Quantum Constraints in π Systems: The Role of the Pauli Antisymmetry Principle for π Electronic Properties

Abstract

Abstract It is demonstrated that the Pauli antisymmetry principle (PAP) is without influence in the π electron subspace of polyenes and (4n + 2) annulenes (n = 0, 1, 2...) as long as the hoppings are restricted to nearest-neighbour centers. Here the π electrons behave like a hard core bosonic (hcb) ensemble where fermionic on-site and bosonic intersite properties are combined. In 4n and (2n + 1) annulenes (n = 1,2, 3...) π electron jumps between the first and last ring atom lead to a Pauli antisymmetry-based destabilization. The second quantum constraint in fermionic systems is the Pauli exclusion principle (PEP). In the many-electron basis adopted in the present work it is possible to treat the PAP and PEP as two decoupled constraints. The electronic destabilization due to the PEP is enhanced with increasing size of the system. The influence of the PAP and PEP on the π electrons is discussed in terms of π energies and charge fluctuations. The model Hamiltonians adopted are of the Hückel molecular orbital (HMO) and Pariser-Parr-Pople (PPP) type. We suggest quantum statistical definitions of the quantities "aromaticity" and "antiaromaticity", qualitative descriptors which are widely employed in the chemical literature.