A general self-consistent-field tight-binding linear-combination-of-atomic-orbitals (LCAO) formalism is given for three-dimensional polymers containing many atoms in the elementary cell with all neighbors interacting, taking overlap explicitly into account. This formalism, which corresponds essentially to the formulation given by Roothaan for closed-shell molecules, has been developed with the aid of Hermitian complex matrices. The special cases of nearest-neighbor approximation and of a linear chain are then derived from the general expression obtained. Finally, formulas are given, again in complex-matrix formulation, for the dependence of the energy levels and wave functions of the polymer on the wave number k.

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Conceptual and mathematical difficulties arise in the study of transitions between vibronic states belonging to crossing Born᎐Oppenheimer hypersurfaces with significantly different positions and shapes of the minimum-energy nuclear configurations Ž . Duschinsky effect . This article presents an analytic procedure for the evaluation of the pertinent coupling integrals, adopting a normal coordinate reference system for the internal nuclear motion and harmonic approximation. The Duschinsky effect is properly considered. The procedure was applied to the dynamics of electron transfer in neutral mixed valence monoradicals, using the diabatic representation.

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The possibility that aromatic nitration proceeds via the formation of an electron donor−acceptor complex and its possible evolution in a “contact” radical pair is discussed on the basis of ab-initio configuration interaction computations on benzene/toluene NO2 + systems. The analysis of the region of the potential energy hypersurfaces corresponding to the two reactants kept at van der Waals distances shows the existence of a conical intersection between the ground state and the first excited charge transfer singlet, leading to electron transfer from the aromatic substrate to the nitronium ion. The activated state for electron transfer (ET) might then be identified with the “early” transition state invoked by Olah to explain the high positional selectivity of substitution in spite of a low substrate selectivity. The retention of positional selectivity at encounter-limited rates may then be ascribed to the fact that the formation of a Wheland intermediate corresponds to a radical pair recombination and as such is spin density driven. The objection that ET is a kinetically difficult step is met, the computed upper limit of the barrier to ET being 13 kcal/mol for the toluene substrate.

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The case for highly selective long range “proton assisted” electron transfer in biomolecules (PA-ET), involving the hopping of protons and hydrogen atoms along H-bond chains connecting two redox sites, is discussed and analyzed on systems closely resembling typical biochemical sequences. These systems consist of an electron acceptor, an H-bond/covalent-bridge chain and an electron donor, and monohydroparabenzoquinone as the electron acceptor and a xanthine-like molecule as the electron donor and acceptor species held together by one or more peptide bridges. It is shown that, in biochemical structures, despite the involvement of the imidol (oximine) form of the peptide link, (a) PA-ET is energetically efficient and (b) the rate constants for proton-transfer, which is arguably the rate-controlling step, are reasonably high, the transfer times being on the order of hundreds of picoseconds.