A TOPOLOGICAL THEORY OF STEREOCHEMICAL STABILITY
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Date
1962
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Ohio State University
Abstract
The topography of electronic potential energy surfaces of polyatomic systems is derived by means of group theoretic and permutational symmetry principles. It is demonstrated that the relative placement of the surface reliefs may be completely specified by such principles for systems which contain sufficient numbers of identical nuclei. The results obtained reveal a number of important maxims: 1) the topography of a polyatomic electronic potential energy surface is completely determined by that of its most symmetric hypothetical geometry (law of eurythmy); 2) given a hypothetical geometry of high group theoretic symmetry, the topographical behavior of a polyatomic electronic potential energy surface is completely determined by that of its elemental symmetrical subgroups (principle of mathematical inheritance); 3) isomorphous group theoretical conformations exhibit isomorphous topological deportments (formation of topological families; 4) whereas the prime number groups theoretic constellations produce a single unique electronic potential energy topography, the non-prime number constellations produce all those topographies which are required by the principle of mathematical inheritance (2) (law of prime numbers); 5) the dynamical quantization and the topography of the electronic-nuclear problem are completely specified by group theoretic and permutational symmetry precepts (symmetrical transcendance); 6) certain nuclear structures can never be topologically stabilized without external aid (exclusion principle); 7) it is impossible to distinguish between ordinary anhamonic elastic distortions and Jahn-Teller distortions in non-homologous series of compounds (indistinguishability theorem); 8) experimental proofs of Jahn-Teller-Renner consequences can only be obtained from studies of homologous series of compounds (criterion of probity), Particular care has been taken to graphically illustrate all the important consequences of the mathematical derivations. So that their chief predictions should be available to theoretician and experimentalist alike. A discussion of the theoretical and experimental status of the electronic-nuclear problem is presented, and courses for future advance are sign-posted. A master plan is sketched for the solution of the numerous as yet unsolved theoretical and experimental electronic-nuclear puzzles.
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Author Institution: Bell Telephone Laboratories, Inc., Murray Hill, New Jersey and Mellon Institute