MATHEMATICAL CHEMISTRY, FROM DISCRETE TO CONTINUOUS AND BACK, WITHOUT INDISCRETION . . .
Presented by Prof. Paul MEZEY
Type: Oral presentation
The chemically important interrelations between discrete and continuous models of molecules and molecular fragments, such as functional groups, have received considerable attention recently. Some of the relations, discovered long ago, can be extended within a novel framework that allows the application of a wider range of mathematical tools, especially, those of algebraic and differential topology, connected to discrete mathematics including graph theory [1-8]. The underlying principle in these approaches is the unification of discrete and continuous models, and the “smooth” transformation between them. As a consequence of the specific nature of the interplay between the essentially particle-like nuclei and the fuzzy distributions of the electron density, their interrelations can be exploited within a dual, discrete-continuous framework, and new relations can be found using not only mutually complementing discrete and continuous models, but various “in-between” models based on fuzzy set approaches. The new results include systematic approaches to through-space and through-bond interactions, detailed analysis of substituent effects, simple derivations of new energy relations between molecules, as well as new algorithms for computational chemistry. References:  P.G. Mezey, The T-Hull Approach to Transformations of Discrete Point Sets to Continua and Shape Transformations Between Discontinuous Objects Using Alpha Hulls, J. Math. Chem., 27, (2000) 53-60.  P.G. Mezey, Fuzzy Electron Density Fragments in Macromolecular Quantum Chemistry, Combinatorial Quantum Chemistry, Functional Group Analysis, and Shape – Activity Relations, Accounts of Chem. Research, 47, (2014) 2821-2827 (invited paper).  P.L. Warburton, J.L. Wang, and P.G. Mezey, On the Balance of Simplification and Reality in Molecular Modeling of the Electron Density, J. Chem. Theory Comput. 4 (2008) 1627–1636.  P.G. Mezey, On Discrete to Continuum Transformations and the Universal Molecule Model - A Mathematical Chemistry Perspective of Molecular Families, AIP (American Institute of Physics) Conf. Proc. 963/2 (2013) 513-516.  Z. Antal, P. L. Warburton, and P. G. Mezey, Electron Density Shape Analysis of a Family of Through-Space and Through-Bond Interactions, Phys. Chem. Chem. Phys., 16 (2014) 918-924.  Z. Antal and P. G. Mezey, Substituent Effects and Local Molecular Shape Correlations, Phys. Chem. Chem. Phys., 16, (2014) 6666-6678.  P.G. Mezey, The Holographic Electron Density Theorem and Quantum Similarity Measures, Mol. Phys., 96, (1999) 169-178.  P.G. Mezey, Discrete Skeletons of Continua in the Universal Molecule Model, AIP (American Institute of Physics) Conf. Proc. 1504 (2012) 725-728.  P. G. Mezey, Compensation Effects in Molecular Interactions and the Quantum Chemical le Chatelier Principle, J. Phys. Chem. A, invited, Tomasi issue, published online, DOI 10.1021/jp5100044