Hiickel valence theory

Nitrenium ions are isoelectronic to carbenes [177]. They contain a dicoordinated nitrogen atom formally with two valence electrons. The possible electronic structures of the parent nitrenium ion NHj are shown in Figure 7.9. On the basis of Hiickel MO theory one would expect that the lowest energy configuration, that is, the electronic ground... 

All carbon-carbon bonds in the skeleton have 50% double bond character. This fact was later confirmed by X-ray diffraction studies. A simple free-electron model calculation shows that there is no energy gap between the valence and conduction bands and that the limit of the first UV-visible transition for an infinite chain is zero. Thus a simple free-electron model correctly reproduces the first UV transition with a metallic extrapolation for the infinite system. Conversely, in the polyene series, CH2=CH-(CH=CH) -CH=CH2, he had to disturb the constant potential using a sinusoidal potential in order to cover the experimental trends. The role of the sinusoidal potential is to take into account the structural bond alternation between bond lengths of single- and double-bond character. When applied to the infinite system, in this type of disturbed free-electron model or Hiickel-type theory, a non-zero energy gap is obtained (about 1.90 eV in Kuhn s calculation), as illustrated in Fig. 36.9. 

We noted in Chapter 1 that valence bond theory and molecular orbital theory provide complementary beginning points for a theoretical description of H2. This chapter has focused on applications of molecular orbital theory, particularly Hiickel MO theory. Still, organic chemists have long used resonance theory, which is an approximate form of valence bond theory, to predict... 

Brief mention may be made of earlier bonding indices (often originating from Hiickel MO theory) whose usefulness can be enhanced in the modem ab initio context by using NAOs or NHOs. These allow a closer connection to be drawn between the qualitative Huckel-type concepts of elementary valence theory and the quantitative results of rigorous quantum chemical methods. 

Extended Hiickel theory Generalised valence bond model Hartree-Fock... 

Bond strengths are essentially controlled by valence ionization potentials. In the well established extended Hiickel theory (EHT) products of atomic orbital overlap integrals and valence ionization potentials are used to construct the non-diagonal matrix elements which then appear in the energy eigenvalues. The data in Table 1 fit our second basic rule perfectly. 

Heterocyclic systems have played an important role in this historical development. In addition to pyridine and thiophene mentioned earlier, a third heterocyclic system with one heteroatom played a crucial part protonation and methylation of 4//-pyrone were found by J. N. Collie and T. Tickle in 1899 to occur at the exocyclic oxygen atom and not at the oxygen heteroatom, giving a first hint for the jr-electron sextet theory based on the these arguments.36 Therefore, F. Arndt, who proposed in 1924 a mesomeric structure for 4//-pyrone, should also be considered among the pioneers who contributed to the theory of the aromatic sextet.37 These ideas were later refined by Linus Pauling, whose valence bond theory (and the electronegativity, resonance and hybridization concepts) led to results similar to Hiickel s molecular orbital theory.38... 

All electron calculations were carried out with the DFT program suite Turbomole (152,153). The clusters were treated as open-shell systems in the unrestricted Kohn-Sham framework. For the calculations we used the Becke-Perdew exchange-correlation functional dubbed BP86 (154,155) and the hybrid B3LYP functional (156,157). For BP86 we invoked the resolution-of-the-iden-tity (RI) approximation as implemented in Turbomole. For all atoms included in our models we employed Ahlrichs valence triple-C TZVP basis set with polarization functions on all atoms (158). If not noted otherwise, initial guess orbitals were obtained by extended Hiickel theory. Local spin analyses were performed with our local Turbomole version, where either Lowdin (131) or Mulliken (132) pseudo-projection operators were employed. Broken-symmetry determinants were obtained with our restrained optimization tool (136). Pictures of molecular structures were created with Pymol (159). 

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