Ethylene overlap integral

What is the energy separation E2 — E of the bonding and antibonding orbitals in ethylene, assuming that the overlap integral S is 0.27 ... 

The chemical reactions through cyclic transition states are controlled by the symmetry of the frontier orbitals [11]. At the symmetrical (Cs) six-membered ring transition state of Diels-Alder reaction between butadiene and ethylene, the HOMO of butadiene and the LUMO of ethylene (Scheme 18) are antisymmetric with respect to the reflection in the mirror plane (Scheme 24). The symmetry allows the frontier orbitals to have the same signs of the overlap integrals between the p-or-bital components at both reaction sites. The simultaneous interactions at the both sites promotes the frontier orbital interaction more than the interaction at one site of an acyclic transition state. This is also the case with interaction between the HOMO of ethylene and the LUMO of butadiene. The Diels-Alder reactions occur through the cyclic transition states in a concerted and stereospecific manner with retention of configuration of the reactants. 

The frontier orbital interaction is forbidden by the symmetry for the dimerization of ethylenes throngh the rectangular transition state. The HOMO is symmetric and the LUMO is antisymmetric (Scheme 25a). The overlap integrals have the opposite signs at the reaction sites. The overlap between the frontier orbitals is zero even if each overlap between the atomic p-orbitals increases. It follows that the dimerization cannot occur throngh the fonr-membered ring transition states in a concerted and stereospecfic manner. 

The ir-bond between two silicon atoms (>Si=Si<) was formerly thought to be non-existent and then was found to be extremely weak. This has been explained in the past by the extended bond length, with respect to ethylene, which was thought to be the origin of a seemingly low 3p-3p(ir) atomic overlap S(tt) [1]. However, the overlap actually has never been calculated before. Calculations indicate quite similar p-p(ir) overlap integrals in disilene and ethylene so that the different bond lengths for C=C and Si=Si must be explained by the different orbital radii (Fig. 1). 

The last condition, the orientation principle, is illustrated for the benzene-iodine and ethylene-platinum complexes. It is seen that the orientation depicted in Fig. 2a leads to a positive overlap integral and... 

We will, first of all, briefly resume the method1-2 3 of calculation by considering the particularly simple case of the electronic transitions of the rr electrons of ethylene. The problem may be treated, to a first approximation at least, as a mono-electronic problem. The normal orbital N is, as is well known, described by the 2p, orbitals of the bound atoms, written yx and y>2, and-the overlap integral S by ... 

Problem 9.15 Confirm that the tt bond order in ethylene is 1 (ignore the overlap integral). 

Problem 12.17 The overlap integrals for Slater sp hybrid orbitals in ethylene are ... 

Similar considerations for a non-zero overlap integral between the occupied ttu molecular orbital of ethylene and the unfilled Ss atomic orbital... 

The difference between the various l,n-biradicals is due to the first factor in eq. (30), the structural factor. For ethylene with w = 90°, these factors become 0, 1 and 0 for the x, y and z component, respectively, and together with the sin2d proportionality of the y component, this completely describes the computational SOC results shown in Figure 2b. For trimethylene (w = 60°) the structural factors of all three component are nonzero since the overlap integral (A B) exhibits a similar dependence on the rotational angles as the z component of the angular momentum, while the x and y component are zero at the [90,90] conformation... 

Table 23. Pi overlap integrals between the substituents in the three possible isomers of disubsti-tuted ethylenes ...

The trajectory of nucleophilic attack upon the double bond of VIII is quite close to that of the addition of nucleophiles to the carbonyl bond. For the addition reaction of the hydride-ion (Y = H) to ethylene (R = Z = H), and propene (R = CH3) the angle d is 123° (according to the ab initio 3-21G calculations in Ref. [23]. The driving force of the reaction is the charge transfer from the electron lone pair orbital of the nucleophile Y to the 7i -orbital of olefine. The latter has, unlike the orbital n Q (see Fig. 4.1), no loop on the a-atom of carbon and is delocalized, which diminishes the overlap integral and thereby the energy of interaction AE from Eq. (4.10) of the nucleophile with alkene as compared to the energy of interaction with the carbonyl... 

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