Transition state theory regularity

T. Komatsuzaki and R. S. Berry, Local regularity and non-recrossing path in transition state - a new strategy in chemical reaction theories, J. Mol. Struct. (Theochem) 506, 55 (2000). 

F. A Brief Comment on Semiclassical Theories Hierarchical Regularity in Transition States Concluding Remarks and Future Prospects Acknowledgments... 

The reactivity of the transition metals towards other elements varies widely. In theory, the tendency to form other compounds both in the solid state (for example reactions to form cations) should diminish along the series in practice, resistance to reaction with oxygen (due to formation of a surface layer of oxide) causes chromium (for example) to behave abnormally hence regularities in reactivity are not easily observed. It is now appropriate to consider the individual transition metals. 

We shall extensively employ the notation of graph theory it provides a powerful and elegant formalism for the description of both the structure of the discrete lattices on which the CA live, and the complete dynamics (he. the global state transitions) induced by those structures. Graph theory also allows the correspondence between CA configurations and the words of a regular language to be made in a very natural fashion. 

---