Chemical waves three-dimensional

An alternative strategy is to synthesize a molecular wave function, on chemical intuition, and progressively modify this function until it solves the molecular wave equation. However, chemical intuition fails to generate molecular wave functions of the required spherical symmetry, as molecules are assumed to have non-spherical three-dimensional structures. The impasse is broken by invoking the Born-Oppenheimer assumption that separates the motion of electrons and nuclei. At this point the strategy ceases to be ab initio and reduces to semi-empirical quantum-mechanical simulation. The assumed three-dimensional nuclear framework is no longer quantum-mechanically defined. The advantage of this model over molecular mechanics is that the electron distribution is defined quantum-mechanically. It has been used to simulate the H2 molecule. 

For purposes of further analyses of detonation structure, the shock wave may be treated as a discontinuity. Both the viscous interaction between the shock and the reaction region and the molecular transport within the reaction region are small perturbations that do not appear to exert qualitatively significant influences on the wave structure. This conclusion appears to apply not only to steady, planar waves but also to unsteady, three-dimensional structures it affords one helpful simplification in the complicated analyses of transverse wave structures. It also alters the interpretation of a detonation as a deflagration-supported shock the support provided by the chemical reactions is of a nonplanar compressible gasdynamic character with negligible molecular transport. 

Winfree. A. T., and Strogatz, S. H. (1984) Organizing centers for three-dimensional chemical waves. Nature 311, 611. 

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