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Gas phase and surface reactions involving polyatomic molecules are of central importance to chemical physics, and require accurately fit potential energy surfaces describing the interaction in their systems. Here, we propose a method for generating a High Dimensional Model Representation (HDMR) of a multidimensional potential energy surface (PES) and apply it to reactive molecule-surface scattering problems. In the HDMR treatment, all N degrees of freedom (DOF) of an N-dimensional PES are represented but only n < N are explicitly coupled. The HDMR is obtained from Chebyshev polynomial expansions for each degree of freedom, where expansion coefficients are efficiently evaluated using discrete cosine transform (DCT) algorithms and properties of Chebyshev polynomials. HDMR surfaces constructed for the reactive scattering of H2 from Pt(111) and Cu(111) are used in quantum dynamics simulations; the resultant state-resolved reaction and scattering probabilities are compared to those from simulations using full (6D) PESs and n-mode PESs from previous work. The results are encouraging, and suggest that this method may be applicable to "late barrier" reactive systems for which the previously-used n-mode representation fails.
Thomas et al. (Sun,) studied this question.