Progress in the Physical Chemistry of Hypersonic Flows: A New Implementation of the Local Interpolating Moving Least Squares Method for Fitting Potential Energy Surfaces

Jason Bender, University of Minnesota

Understanding hypersonic reacting flows is crucial to the development of advanced aerospace technologies like new planetary re-entry systems and scramjet propulsion. The extreme nonequilibrium character of these flows, in which post-shock temperatures may reach as high as 20,000 K, presents significant computational modeling challenges both for fluid mechanics and physical chemistry. We are pursuing a fundamental study of key gas-phase chemical reactions in air at hypersonic speeds. Central to this effort is a collaboration between experts in compressible gas dynamics and computational chemistry.

A new global potential energy surface for the N4 supermolecule is presented. This work consisted of two major components. First, over 16,000 ab initio electronic structure calculations were performed using the CASSCF and CASPT2 methods for a range of geometric configurations encompassing the bond dissociation regimes. Then a six-dimensional potential energy surface was fit to the data. To accomplish this task, a new implementation of the Local Interpolating Moving Least Squares method was developed. The approach features two notable innovations: a new scheme for efficiently incorporating four-atom permutational invariance, and a localizing cutoff radius statistically correlated with a characteristic coordinate to reduce computational cost. The approach is highly accurate and well suited to a potential energy surface with rugged features. We discuss the performance of the method and possible directions for future work.

The completed N4 potential energy surface will be used to study vibrational energy transfer and dissociation from electronically adiabatic collisions, using quasiclassical trajectory techniques. Analogous efforts are also ongoing to model the N2O2 and O4 supermolecules. Our ultimate goal is to compute cross sections and reaction rates for use in state-of-the-art computational fluid dynamics simulations of hypersonic flows.

Abstract Author(s): Jason D. Bender, Sriram Doraiswamy, Yuliya Paukku, Zoltan Varga, Ke Yang, Graham V. Candler, Donald G. Truhlar