ISSN:
0020-7608
Keywords:
π electron systems
;
quantum statistics
;
electronic counting rules
;
quantum Monte Carlo simulations
;
model Hamiltonians
;
Chemistry
;
Theoretical, Physical and Computational Chemistry
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
Notes:
The electronic properties of π systems are studied under special consideration of the quantum statistical constraints experienced by a fermionic ensemble. In a many-electron basis of atomic occupation numbers these constraints decompose into a formal on-site constraint and a formal intersite constraint. The on-site constraint can be equated with the 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 are suppressed. In this case the conventional fermionic statistics coincides with a mixed quantum statistics with fermionic on-site and bosonic intersite properties. Such a mixed statistics is realized in the π subspace of polyenes, (4n+2) Hückel annulenes (n=0, 1, 2,…) and the odd spin space of (2n+1) annulenes (n=1, 2, 3,…) if the π electron hoppings are restricted to nearest-neighbor centers. We discuss the topological conditions to conserve this statistical peculiarity at least approximately in two-dimensional (2D) π topologies. The quantities “aromaticity” and “antiaromaticity,” widely used in the chemical literature, are traced back to quantum statistical, topological, and molecular size considerations. The competition between the quantum constraints PEP and PAP, on the one hand, and the strength of the two-electron interaction in a given π Hamiltonian, on the other, is analyzed on the basis of Pariser-Parr-Pople (PPP), Hubbard (Hu), and simple Hückel molecular orbital (HMO) calculations. The influence of the PAP is reduced with increasing correlation strength while the influence 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. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 727-752, 1998
Additional Material:
11 Ill.
Type of Medium:
Electronic Resource
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