Theory of Orbital Interactions

Let us now examine the nature of orbital interactions at a more quantitative level. 

The interaction between the frontier MO s of the reactants, i.e., the HOMO of the donor component and the LUMO of the acceptor component, is usually the most important but by no means the unique orbital interaction arising during a reaction. The total interaction energy can be represented by the sum of all the pairwise interactions each of which is either of attractive or of repulsive type. 

The mathematical formalism employed in the theory of orbital interactions has been elaborated both in general terms [8-12] and at different levels of the MO theory approximation, including the Hiickel [13] and extended Hiickel molecular orbital [14] as well as the SCF MO [15] and configuration interaction [16, 17] methods. In what follows, only the principal general relationships and conclusions will be dealt with. 

When two reactants A and B are drawing together, their oribitals (p and (pf, with the energy levels of and 8, respectively, interact to produce two new orbitals and of the forming molecular system A-B (Fig. 4.3). Through this interaction the energy level of the orbital cp is lowered relative to that of the orbital (p by the value of  

The proportionality coefficient k is varied depending on the initial approximation for calculating the orbitals and cp, (—39.7eV in the SCF MO approximation). 

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The theory of two-orbital interactions leads to some general rules of orbital interactions ... 

Abstract A theory of the interaction of three orbitals, i.e., the interaction,... 

The theory of interaction between a pair of orbitals, (J) and (Scheme la) is well established (Chapter Elements of a Chemical Orbital Theory by Inagaki in this volume) and snccessfnlly applied to nnderstanding and designing molecnles and reactions (Chapter A Mechanistic Spectrum of Chemical Reactions by Inagaki in this volnme). Here, we describe a theory of the interaction of three orbitals, (j), (J), and (j), (Scheme lb). The interactions include indirect interactions of... 

In addition, appreciable lengthening of the interbridgehead C—C bond is indicated (Schafer, O. Allan, M. Szeimies, G. Sanktjohanser, M., J. Am. Chem. Soc., 1992, 114, 8180-8186). Can you explain these observations on the basis of orbital interaction theory Compare your explanation with that offered in the reference. 

Use principles of orbital interaction theory to explain the lower Lewis acidity of the allyl cation, [CH2CHCH2]+, compared to the methyl cation, [CH3]+. 

V. G, J. Am. Chem. Soc., 1995, 117, 12863-12864). Dynamic 13C NMR evidence indicates that the complex is fluxional. A structure was postulated, based on semi-empirical calculations, in which the NO+ is attached to a single n bond. Use principles of orbital interaction theory to discuss the structure and bonding of such a complex (see also Figure 4.8 and question 4, Chapter 11). 

Unlike carbonyl compounds, /nbcarbonyl compounds such as thioketones, RiR2C=S, are very reactive and often impossible to isolate in a pure state. Apply principles of orbital interaction theory to explain ... 

It was established that the oxygen transfer takes place via an Sn2-like transition state (a), rather than a pathway which resembles a 1,3-dipolar addition (b). Comment on the relative merits of the two transition states using principles of orbital interaction theory. A spiro structure similar to (a) for the transition state has been located by ab initio calculations (Bach, R. D. Owensby, A. L. Gonzalez, C Schlegel, H. B. McDouall, J. J. W., J. Am. Chem. Soc., 1991, 113, 2338). 

The operation of the anomeric effect and the stabilization of carbocations are beautifully illustrated in a conformational study of 2-oxanol (2-oxacyclohexanol) (Smith, B. J., /. Am. Chem. Soc., 1997, 119, 2699-2706). 2-Oxanol prefers the OH axial form by 12 kJ/mol and, upon protonation of the OH group, spontaneously loses water to form the oxonium ion. Use principles of orbital interaction theory to explain ... 

Chapters 6-11 describe applications of orbital interaction theory to various chemical systems in order to show how familiar concepts such as acid and base strengths, nucleo-... 

Sample problems and quizzes, grouped approximately by chapter, are presented in Appendix B. Many are based on examples from the recent literature and references are provided. Detailed answers are worked out for many of the problems. These serve as further examples to the reader of the application of the principles of orbital interaction theory. 

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