Stabilized orbitals

Delocalization of electrons is important in chemistry. Electron delocalization is a major factor of the stabilities and the reactivities of molecules. The delocalization occurs through the interaction of an occupied orbital with a vacant orbital (Scheme 13). The two electrons occupy the stabilized orbital. There are no electrons in the destabilized orbital. The stabilization results from the interactions between the occupied and unoccupied orbitals. 

The interaction between the occnpied orbitals leads to the destabilization (Scheme 14). The two electrons in the stabilized orbital lead to stabilization, bnt there are two more electrons, which occnpy the destabilized orbitals. The destabilization overcomes the stabilization, and net destabilization results. 

Radicals and excited states have an orbital occupied by one electron. The interaction of the singly occupied orbital with a vacant orbital (Scheme 15) and with a singly occupied orbital (Scheme 16) leads to the stabilization. The stabilized orbitals occupy one and two electrons, respectively. There are no electrons in the destabilized orbital. For the interaction with a doubly occupied orbital there are two electrons in the stabilized orbital and one electron in the destabilized orbital (Scheme 17). Although the destabilization of the out-of-phase combined orbital is greater than the stabilization of the in-phase combination, there is one more electron in the stabilized orbital. Net stabilization is then expected. 

Keywords Diradical, Kinetic stability. Orbital phase theory. Spin preference... 

We shall first consider how nonbonded interactions influence bond angles in molecules. Our approach will be illustrated by reference to the model systems difluoro-methane and 1,1-difluoroethylene. In these problems, we shall consider not only stabilizing orbital interactions but also overlap repulsion in order to demonstrate some interesting trends which obtain in these angle problems. 

The ethane molecule can be constructed by union of two pyramidal methyl radical fragments. The interaction diagram is shown in Fig. 16 and the key stabilizing orbital interactions are depicted below. 

Fig. 17. Sigma type stabilizing orbital interactions in syn and anti 1,2-difluoroethane...

Fig. 18. Pi type stabilizing orbital interactions in syn and anti 1,2-difluoroethane. The symmetry labels are assigned with respect to a mirror plane (syn conformer) or a rotational axis (anti con-former)...

Fig. 21. Stabilizing pi orbital interactions in propene The key stabilizing orbital interactions are sketched below...

Fig. 24. Stabilizing orbital interactions in cis and trans 1,2-difluoro-l,2-dihydroxy ethylene. Symmetry labels are with respect to a rotational axis (trans isomer) and mirror plane (cis isomer)...

Fig. 35. Dominant stabilizing orbital interactions in the boat and chair conformers of...

Fig. 39. Stabilizing orbital interactions involved in the syn and anti transition states of the Sn2 reaction...

Table 31. Angle variation with change of electron occupancy of stabilized orbital in AB3 molecules... 

The very marked anomeric effect shown by 2-alkoxytetrahydropyran-3-ones (199) has been interpreted in terms of stabilizing orbital interactions (77NJC79). The influence of the heteroatom and the carbonyl group on the stabilization of the conformer in which the alkoxy group is axial is apparent. 

The interaction energy is further split up into three physically meaningful components as discussed earlier (1) the classical electrostatic interaction A Vc stat between the unperturbed charge distributions of the prepared fragments which is usually attractive, (2) the Pauli repulsive orbital interactions AEpauii, and (3) the stabilizing orbital interaction AEoi (Eq. [38]) ... 

Both in the Cram (Figure 10.16, left) and Felkin-Anh transition states (Figure 10.16, middle) a stabilizing orbital overlap occurs that was already encountered in connection with the discussion of Figure 10.13 there is a—in each case bonding—overlap between the o-MO assigned to the resulting C-Nu bond and... 

The foregoing statements concerning stabilizing orbital interactions can be extended to transition states. For them, they can be formulated more concisely and more generally using the term frontier orbitals, as introduced in the discussion of Figure 15.3 ... 

The substitution also destroys the degeneracy in the frontier orbitals of benzene thus, on formation of an anion-radical from pyridine, it is i/t4 which receives the electron. As indicated in Fig. 1, the stabilized orbitals in pyridine are distorted from their symmetry in benzene. Thus, the coefficient of i//4 at the 2- and 6-positions is increased in pyridine, relative to benzene at the expense of the other positions, especially the 3- and 5-positions. The Hiickel orbital coefficients c,- are related to spin population pt by Eq. (7) thus, the simple Hiickel model of the pyridine anion-radical predicts high spin population at positions 1, 2, 4, and 6, which is in good agreement with reality (see Section III,A,1), although the McLachlan procedure gives a rather more accurate quantitative description.15,29... 

Tlre phenyl cation is a quite aggressive intermediate, since heterolytic cleavage of a CTc-x bond leaves an empty a orbital, while the upper-lying 71 orbitals are filled. Taking away electron from a more stabilized orbital is obviously more expensive and the phenyl cation is more reactive than the corresponding anion, where the ct orbital is filled. One may expect that the reactivity is so high that any selectivity is precluded and the reaction can have no sensible application. 

The second term in Eq. (2), AEp ui , refers to the repulsive interactions between the fragments, which are caused by the fact that two electrons with the same spin cannot occupy the same region in space. AEp ui is calculated by enforcing the Kohn-Sham determinant on the superimposed fragments to obey the Pauli principle by antisymme-trization and renormalization. The stabilizing orbital interaction term, which is... 

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