Interaction diagrams

Two orbitals of the oxygen atom have not been involved in the interaction so far, the Py orbital and the other sp hybrid. These are transferred to the middle of the diagram unchanged in energy or shape, although, for completeness, they should be redrawn in place they are nonbonding orbitals of the carbonyl group, h q and no- 

Lastly, one must occupy the MOs with the correct number of electrons. A neutral dicoordinated carbon atom has two valence electrons and a neutral uncoordinated oxygen atom has six, for a total of eight. Place electrons into the MOs two at a time. The HOMO is seen to be the higher nonbonding MO, no, and the LUMO is ti q. 

Bonding. Of the four occupied MOs, two are bonding and two are nonbonding, resulting in a net bond order of 2, that is, a double bond. Both the a and n bonds are polarized toward oxygen, the ti more than the cr because of the smaller intrinsic overlap (rr-type overlap is smaller than cr-type overlap). 

Dipole Moment. A large bond dipole moment is expected, with the negative end at oxygen and the positive end at carbon. 

Geometry. The combination of a and ti bonds forces coplanarity of the oxygen atom, the carbon atom, and the other two atoms attached to the carbon atom. 

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The Universal Modeling Language is used to describe a software system [4, 5], Several kinds of diagrams exist to model the diverse properties of the system. Thus a description of the system can be developed that enables the systematic and uniform documentation of the system. The class diagram, for example, represents the classes and their relationships. But also interacting diagrams exist, to describe the dynamic behavior of the system and its objects. 

The construction of the pair of (bond orbitals is carried out by combining a carbon hybrid with the Is orbital on hydrogen in a manner similar to the construction of the CC bond orbitals. The interaction diagram is shown below in Fig. 3. The bonding orbital is occupied by the two bond electrons. These two... 

The methylene group carries an empty p orbital. Howr will the methyl group interact w ith this empty orbital Clearly the 7r-type orbitals of the methyl group (ttu in E, tt. in B) have the appropriate symmetry to mix with the p orbital. A typical orbital interaction diagram (for E) is shown in Fig. 37. Several conclusions emerge immediately from this diagram ... 

Figure 4.46 Orbital interaction diagram for the Au6C framework in (H3PAu)6C2+showing the important bonding interactions of the carbon 2s and 2p orbitals with the MOs of the gold cluster. (Reprinted from J. Organomet. Chem., 384, 405, 1990, with kind permission from Elsevier Science S.A., P.O. Box 564, 1001 Lausanne, Switzerland.)...

Figure 1,4 SOMO-1IOMO and SOMO-LUMO orbital interaction diagrams.

This conclusion from the orbital interaction diagram cannot be demonstrated experimentally for the addition of N2 to C6H. The relationship />r < / f is, however, verified experimentally by the corresponding reaction with CO (Ravenscroft et al., 1988). 

Analogous effects may allow aromatic assignments to the thiirene 1-oxide and dioxide, and may be demonstrated through the interaction diagrams given below52. 

Fig. 13.4 An orbital interaction diagram for NbAsj made of the fragments AsyNb and bent [As-As-As] .

Fig. 1. Orbital interaction diagram for the formation of thiirane through interaction of ethylene and sulfur...

CHART 3. Molecular orbital interaction diagram between the two [W(calix)] fragments in 22. 

The overall results of substituent effects are observed in the products of a reaction, their rates of formation, and their stereochemistries. The purpose of this article is to apply very simple theoretical techniques to correlations and predictions of the rate and stereoselectivity effects of substituents in [2+2] photocycloadditions. The theoretical methods that will be used are perturbational molecular orbital (PMO) theory and its pictorial representation, the interaction diagram. Only an outline of the theory will be given below, since several more detailed descriptions are available. 4,18-34)... 

In calculations and interaction diagrams, only the most simplistic MO models will be chosen to represent ground and excited states of reactants. An olefin then has a bond framework largely neglected in discussing the reactivity of the molecule. The bonding level will be characterized by a jr-electron wave function with no nodes between the two basis fi orbitals of the ir-bond. The first jr-antibonding level has one node in the wave function, and a first excited state has electron-occupancy of unity in each level. 

Photolysis of benzaldehyde and trimethylethylene yields a mixture of cis and trans oxetanes with the two orientations shown in Eq. 42. Orientation 7 predominates and biradical intermediates generated after formation of a bond involving the lone nonbonding electron of an n, n excited benzaldehyde have been postulated. 66> Fig. 5 is the interaction diagram, the molecular parameters being based on HMO calculations, and spectroscopic experiments. 55,56,109) The orbital interaction E(n) F(n) is obviously dominant since the energy gap between F n ) and E n ) is over 4 eV. Therefore, a biradical mechanism should be postulated. The dominant orbital interaction is largest for attack of the... 

Qualitatively, the interaction diagram would closely resemble that in Fig. 3, since electron-donating substituents in both addends would raise the molecular levels of both the carbonyl compound and the olefin. Only the energy gap, E(n)-> F(n), would increase, the net result being that the calculated ratio of concerted to biradical reaction, Eqs. 40 and 41, should be even closer to unity than in the formaldehyde-ethylene case. Detailed calculations 38> support this conclusion, so PMO theory predicts that the overall stereochemical results are due to a combination of concerted (singlet) and biradical (triplet) mechanisms. This explanation agrees with the experimental facts, and it bypasses the necessity to postulate differential rates of rotation and closure for different kinds of biradical intermediates. 

Fig. 6. Qualitative interaction diagram, aromatic ketone and electron-rich olefin...

Several classes of reactions have now been distinguished and the results are summarized in Table 1 39>, where BR stands for biradical and C stand for concerted. The table illustrates the fact that substituents must be considered in tandem, and that biradical mechanisms are more common for these reactions than concerted reactions. The table is not recommended as a device for predicting mechanism and stereochemistry. Instead, a careful interaction diagram using experimental ionization... 

The photocycloaddition of two identical olefins is allowed to be a concerted [27TS+2 s] reaction according to the Woodward-Hoffman 57> rules if the factor of excited state spin multiplicity is ignored. The construction of a simple interaction diagram, Fig. 7, with arbitrary... 

Reaction 38 is relatively easy to understand with reference to the interaction diagram Fig. 8. The molecular parameters were obtained from HMO calculations. 

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