 1  Author
 MichaelC. Böhm, Johannes Schütt  Requires cookie*   Title
 On the Role of the Pauli Antisymmetry Principle in Pericyclic Reactions    Abstract
 In the present work we discuss the role of the Pauli antisymmetry principle (PAP) in synchronous pericyclic reactions. These reactions are allowed in the electronic ground state whenever the PAP does not act as a quantum constraint in the transition state. The possible suppression of the influence of the PAP is a peculiarity of Tr electron systems. The PAP is a hidden (= deactivated) variable in the 7t electron subspace of polyenes and (An + 2) annulenes (n = 0, 1, 2,...). In An annulenes (n = 1, 2, 3,...) it leads to minority signs in the kinetic hopping matrix of the 7r electronic wave function and thus to an energetic destabilization. The quantum statistical difference between the above families of 7r systems renders possible a microscopical definition of the quantities "aromaticity" and "antiaromaticity". The sign behaviour of the kinetic hopping elements is used in the discussion of pericyclic reactions. The present quantum statistical description of these reactions is related to the DewarZimmermann and WoodwardHoffmann rules.   
Reference
 Z. Naturforsch. 52a, 727—738 (1997); received September 4 1997   
Published
 1997   
Keywords
 IT Electron Systems, Pericyclic Reactions, Quantum Statistics, Pauli Antisymmetry Principle   
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2  Author
 MichaelC. Böhm, Christoph Saal  Requires cookie*   Title
 On a Direct Superconducting Pairing Mechanism    Abstract
 We suggest that superconductivity can be traced back to a firstorder interaction between the charge carriers which does not necessarily involve secondorder electronphonon coupling. For small molecular model systems it is demonstrated that the formation of Cooper pairs can lead to an attenuation of the destabilizing influence of the Pauli antisymmetry principle (PAP). We suggest that this attenuation of a fermionic quantum constraint is the driving force for the superconducting transition. Whenever the PAP is activated in singleparticle hoppings of electrons, the corresponding moves reduce the electronic derealization; they raise the ensemble energy. The stability of a fermionic system is enhanced with decreasing influence of the PAP. Moves of Cooper pairs are not influenced by any quantum constraint of the intersite type. This behaviour differs from the wellknown fermionic constraints. The quantum statistics of Cooper pairs is of a mixed type combining a fermionic onsite and a bosonic intersite behaviour. It coincides with the quantum statistics of socalled hard core bosonic ensembles. In the present work Cooper pair formation has been studied for smaller molecular models. The electronic Hamiltonian employed is of the twoparameter Hubbardtype. The solid state phenomenon superconductivity is correlated with the molecular concepts of "antiaromaticity" and "aromaticity". Arguments are given which support the present interpretation.   
Reference
 Z. Naturforsch. 54a, 718—738 (1999); received May 26 1999   
Published
 1999   
Keywords
 Superconductivity, Possible FirstOrder Pairing Interaction, Quantum Statistics, Pauli Antisymmetry Principle, Superconductivity vs Antiaromaticity and Aromaticity   
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3  Author
 MichaelC. Böhm, Johannes Schiitt, K G Dr, Weil  Requires cookie*   Title
 Quantum Constraints in 7r Systems: The Role of the Pauli Antisymmetry Principle for 7r Electronic Properties    Abstract
 It is demonstrated that the Pauli antisymmetry principle (PAP) is without influence in the 7r electron subspace of polyenes and (4n + 2) annulenes (n = 0, 1, 2...) as long as the hoppings are restricted to nearestneighbour centers. Here the 7r electrons behave like a hard core bosonic (heb) ensemble where fermionic onsite and bosonic intersite properties are combined. In An and (In + 1) annulenes (n = 1,2, 3...) 7r electron jumps between the first and last ring atom lead to a Pauli antisymmetrybased destabilization. The second quantum constraint in fermionic systems is the Pauli exclusion principle (PEP). In the manyelectron 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 7t electrons is discussed in terms of 7r energies and charge fluctuations. The model Hamiltonians adopted are of the Hückel molecular orbital (HMO) and PariserParrPople (PPP) type. We suggest quantum statistical definitions of the quantities "aromaticity" and "antiaromaticity", qualitative descriptors which are widely employed in the chemical literature.   
Reference
 Z. Naturforsch. 52a, 717—726 (1997); received July 31 1997   
Published
 1997   
Keywords
 tt Electronic Properties, Quantum Statistics, Pauli Antisymmetry and Exclusion Principle, Green's Function Quantum Monte Carlo Simulations, Aromaticity vs Antiaromaticity   
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