Dewar PMO method

Dewar s perturbation molecular orbital (PMO) method analyzes the interactions that take place on assembling p orbitals in various ways into chains and rings.44 It is similar to the methods we have used in Section 10.4 in considering aromaticity, but lends itself better to a semiquantitative treatment. We shall nevertheless be concerned here only with the qualitative aspects of the theory as it applies to pericyclic transition states. 

Algebraic expressions for terms M and C were derived using Dewar s PMO method (for C in a version similar to the co-technique [57] in order to calculate carbocation stabilization energies). The size factor S is simply a cubic function of the number of carbon atoms [97], The three independent variables of the model were assumed to be linearly related to the experimental Iball indices (vide supra). By multilinear regression analysis (sample size = 26) an equation was derived for calculating Iball indices from the three theoretical parameters. The correlation coefficient for the linear relation between calculated and experimental Iball indices is r = 0.961. 

Antiaromaticity [1] is the phenomenon of destabilization of certain molecules by interelectronic interactions, that is, it is the opposite of aromaticity [2], The SHM indicates that when the n-system of butadiene is closed the energy rises, i.e. that cyclobutadiene is antiaromatic with reference to butadiene. In a related approach, the perturbation molecular orbital (PMO) method of Dewar predicts that union of a C3 and a Ci unit to form cyclobutadiene is less favorable than union to form butadiene [3]. 

The Dewar PMO (perturbational MO) method9 avoids calculations by making clever use of alternants. The idea is to divide a molecule formally into two alternant radicals, whose recombination is studied. When the radicals are different, only their NBMOs lie at the same energy (Figure 3.4). Hence their interaction provides almost all of the recombination energy. The other interactions, which are second order in PAB, can then be neglected. We will illustrate the method by deriving the aromaticity rules. 

Cyclooctatetraene itself does not undergo 4 + 2 cycloadditions it is its valence isomer bicyclo[4.2.0]octatriene which reacts with dienophiles.36 Use Dewar s PMO method to explain why the direct reaction with cyclooctatetraene is disfavored. 

Even more important is the fact that the formation of the triol carbocations (PAHTC) has not been correctly calculated. Any treatment based on a simple Hiickel-MO or PMO calculations for odd AH ions neglect the effect of the differently charged carbon atoms and hence, must be in error. The ionic charge distributed over the aromatic system affects the electronegativity of carbon atoms in specific ways and this has a profound effect on the 7i-energy. Breakdowns of both the PMO and HMO approximations with ionic reaction intermediates are documented in the work of Dewar and Thompson [36,70], Streitwieser et al [35,71] and Szentpaly [39]. The reactivity patterns with radical and ionic reaction intermediates of PAH are different [34-39]. It has been pointed out by Dewar [36] that the PMO method works better for radical than ions, and adequate modifications of the PMO method have been developed for ionic intermediates [16,38,39]. 

The application of the PMO method to the problems of aromaticity Dewar (1966, 1967) requires only two rules, which will be stated here without rigorous proof. 

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. 

The Coulson Rushbrooke theorems have many important consequences that will lead us a long way towards a qualitative understanding of the electronic structure of conjugated molecules, particularly of their excited states. Dewar developed a simple perturbation method PMO theory) to evaluate the HOMO LUMO gap and the associated excitation energy for 7t-systems with an even number of conjugated atoms.284,285,288 Because the NBMO of odd AHs can be determined so easily, the system of interest is dissected into two odd AHs. Some examples are shown in Scheme 4.1. 

In 1952 Dewar developed Perturbational Molecular Orbital (PMO) theory, a 7t-electron method calibrated directly on the energies of model organic compounds. The accuracy of this simple method is remarkable for 20 conjugated hydrocarbons the average error in the heat of atomization was 6.5 kcal/mol, and, if the worst case, biphenylene, were left out, the average error dropped to 3.33 kcal/mol. ... 

The perturbational MO method of Longuet-Higgins (11) and Dewar (12), which was thoroughly reviewed by Dewar and Dougherty (6), has been the pencil-and-paper method of choice in numerous applications. More recently, a modified free-electron (MFE) MO approach (13-15) and a valence-bond structure-resonance theory (VBSRT) (7, 16, 17) have been applied to several PAH structure and reactivity problems. A new perturbational variant of the free-electron MO method (PMO F) has also been derived and reported (8, 18). Both PMO F and VBSRT qualify as simple pencil-and-paper procedures. When applied to a compilation of electrophilic substitution parameters (ct+) (19-23), the correlation coefficients of calculated reactivity indexes with cr+ for alternant hydrocarbons are 0.973 and 0.959, respectively (8). In this case, the performance of the PMO F method rivals that of the best available SCF calculations for systems of this size, and that of VBSRT is sufficient for most purposes. 

This was the situation when Professor M. J. S. Dewar took an interest in quantitative methods. PMO theory had demonstrated that quantum mechanical methods could yield useful results for organic systems, and the allvalence-electron methods allowed inorganic as well as organic systems to be studied. His objective was to create a computational tool that was accurate (so that confidence could be placed in the results), fast (to be practical), generally applicable, and easy to use. 

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