PMO method

In addition to these systems, application of the PMO method leads to the prediction of the possible existence of many new and interesting classes of betaines. This predictive approach can be demonstrated by considering perturbations of the 1,3-dipoles 500, which are isoconjugate with the... 

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. 

Hilal (1994) calculated the pKa values of 214 dye molecules using the SPARC (SPARC Performs Automated Reasoning in Chemistry) computer program. SPARC computational methods use the knowledge base of organic chemistry and conventional Linear Free Energy Relationships (LFER), Structure/Activity Relationships (SAR), and Perturbed Molecular Orbital (PMO) methods. 

More recently a free electron version (PMO-F) of the first-order PMO method has been introduced [32, 33]. According to the branching conditions [34] of the FEMO model three types of resonance integral p are used ... 

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. 

The paralocalization energies can also be estimated14 by the simple PMO method. To a first approximation, the energy (PiS) required to remove two atoms simultaneously from a conjugated system is given by ... 

The it energy of a non-classical conjugated hydrocarbon can be compared directly with that of a classical analogue by the PMO method.14 Consider an even monocyclic polyene. This can be formed by fusion of methyl with an odd AH with one atom less. These components can also be fused to form an acyclic polyene. Comparison gives the aromatic energy of the cyclic system by difference. In this way we find that rings with An + 2 atoms are more stable, and those with An atoms less stable, than analogous acyclic compounds. The same method can be used for the bicyclic systems XVII, XIX, XXI, XXII, XXIII. The procedure is indicated below... 

It is of course possible to calculate dE indirectly by difference from the delocalization energies of the reactants and of the products or transition state. Indeed most of the reported calculations have made use of this procedure, the ir energies usually being estimated by using the Hiickel method. The trouble with this approach is that the assumptions underlying the Hiickel method break down for compounds other than AH s, while in the case of AH s the PMO method is not only much simpler but also more... 

A similar failure in the case of heterocyclic compounds is shown by the basicity of even heteroaromatic bases such as pyridine or quinoline. These all have similar basic strengths, as the simple PMO method predicts (Section IX). However the charge densities on the nitrogen atoms calculated51 by the Hiickel method are not the same (Table IV) application of Eq. (101) would then imply that the bases should differ considerably in strength. 

A much more promising way of using the SCF method seems to be to apply perturbation theory to it. Pople53 has published the necessary equations for treating various problems in this way the differences from the simple Hiickel PMO method are relatively small. 

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 selection rules for sigmatropic rearrangements were derived for open-chain systems. A priori, it is not obvious that they also apply to cyclic systems. Using the PMO method, show that the following sigmatropic migrations21 are allowed ... 

In the PMO method, we need only to examine one interaction. In the FMO approach, two are sometimes necessary. The PMO method has firm theoretical foundations because the only first-order interaction is retained all the neglected interactions are second order in PAB. 

PMO methods can be easily applied only if the system can be modeled as a hydrocarbon, and can be disconnected into two alternant radicals. It cannot be used to determine the site of electrophilic attack on azulene, for example. Such a problem can easily be solved using the frontier orbital approximation see p. 119. 

The PMO method makes enormous approximations. For example, carbons are used to model heteroatoms.22 Substituents have to be either removed altogether, or modeled using (doubly filled or empty) p orbitals. Such a simplified treatment has obvious limitations in chemical terms. Although it is possible to employ an allyl anion as a model for an enolate, it is not particularly desirable we lose all understanding of the difference between the reactivity at C and O. 

To take the heteroatoms explicitly into account, correction terms have to be calculated and PMO method is then rather unwieldy... 

Model the transition states of Reactions (4.1)-(4.4) by the conjugated molecules 8, 9, 10 and 11, and use the PMO method to calculate their resonance energies (defined as the difference between the energy of the cyclic structure and its open chain polyene counterpart). Hence, deduce the feasibility of Reaction (4.1). 

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. 

Applications of the PMO Method within the Extended Perimeter Model... 

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