NEW ASPECTS IN THE THEORY OF PI-ELECTRON SYSTEMS ON THE BASIS OF QUANTUM-STATISTICAL CONSIDERATIONS

The electronic properties of pi systems are studied under special cons ideration of the quantum statistical constraints experienced by a ferm ionic ensemble. in a many-electron basis of atomic occupation numbers these constraints decompose into a formal on-site constraint and a for mal intersite constraint. The on-site constraint can be equated with t he Pauli exclusion principle (PEP) while the intersite constraint can be equated with the Pauli antisymmetry principle (PAP). Under special molecular topologies the intersite constraints of fermion ensembles ar e suppressed. In this case the conventional fermionic statistics coinc ides with a mixed quantum statistics with fermionic on-site and bosoni c intersite properties. Such a mixed statistics is realized in the pi subspace of polyenes, (4n + 2) Huckel annulenes (n = 0, 1, 2, ...) and the odd spin space of (2 n + 1) annulenes (n = 1, 2, 3,...)if the pi electron hoppings are restricted to nearest-neighbor centers. We discu ss the topological conditions to conserve this statistical peculiarity at least approximately in two-dimensional (2D) pi topologies. The qua ntities ''aromaticity'' and ''antiaromaticity,'' widely used in the ch emical literature, are traced back to quantum statistical, topological , and molecular size considerations. The competition between the quant um constraints PEP and PAP, on the one hand, and the strength of the t wo-electron interaction in a given pi Hamiltonian, on the other, is an alyzed on the basis of Pariser-Parr-Pople (PPP), Hubbard (Hu), and sim ple Huckel molecular orbital (HMO) calculations. The influence of the PAP is reduced with increasing correlation strength while the influenc e of the PEP does not depend on this coupling parameter. The numerical results have been derived by Green's function quantum Monte Carlo (GF QMC) simulations. (C) 1998 John Wiley & Sons, Inc.