QUANTUM CONSTRAINTS IN PI-SYSTEMS - THE ROLE OF THE PAULI ANTISYMMETRY PRINCIPLE FOR PI-ELECTRONIC-PROPERTIES

It is demonstrated that the Pauli antisymmetry principle (PAP) is with out influence in the ii electron subspace of polyenes and (4n + 2) ann ulenes (n = 0, 1, 2...) as long as the hoppings are restricted to near est-neighbour centers. Here the ir electrons behave like a hard core b osonic (hcb) ensemble where fermionic on-site and bosonic intersite pr operties are combined. In 4n and (2n + 1) annulenes (n = 1, 2, 3...) p i electron jumps between the first and last ring atom lead to a Pauli antisymmetry-based destabilization. The second quantum constraint in f ermionic systems is the Pauli exclusion principle (PEP). In the many-e lectron basis adopted in the present work it is possible to treat the PAP and PEP as two decoupled constraints. The electronic destabilizati on due to the PEP is enhanced with increasing size of the system. The influence of the PAP and PEP on the n electrons is discussed in terms of ir energies and charge fluctuations. The model Hamiltonians adopted are of the Huckel 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.