PMO theory

Coulson and H. C. Longuet-Higgins, Proc. R. Soc. London Ser. A 192, 16 (1947) L. Salem, J. Am. Chem. Soc. 90, 543 (1968) M. J. S. Dewar and R. C. Dougherty, The PMO Theory of Organic Chemistry, Plenum Press, New York, 1975 G. Klopman, Chemical Reactivity and Reaction Paths, Wiley-Interscience, New York 1974, Chap. 4. 

57 (1971) I. Fleming, Frontier Orbital and Organic Chemical Reactions, Wiley, New York, 1976 L. Salem, Electrons in Chemical Reactions, Wiley, New York, 1982, Chap. 6. 

Let us illustrate these ideas by returning to the comparisons of the reactivity of ethylene and formaldehyde toward a nucleophilic species and an electrophilic species. The interactions (perturbations) which arise as both a nucleophile and electrophile approach are sketched in Fig. 1.26. 

The electrophilic species must have a low-lying empty orbital. The strongest interaction will be with the ethylene tt orbital and this leads to a strong perturbation which has a stabilizing effect. The same species would lie closer to tt of formaldehyde since the formaldehyde orbitals are shifted to lower energy. The strongest interaction would then be with tt but since both tt and are empty orbitals it does not 

TT MO energy levels for ethylene with a 7r-donor substituent. 

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Another aspect of qualitative application of MO theory is the analysis of interactions of the orbitals in reacting molecules. As molecules approach one another and reaction proceeds, there is a mutual perturbation of the orbitals. This process continues until the reaction is complete and the new product (or intermediate in a multistep reaction) is formed. PMO theory incorporates the concept of frontier orbital control. This concept proposes that the most important interactions will be between a particular pair of orbitals. These orbitals are the highest filled oihital of one reactant (the HOMO, highest occupied molecular oihital) and the lowest unfilled (LUMO, lowest unoccupied molecular oihital) orbital of the other reactant. The basis for concentrating attention on these two orbitals is that they will be the closest in energy of the interacting orbitals. A basic postulate of PMO... 

M. J. S. Dewar and R. C. Dougherty, The PMO Theory cf Organic Chemistry, Plenum Press, New York, 1975. 

Use PMO theory to describe the effect of the substituents on the ionization potential. Use an MO diagram to explain the interaction of the substituents with the n bonds. Explicitly take into account the fact that the two orbitals interact and therefore cannot be treated as separate entities (see Problem 10). 

PMO Theory of Organic Chemistry Plenum NY, 1975 Zimmerman, H.E. Quantum Mechanics for Organic Chemists Academic Press NY, 1975 Borden, W.T. Modem Molecular Orbital Theory for Organic Chemists Prentice-Hall Englewood Cliffs, NJ, 1975 Dewar, M.J.S. The Molecular Orbital Theory of Organic Chemistry McGraw-Hill NY, 1969 Liberies, A. Introduction to Molecular Orbital Theory Holt, Rinehart, and Winston NY, 1966. 

Using PMO theory, it is possible to estimate the relative activation energy of reactions by assuming some reasonable structure for the transition state and then using perturbation theory to calculate the difference between the energy of the transition state and the energy of the reactants.(130)... 

As a simple introduction to PMO theory suppose we consider the bond formation between the two-atom, two-orbital system shown in Figure 4.8. The energy gained on forming the bond A—B is given by the second-order perturbation equation... 

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)... 

Considering only the interaction between HOMO of R and LVMO of S, elementary perturbation theory shows that the result of the orbital interaction is a repulsion of the levels, the occupied level becomes more stable, the unoccupied level less stable. The simplest Huckel-type formulation of PMO theory gives equations for the intermolecular perturbation energy change A that are quite simple in form, Eqs. 3—6 18,20,22,26-28) Q is a first-order Coulombic energy that can be calculated in terms of... 

An advantage of PMO theory is that it is capable of elaboration in many different ways. A simple theory, capable of elaboration, is desirable for many reasons, the most important being that simple theory is simply applied, and more elaborate theory is more easily dissected into parts, to each of which theoretical or physical interpretation may be given. 

The first photochemical reactions to be correlated with PMO theory were the dimerizations of anthracene, tetracene, pentacene, and acenaphthylene. 36> More detailed energy surfaces for the photodimerization reactions of butadiene have also been calculated. 30> In the category of simplified calculations lie studies of the regiospecificity of Diels-Alder reactions 37>, and reactivity in oxetane-forming reactions. 38,39) jn these... 

A very complex group of observations and speculations has been presented in Section IV. It might almost seem illogical to apply a single theoretical approach to so diverse a set of reactions, but the utility of PMO theory for correlating the several aspects of Paterno-Buchi reactions has already been demonstrated. 38-39> The newer results to be presented below will help to confirm the idea that PMO theory gives a unified useful theoretical picture for the majority of [2+2] photocycloaddition reactions. First, however, the many approximations and postulates inherent in this work should be made clear. 

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. 

Many derivatives of quinones, cinnamic acids, and mucconic acids photodimerize in solid phases to give results 16> that in many cases are not in agreement with the general PMO rule of head-to-head reaction. However, it is clear that those reactions are controlled by topochemical effects, i.e. the geometry and proximity of the reactants in the solid phase. 135> Consequently, PMO theory will not be useful for calculating reactions of that type. 

Early PMO theory by Haddon (1975) predicted that the homophenalenyl anions [143], [144] and [145] should be good candidates for anionic homoaromaticity. Murata and Nakasuji (1980) attempted to synthesize these systems. They were unable to obtain any anions similar to [143] and [144]. However, NMR analysis of the potential product [145] indicated that anion [146] was formed instead. 

One of the most used approaches for predicting homoaromaticity has been the perturbational molecular orbital (PMO) theory of Dewar (1969) as developed by Haddon (1975). This method is based on perturbations in the Hiickel MO theory based on reducing the resonance integral (/3) of one bond. This bond represents the homoaromatic linkage. The main advantage of this method is its simplicity. PMO theory predicted many potential homoaromatic species and gave rise to several experimental investigations. 

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