Modified Shepard interpolation based on second order Taylor series expansions has proven to be a flexible tool for constructing potential energy surfaces in a range of situations. Extending this to gas-surface dynamics where surface atoms are allowed to move represents a substantial increase in the dimensionality of the problem, reflected in a dramatic increase in the computational cost of the required Hessian (matrix of second derivatives) evaluations. This work demonstrates that using approximate Hessians derived from well known Hessian update formulae and a single accurate Hessian can provide an effective way to avoid this expensive accurate Hessian determination. [ABSTRACT FROM AUTHOR]
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