Abstract
In a previous note1, I gave an example of why an effective bond can exist when a real bond is absent within Single Determinant SCF-MO (SD-SCF-MO) theory. I now consider a much more complex problem, which is soluble only at the level of SCF-MO-CI theory, in order to further illustrate the conceptual and formal advantages of VB-type theories.
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References
See Chapter 13.
Epiotis, N.D., Larson, J.R., Eaton, H. “Unified Valence Bond Theory of Electronic Structure” in Lecture Notes in Chemistry, Vol. 29; Springer-Verlag: New York and Berlin, 1982.
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The product sign is defined with respect to the signs preceding each negative interaction matrix element.
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According to the Independent Bond Model (IBM) F2 can be viewed as a composite of three subsystems; A, B, and C with the total wavefunction Ψ being a product of the subsystem wavefunctions and ΩA, ΩB, and ΩC. \( \begin{array}{*{20}{c}} {{{\Omega }_{{\text{A}}}}\quad :\quad 2{{{\text{p}}}_{{\text{x}}}},\;2{{{{\text{p'}}}}_{{\text{x}}}},\;2{\text{s,}}\;{\text{2s'}}\;/\;6} \\ {{{\Omega }_{{\text{B}}}}\quad :\quad 2{{{\text{p}}}_{{\text{y}}}},\;2{{{{\text{p'}}}}_{{\text{y}}}},\;/\;4} \\ {{{\Omega }_{{\text{C}}}}\quad :\quad 2{{{\text{p}}}_{{\text{Z}}}},\;2{{{{\text{p'}}}}_{{\text{y}}}},\;/\;4} \\ {\psi \quad = \quad {{\Omega }_{{\text{A}}}} \cdot \;{{\Omega }_{{\text{B}}}} \cdot \;{{\Omega }_{{\text{C}}}}} \\ \end{array} \) That subsystem A is C-aromatic in a monoelectronic CT sense can be seen without writing down the individual CW’s but, rather, by observing that the four orbitals 2pX, 2pX, 2s, and 2s1 interact in-phase in a cyclic manner and they contain six electrons.
The distinction between Hückel and Mobius atomic orbital overlap was first brought to the attention of chemists by Heilbronner and Zimmerman. The chemical implications of this distinction were first discussed by Zimmerman and Woodward and Hoffmann:
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The way in which the signs of VB matrix elements determine stereoselection in N-electron/N-orbital systems was discussed in. Mulder, J.J.C., Oosterhoff, L.J., Chem. Commun. 1970, 305, 307.
The way in which the signs of VB matrix elements determine spin selection is discussed in; Fischer, H.; Murrell, J.N. Theor. Chim. Acta 1963, 1, 464.
For recent attempts toward the development of a qualitative VB theory, see, inter alia:
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Epiotis, N.D. (1983). Why a Net Bond exists when it appears to be Nonexistent: The Electronic Structures of F2 and Inert Gas Fluorides. In: Unified Valence Bond Theory of Electronic Structure. Lecture Notes in Chemistry, vol 34. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93239-7_18
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