Biradicaloid homosymmetric

Homosymmetric Biradicaloids The Hamiltonian matrix for the singlet state is... 

Figure 4.20. The two-electron two-orbital model a) for a homosymmetric biradicaloid and b) for a heterosymmetric biradicaloid schematic representation of state energies, relative to the T state, as a function of the interaction integral y or as a function of the electronegativity difference 6 of the orbitals x and Xt (by permission from Michl and Bona i(5-Koutecky. 1990).

Xi - Xi + Xt)- The most stable MO , = j( f, + Xi Xi X ) >s neglected in this example it is always doubly occupied and forms a nonpolar-izable core. At square or nearly square geometries the system is a perfect biradical or a homosymmetric biradicaloid, respectively, and the energy ordering of the three singlet states may be obtained from Figure 4.19 or 4.20 ... 

Ethylene. 90°-twisted ethylene is a perfect biradical distortion toward planarity (cj) < 90°) leads to an interaction /= 0 of the localized orbitals A and B, yielding a homosymmetric biradicaloid, and the coefficient Cq of the hole-pair configuration in the singlet ground state increases with increasing y- That is to say, ethylene violates condition (1) but satisfies condition (2) when it is orthogonally twisted, and satisfies condition (1) but violates condition (2) when it is planar. In partially twisted ethylene, however, conditions (1), (2) and (3) are fulfilled. Therefore, SOC is expected to vanish for ( ) = 0 and maximum value for (j) = 45°, as has been pointed out first by Caldwell et al. [29], and is apparent from Figure 3. 

In homosymmetric biradicaloids, a bonding interaction between the most localized orbitals is the only perturbation ( covalent perturbation ). Its magnitude is described by y, approximately equal to twice the resonance integral of simple theories. Its presence causes a mixing of the state functions (XoXfr) + xi) of the perfect biradical, which stabilizes its ground... 

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