Scaling a one-electron density for M electrons to the correct normalization for N electrons is known to give an N-representable density. Here we show that a similar scaling for the electron pair distribution is generally not N-representable. The two-body r( x,x,; X:x;)
The electron-pair origin of antiaromaticity: Spectroscopic manifestations
β Scribed by Shmuel Zilberg; Yehuda Haas
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 359 KB
- Volume
- 71
- Category
- Article
- ISSN
- 0020-7608
No coin nor oath required. For personal study only.
β¦ Synopsis
It is shown that the antiaromatic character of certain conjugated cyclic hydrocarbons is due to the presence of an even number of distinct electron pairs in the Ε½ . system such as, but not necessarily electrons . In these systems, the ground state is Ε½ . constructed from an out-of-phase combination of two valence bond VB structures, and its equilibrium geometry is necessarily distorted along the coordinate that interchanges these structures. If a new symmetry element appears during the transition between the two structures, the ground electronic state at the symmetric point transforms as one of the nontotally symmetric irreducible representations of the point group. The conjugate excited state, formed from the in-phase combination of the same two structures, transforms as the totally symmetric representation of the group and is strongly bound. Its structure is similar to that of the ground state at the symmetric point, and the energy separation between the two states is small compared to that of conjugated cyclic hydrocarbons having an odd number of distinct electron pairs. Motion along the ''Kekule-type'' vibrational mode on the excited-state potential surface is very similar to αΈΏotion along the reaction coordinate connecting the two distorted structures on the ground-state surface. It is characterized by a significantly higher vibrational frequency compared to frequencies of similar modes in ground-state molecules. These qualitative predictions are supported by quantum chemical calculations on cyclobutadiene, cyclooctatetraene, and pentalene.
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