Peculiarities in the quantum statistics of π electron systems

Abstract

The peculiarities in the quantum statistics of π electron systems are analyzed by comparing π energies derived for the conventional fermionic (fe) ensemble with so-called hard core bosonic (hcb) energies. hcb ensembles combine fermionic on-site and bosonic intersite properties. They obey the Pauli exclusion principle (PEP) but not the Pauli antisymmetry principle (PAP). In the present study we extend our previous theoretical findings evaluated for one-dimensional (1D) model structures to 2D arrangements realized in hydrocarbon π molecules. Topological electronic ordering principles which have been derived for 1D order can be transferred to 2D networks. It is demonstrated that π systems are destabilized with increasing deviations from the hcb boundary. In the annulene series this destabilization occurs in the 4 n anti-Hückel rings ( n = 1, 2, 3,…). The competition between quantum constraints (PEP, PAP) and the two-electron interaction of π Hamiltonians on the energy of π systems is discussed. Numerical results are given for the Pariser-Parr-Pople, Hubbard and Hückel molecular orbital π Hamiltonians.