Ethylene localized orbitals

The reason for this becomes apparent when one compares the shapes of the localized it orbitals with that of the ethylene 7r orbital. All of the former have a positive lobe which extends over at least three atoms. In contrast, the ethylene orbital is strictly limited to two atoms, i.e., the ethylene 7r orbital is considerably more localized than even the maximally localized orbitals occurring in the aromatic systems. This, then, is the origin of the theoretical resonance energy the additional stabilization that is found in aromatic conjugated systems arises from the fact that even the maximally localized it orbitals are still more delocalized than the ethylene orbital. The localized description permits us therefore to be more precise and suggests that resonance stabilization in aromatic molecules be ascribed to a "local delocalization of each localized orbital. One infers that it electrons are more delocalized than a electrons because only half as many orbitals cover the same available space. It is also noteworthy that localized it orbitals situated on joint atoms (n 2, it23, ir l4, n22 ) contribute more stabilization than those located on non-joint atoms, i.e. the joint provides more paths for local delocalization. 

The simplest way to illustrate physical meaning of these quantities is to consider the perturbations of orthogonally twisted ethylene for which SAB = yAB = <5ab = yab = 0 holds via (1) return to planarity or (2) substitution at one end of the C=C bond. For (1), localized orbitals interact, yAB 0, but their energies are the same, 5AB = 0. Since delocalized orbitals become eventually HOMO and LUMO of planar ethylene, they do not have the same energy, Sab 0, but they do not interact, yab = 0. For (2), orthogonal-substituted ethylene, the situation is different. In the localized basis SAB 0, but the interaction is not present due to the symmetry yAn = 0. (A and 2 S belong to different irreducible representations.) For the delocalized description the energies of these orbitals are the same 5ab = 0 since the orbitals are equally distributed over both carbon atoms. But yab 0, since a and b are not canonical orbitals. 

Figure 4.25. Sum-over-atoms factor in the spin-orbit coupling vector // a) in orthogonally twisted ethylene and b) in (0, 90°) twisted trimethylene biradical, using Equation (4.12) and (4.13) most localized orbitals x - Xh and nonvanishing atomic vectorial contributions from Xh (white through-space, black through-bond).

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. 

From the electronic structure point of view, there are similarities between the two SS and SA bonding molecular orbitals of the xr complex (3-42 and 3-43, left-hand side) and the corresponding orbitals of the metallacyclopropane. The latter can be represented schematically by considering the in-phase and out-of-phase combinations of two localized orbitals, each of which characterizes a CTmc bond (3-42 and 3-43, right-hand side). ° The first combination corresponds to the orbital tx +z of the molecular ethylene complex, the second to the orbital yz + tt. ... 

An orbital correlation diagram can be constructed by examining the symmetry of the reactant and product orbitals with respect to this plane. The orbitals are classified by symmetry with respect to this plane in Fig. 11.8. For the reactants ethylene and butadiene, the classifications are the same as for the consideration of electrocyclic reactions on p. 600. An additional feature must be taken into account in the case of cyclohexene. The cyclohexene orbitals o-j, 0 2, o-f, and a are called symmetry-adapted orbitals. We might be inclined to think of the a and a orbitals as localized between specific pairs of carbon atoms. This is not the case for the MO treatment, and localized orbitals would fail the test of being either symmetric or antisymmetric with respect to the plane of symmetry. In the construction of orbital correlation diagrams, all orbitals involved must be either symmetric or antisymmetric with respect to the element of symmetry being considered. 

Structure. The straiued configuration of ethylene oxide has been a subject for bonding and molecular orbital studies. Valence bond and early molecular orbital studies have been reviewed (28). Intermediate neglect of differential overlap (INDO) and localized molecular orbital (LMO) calculations have also been performed (29—31). The LMO bond density maps show that the bond density is strongly polarized toward the oxygen atom (30). Maximum bond density hes outside of the CCO triangle, as suggested by the bent bonds of valence—bond theory (32). The H-nmr spectmm of ethylene oxide is consistent with these calculations (33). 

The n molecular orbitals described so far involve two atoms, so the orbital pictures look the same for the localized bonding model applied to ethylene and the MO approach applied to molecular oxygen. In the organic molecules described in the introduction to this chapter, however, orbitals spread over three or more atoms. Such delocalized n orbitals can form when more than two p orbitals overlap in the appropriate geometry. In this section, we develop a molecular orbital description for three-atom n systems. In the following sections, we apply the results to larger molecules. 

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