... 

T. Ishida, G.C. Schatz, Automatic potential energy surface generation directly from ab initio calculations using Shepard interpolation A test calculation for the H2 -pH system, /. Chem. Phys. 107 (9) (1997) 3558-3568. 

Energy derivatives are essential for the computation of dynamics properties. There are several dynamics-related methods available in gamess. The intrinsic reaction coordinate (IRC) or minimum energy path (MEP) follows the infinitely damped path from a first-order saddle point (transition state) to the minima connected to that transition state. In addition to providing an analysis of the process by which a chemical reaction occurs (e.g. evolution of geometric structure and wavefunction), the IRC is a common starting point for the study of dynamics. Example are variational transition state theory (VTST [55]) and the modified Shepard interpolation method developed by Collins and co-workers... 

Gradient methods discussed above use a quadratic function (energy, gradient and approximate Hessian) to model the energy surface near the transition state. Distance-weighted interpolants provide a more flexible functional form that can interpolate arbitrarily spaced points with a smooth differentiable function. For a gradient-based optimization, the Shepard interpolation functions seem appropriate... 

In the Shepard interpolation method, the potential is written in the form... 

Crespos C, CoUins MA, Pijper E, Kroes GJ (2004) Application of the modified Shepard interpolation method to the determination of the potential energy surface for a molecule-surface reaction H2-b Pt(lll). J Chem Phys 120 2392... 

Dfaz C, Olsen RA, Busnengo HF, Kroes GJ (2010) Dynamics on six-dimensional potential energy surfaces for Hz/Cu(lll) Corrugation reducing procedure versus modified Shepard interpolation method and PW91 versus RPBE. J Phys Chem C 114 11192... 

Frankcombe TJ, CoUins MA, Worth GA (2010) Converged quantum dynamics with modified Shepard interpolation and Gaussian wave packets. Chem Phys Lett 489 242... 

Although the PES is uniquely expressed in Cartesian coordinates, the Shepard interpolation is done using internal coordinates to avoid ambiguities relating to the orientation of the system. Therefore, the data are first transformed from Cartesians to internal coordinates, the Shepard interpolation is then completed, and the potential and derivatives are finally transformed back to Cartesians. For a detailed description of how this is accomplished, see Kim et al. ... 

Shepard Interpolation Method for Generating Potential Energy Surfaces for Dynamics Calculations. 

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