TOPOLOGICAL ASPECTS OF THE CONFORMATIONAL STABILITY PROBLEM. PART I. DEGENERATE ELECTRONIC STATES1

Abstract

: ? : 8 8 9 2 ; enner electronic potential energy surfaces of symmetric polyatomic systems is derived by means of group theoretic and permutational symmetry principles. Degenerate penturbation theory is utilized to obtain an explicit analytical expression of this topography. The dependence of the nuclear-electronic interaction matrix elements, which occur in the penturbation development, on the nuclear coordinates is shown to be precisely determinable by group theoretic and permutational symmetry technlques. The numerical coefficients which prefix the nuclear coordinates which appear in these interaction matrix arrays are regarded as phenomenological parameters in their subsequent topographical applications. It is demonstrated that the magnitudes of these parameters determine only the relative placements of the Jahn-Teller- Renner surface reliefs and not their basic character (in this sense, minimal and maximal domains are taken to be of the same character). The formulas derived by means of the penturbation theory (with and without the complication of spin-orbit interactions) are employed to describe the topology of the multiply degenerate electronic energy surfaces of the regular polygons (including the digon) and the regular polyhedra, as well as of a number of selected highly symmetric irregular polygons and polyhedra. The results obtained reveal a number ofmore » important maxims: (1) the Jahn- Teller- Renner behavior of a polyatomic group theoretic system is completely determined by that of its elemental subgroups (principle of mathematical inheritance); (2) isomorphous point groups exhibit isomorphous Jahn- Teller deportments (formation of Jahn- Teller families); (3) whereas the prime number groups produce a single unique Jahn- Teller- Renner topography, the non- prime number groups produce all those topographies which are required by the principle of mathematical inheritance (1) (law of prime numbers); (4) the dynamical quantization and the topography of the Jahn-Teller problem are completely specified by group theoretic and permutational symmetry precepts (symmetrical transcendence); (5) although not mathematically required, the symmetry of the stable Jahn- Teller conformation is always the highest symmetry which is yet compatible with the loss of the initial inherent degeneracy (mimimax rule); (8) the Jahn- Teller- Renner energy resolvants factor only at locations of high nuclear symmetry (factorization theorem); (7) certain nuclear structures can never be JahnTeller stabilized (exclusion principle); (8) it is impossible to distinguish between ordinary anharmonic elastic distortions and Jahn-Teller distortions in non-homologous series of compounds (indistinguishability theorem), (9) spin-orbit forces remove cuspidal Jahn-- Teller radial electroric energy singularities for geometries less regular than the cube (spin-orbit law); (10) ionic and covalent bonding forces always produce complementary Jahn- Teller deformations, whereas conjugate hole-electron electronlc configurations always produce the identical deformation, bonding forces being equal (complementarity rules); (11) pseudo-JahnTeller interactions make conformational isomerisms possible even for dispositions of low regularity (conformational isomerization tenet); (12) doubly degenerate electronic states possess continuous Jahn- Teller- Renner electronic energy surfaces, but triply degenerate electronlc states possess disjoint electronlc energy surfaces in centain directions (canon of dimensional variability); (13) tetragonal Jahn- Teller conformational interconversion takes place in two dimensions for doubly degenerate electronic states, and five dimensions for triply degenerate electronlc states (doctrine of dimensional impenetrability); (14) experimental proofs of Jahn- Teller- Renner consequences can only be obtained from studies of homologous series of compounds (criterion of probity). Panticular care was taken to graphically illustrate all the important consequences of the« less