PMO method and

Sigmatropic reactions can be treated successfully by PMO method, and similar conclusions are arrived at as by other approaches (Figure 3.6). For instance, [1,3] suprafacial shift of hydrogen occurs via a transition state with zero node and four electrons (antiaromatic) and thus is a photochemically allowed... 

Analysis of sigmatropic rearrangement is also possible by PMO method and conclusion about their feasibility are same as by other methods. For instance, 1, 3-sigmatropic suprafacial shift occurs via transition state with 0 nodes and 4 electrons (antiaromatic) and hence it is thermally forbidden. But [1, 3]-antarafacial sigma migration occurs through a transition state with 1 node and four electrons (aromatic T.S.) and is therefore thermally allowed. 

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 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. 

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 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... 

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]. 

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). 

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. 

The purpose of this chapter is to advocate the use of PMO-.F as a general tool for the consideration of PAH structure-reactivity problems, particularly in the case of large and very large PAHs. Therefore, some effort is made to delineate justifications for this method to engender its use. However, we presume that the reader is familiar with the concepts and procedures of the HMO and PMO methods (3-6). Szentpaly has recently demonstated that charge and electron-repulsion effects can be included in PMO procedures (24) and the necessary procedures to include these effects are outlined in this chapter. References and brief listings of published applications are given... 

Thus, the PMO Fw and PMO-w methods correlate the formation of an arylmethyl cation with the following ... 

PMO-.F and PMO Flocalization energies for cationic species and the experimental parameters are listed in Table II nonbenzenoid compounds have been excluded from this table. We treat the correction term for charge interaction that characterizes the PMO Fvalues calculated by CNDO/2, an all-valence-electron SCF method (10), are also included in Table II to facilitate a comparison of PMO Fquantum mechanical procedure that includes the effects of electron repulsion. 

The optimized value of a) is 1.52, the correlation coefficient for equation 20 is 0.995, and the average deviation of a PMO. Fa) PA from the corresponding CNDO/2 PA is only 0.04 electronvolts (eV). A plot of the results is not shown because the deviations from a straight line are too small to indicate any systematic source of the deviations. The results do indicate that the more complex CNDO/2 procedure can be accurately modeled by the PMO Fa) method, at least for this application. Whether or not one can extend this result to other types of SCF procedures is under investigation. The applications of PMO.F and PMO Fo> to other types of reactions with ionic intermediates (see references 37 and 38 for reviews) are also receiving consideration. 

In general, we find that PMO F and PMO Fo> are useful methods to correlate and help understand PAH chemical reactivity. In every case investigated so far, the experimental data are correlated much more precisely with these methods than with the HMO method. In the majority of applications, the... 

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]. 

In the previous, and almost in every calculation on Diels-Alder reactions, it has been assumed that diene and dienophile lie on top of each other in parallel (or roughly parallel) planes. Under this condition, the endo approach is theoretically better than the exo approach only because of secondary interactions. However, it has been shown that, for cyclopentadiene dimerisation, if the two molecules are allowed to approach in a non-parallel way, the endo preference can be mainly attributed to a more favourable primary interaction, due to an approach at an angle of ca. 60°, which could be allowed only to the c/ido-oriented dienophile because of steric reasons . The pmo method has also been applied to a simplified treatment of some competing 1,4 and 1.2 thermal cycloadditions involving diradical intermediates . 

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