Perturbational Molecular Orbital PMO Method

In cycloaddition reactions an olefinic system with mic electrons adds up to a system with nrc -electrons to give a cyclic partner with (m-2)+(n -2)7c-electrons. In the process two a-bonds are formed at the cost of four rt-electrons. These addition reactions are called (m+n) cycloadditions. They occur with high degree of stereoselectivity under thermal as well as photochemical conditions. They are referred to as (m+n) or (m+n+...) reactions keeping in view number of 7t-electrons involved in the process. Some examples are cited below  

Because during cycloaddition, there is addition of two olefinic systems, therefore, two feasibilities are there (a) addition may take place in such a way that lobes of same phases of one component with the lobes of same phases of other component may overlap (b) lobes of same phase of one component may overlap with the lobes of opposite faces of other component, (a) is known as suprafacial cycloaddition and (b) as antarafacial cycloaddition.  

Antarafacial processes are difficult because in them twisting of p-orbitals is required though both the process are feasible on symmetry ground. 

As both the n-systems are involved in the cyclo addition, it is essential to specify the modes with respect to each of them. Specification is made by placing subscript S or a after the number refering to n-component. For instance, suprafacial addition with respect to each component of Diels-Alder reaction is specified as n] +n J cycloaddition. Another way is simply writting it as 2s+4s cycloaddition. 

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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. 

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]. 

For the analysis of sigmatropic rearrangements, the correlation diagrams are not relevant since it is only the transition state and not the reactants or products that may possess molecular symmetry elements. However, these reactions can be analyzed satisfactorily by using frontier molecular orbital (FMO) and perturbation molecular orbital (PMO) methods. 

The book opens with an introduction (Chapter 1), which, besides providing background information needed for appreciating different types of pericyclic reactions, outlines simple ways to analyze these reactions using orbital symmetry correlation diagram, frontier molecular orbital (FMO), and perturbation molecular orbital (PMO) methods. This chapter also has references to important published reviews and articles. 

Pomerantz and coworkers reported in 1989 [83] that very simple perturbational molecular orbital (PMO) methods could be applied to a number of hydrocarbon aromatic oligomers and conducting polymers. These calculations provided band gaps and UV-vis absorption maxima that were in excellent agreement with both observed data, where available, and data calculated by more sophisticated procedures. Thus for polymer 49 the PMO method gave a value of 0.54 eV [83], while the VEH calculations mentioned above gave a band gap of 0.44 eV [81] and the PPP-SCF band gap calculations gave 0.73 eV [84]. 

All the three methods viz correlation diagram method. Frontier molecular orbital (FMO) method as well as perturbational molecular orbital (PMO) method can be used to predict feasiblity of electrocyclic reactions. 

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)... 

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. 

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. ... 

Electrocyclic reactions can be analyzed by correlation-diagram, perturbation molecular orbital (PMO) and frontier molecular orbital (EMO) methods. 

Abbreviations PAH, polycyclic aromatic hydrocarbon DE, diol epoxide PAHDE, polycyclic aromatic hydrocarbon diol epoxide PAHTC, polycyclic aromatic hydrocarbon triol carbocation TC, triol carbocation BaP, benzo[a]pyrene BeP, benzo[e]pyrene BA, benz[a]anthracene DBA, dibenz[a,h]anthracene BcPh, benzo[c)phenanthrene Ch, chrysene MCh, methylchrysene MBA, 7-methyl benz[a]anthracene DMBA, 7,12-dimethyl benz[a]anthracene EBA, 7-ethyl benz[a]anthracene DB(a,l)P, dibenzo[a,l]pyrene MSCR, mechanism-based structure-carcinogenicity relationship PMO, Perturbational molecular orbital method dA, deoxyadenosine dC, deoxycytosine dG, deoxyguanosine MOS, monoxygenase enzyme system EH, epoxide hydrolase enzyme system N2(G), exocyclic nitrogen of guanine C, electrophilic centre of PAHTC K, intercalation constant CD, circular dichroism LD, linear dichroism. 

PMO perturbational molecular orbital (quantum chemical method)... 

In this chapter the molecular orbital theory covered in Chapter 1 is applied to the problem of aromaticity. The HMO approach is shown to be somewhat limited in its usefulness. However the PMO (perturbational molecular orbital) method, which uses Hiickel orbitals, does lead to satisfactory criteria of... 

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