The Role of Mathematics in the Experimental/Theoretical/Computational Trichotomy of Chemistry

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The drastically increasing availability of modern computers coupled with the equally drastically lower cost of a given amount of computer power in recent years has resulted in the evolution of the traditional experimental/theoretical dichotomy in chemistry into an experimental/theoretical/computational trichotomy. This trichotomy can be schematically represented by a triangle (the ETC triangle) with experimental, theoretical, and computational chemistry at the three vertices. The ET and EC edges of the ETC triangle depict the uses of theoretical and computational chemistry, respectively, to predict and interpret experimental results. The TC edge depicts the relationship between theoretical and computational chemistry. Mathematics plays an increasing role in all aspects of chemistry, particularly theoretical chemistry, and has led to the evolution of the discipline of mathematical chemistry. Research in mathematical chemistry can be considered to lie on a chemistry-mathematics continuum depending on the relative depths of the underlying chemistry and mathematics. Examples of the author's own research lying near each end of the chemistry-mathematics continuum include his work on applications of graph theory and topology in inorganic coordination and cluster chemistry lying near the chemistry end and his work on chirality algebra lying near the mathematics end. The general points in this essay are illustrated by an analysis of the roles of computational and theoretical chemistry in developing an understanding of structure and bonding in deltahedral boranes and related carboranes. This work has allowed extension of the concept of aromaticity from two dimensions as in benzene and other planar hydrocarbons to the third dimension in deltahedral boranes.

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