Frontier molecular orbital method

Sigmatropic 1, 5-shift This method of analysis can be illustrated by the example of suprafacial [1, 5] sigmatropic rearrangement of hydrogen in which homolytic cleavage produces H-atom and pentadienyl radical  

Ground state electronic configuration of pentadienyl radical is ViN 3-HOMO among these M. Os is 3 which has same signs on terminal lobes (hence possesses mirror plane S3mimetry). For this reason 1, 5-sigmatropic shift is thermally allowed in suprafacial manner. 

The first excited state of pentadienyl radical has configuration,  

Stereochemical outcomes of 1, 5-sigmatropic shifts witn retention in cyclic systems can be analysed in a thermally allowed suprafacial sigmatropic process by the application of FMO method. Let us illustrate this by the example of thermolysis of hypothetical norcaradiene system. 

5-cycloheptatrienes undergo 1, 5-sigmatropic rearrangement through norcaradiene intermediates. This is another example of peripatetic cyclopropare bridge (Fig. 6.4 and 6.5). Thermally allowed suprafacial 1, 5-shifts proceed 

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From the foregoing survey of heterocyclic hydrazonoyl halides, it appears that the main emphasis has been restricted to both their preparation and use as intermediates for further synthesis. Large areas of their chemistry, particularly regarding their physical and biological properties, remain to be developed. A deeper understanding of some aspects of their 1,3-dipolar cycloaddition reactions, such as regiochemistry and site selectivity in terms of the frontier molecular orbital method, is also needed. 

There have been few applications of theoretical methods in this area, but attempts have been made to rationalize the structure and reactivity toward cycloaddition of the mesoionic compounds (45) using MNDO and FMO (frontier molecular orbital) methods <86CB2308,86CB2317>. 

In these reactions the 1,2,4-triazines are unsymmetrical dienes and, generally, the dienophiles are also unsymmetrical, hence two orientations in the transition state must be considered. Detailed studies have shown that secondary orbital interactions dominate the orientation if these interactions are possible. As a result, in the transition state the substituent of the dienophile with a lone electron pair is always on the same side as substituents with tr-electrons on the 1,2,4-triazine. Only in this orientation can secondary orbital interactions occur between the lone pair in the dienophile and the 7r-electrons of the substituent. In cases where substituents with 7r-eIectrons are in the 3- and the 6-position, only interactions between the substituent in the 6-position and the lone pair of the dienophile substituents are observed. The orientation of the two reactants in the transition state can also be explained by the frontier molecular orbital method and this gives the same results. 

In view of this, early quantum mechanical approximations still merit interest, as they can provide quantitative data that can be correlated with observations on chemical reactivity. One of the most successful methods for explaining the course of chemical reactions is frontier molecular orbital (FMO) theory [5]. The course of a chemical reaction is rationali2ed on the basis of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), the frontier orbitals. Both the energy and the orbital coefficients of the HOMO and LUMO of the reactants are taken into account. 

The importance of FMO theory hes in the fact that good results may be obtained even if the frontier molecular orbitals are calculated by rather simple, approximate quantum mechanical methods such as perturbation theory. Even simple additivity schemes have been developed for estimating the energies and the orbital coefficients of frontier molecular orbitals [6]. 

Emphasis was put on providing a sound physicochemical basis for the modeling of the effects determining a reaction mechanism. Thus, methods were developed for the estimation of pXj-vahies, bond dissociation energies, heats of formation, frontier molecular orbital energies and coefficients, and stcric hindrance. 

This chapter will try to cover some developments in the theoretical understanding of metal-catalyzed cycloaddition reactions. The reactions to be discussed below are related to the other chapters in this book in an attempt to obtain a coherent picture of the metal-catalyzed reactions discussed. The intention with this chapter is not to go into details of the theoretical methods used for the calculations - the reader must go to the original literature to obtain this information. The examples chosen are related to the different chapters, i.e. this chapter will cover carbo-Diels-Alder, hetero-Diels-Alder and 1,3-dipolar cycloaddition reactions. Each section will start with a description of the reactions considered, based on the frontier molecular orbital approach, in an attempt for the reader to understand the basis molecular orbital concepts for the reaction. 

The "principle of microscopic reversibility", which indicates that the forward and the reverse reactions must proceed through the same pathway, assures us that we can use the same reaction mechanism for generating the intermediate precursors of the "synthesis tree", that we use for the synthesis in the laboratory. In other words, according to the "principle of microscopic reversibility", [26] two reciprocal reactions from the point of view of stoichiometry are also such from the point of view of their mechanism, provided that the reaction conditions are the same or at least very similar. A corollary is that the knowledge of synthetic methods and reaction mechanisms itself -according to the electronic theory of valence and the theory of frontier molecular orbitals- must be applied in order to generate the intermediate precursors of the "synthesis tree" and which will determine the correctness of a synthesis design and, ultimately, the success of it. 

The structural requirements of the mesomeric betaines described in Section III endow these molecules with reactive -electron systems whose orbital symmetries are suitable for participation in a variety of pericyclic reactions. In particular, many betaines undergo 1,3-dipolar cycloaddition reactions giving stable adducts. Since these reactions are moderately exothermic, the transition state can be expected to occur early in the reaction and the magnitude of the frontier orbital interactions, as 1,3-dipole and 1,3-dipolarophile approach, can be expected to influence the energy of the transition state—and therefore the reaction rate and the structure of the product. This is the essence of frontier molecular orbital (EMO) theory, several accounts of which have been published. 16.317 application of the FMO method to the pericyclic reactions of mesomeric betaines has met with considerable success. The following section describes how the reactivity, electroselectivity, and regioselectivity of these molecules have been rationalized. 

The kinetic aspects of these reactions were inspected by the frontier molecular orbital (FMO) method for the 1,3-dipolar cycloaddition reactions of R Ns + R2NCO or R2N3 + R NCO affording the corresponding tetra-zolinone (97JHC113). Making use of the Klopman-Salem equation, from... 

The polarized-TT frontier molecular orbital (PPFMO) method has been employed to study protonation and sulphenylation of sugar-related dihydrofurans and tetrahydropy-rans. The predictions are consonant with the experimental observations62. Contrary to expectations, the proton-catalysed addition of alcohols to glycals, such as 30, has been shown by isotope labelling (2H) not to be anii-diaxial addition. This observation has been rationalized by the initial attack by deuteron from the bottom, giving ion 31, and by the anomeric effect favouring axial substituent at C-l (32)63. 

The ionization potentials, singlet and triplet excited states, and frontier molecular orbitals of 1,4-, 1,8-, and 4,5-diazafluorenones were investigated by the all-valence-electrons INDO/S-CI method. Calculated molecular properties were found to be in accordance with experimental results... 

Although Otto Diels and Kurt Alder won the 1950 Nobel Prize in Chemistry for the Diels-Alder reaction, almost 20 years later R. Hoffmann and R. B. Woodward gave the explanation of this reaction. They published a classical textbook, The Conservation of Orbital Symmetry. K. Fukui (the co-recipient with R. Hoffmann of the 1981 Nobel Prize in Chemistry) gave the Frontier molecular orbital (FMO) theory, which also explains pericyclic reactions. Both theories allow us to predict the conditions under which a pericyclic reaction will occur and what the stereochemical outcome will be. Between these two fundamental approaches to pericyclic reactions, the FMO approach is simpler because it is based on a pictorial approach. Another method similar to the FMO approach of analyzing pericyclic reactions is the transition state aromaticity approach. 

Free Energy Perturbation (FEP) methods, 381 Frequency representation, of propagators, 257 Frontier Molecular Orbital (1 0) theory, 347 Frozen core, frozen virtual orbitals, 101 Fukui function, 352... 

According to the frontier molecular orbital theory (FMO theory), the reactivity of a 1,3-dipole is inversely proportional to the energy difference between the frontier orbitals of a 1,3-dipole and a dipolarophile. The frontier orbital energies of the parent azomethine ylide 110 are calculated by a CNDO/2 method to be highest occupied molecular orbital (HOMO) =... 

Methods other than thermodynamic cycles are often used to calculate acid dissociation constants. Previous publications implement the theoretical relationship between pKa and structural property [6], bond valence methods and bond lengths [33], pKa correlations with highest occupied molecular orbital (HOMO) energies and frontier molecular orbitals [34], and artificial neural networks [35] to predict pKa values. In addition much work has been done using physical properties as quantitative structure-activity relationship (QSAR) descriptors, and regression equations with such descriptors to yield accurate pKa values for specific classes of molecules [36-47]. The correlation of pKas to various molecular properties, however, is often restricted to specific classes of compounds, and it is... 

A related method to interpret the diastereofecial selectivities of the reactions of double bonds has been proposed by Dannenberg and coworkers [8, 13, 14,]. Tins method also relies on the 7t frontier orbitals of non symmetrical molecules, and proposes breaking the symmetry of the n or it orbitals due to polarization induced by the substituents. Application of frontier molecular orbital theory, taking into account only the substrate MOs, gives a qualitative trend of stereoselection in a number of nucleophilic (reductions of carbonyl compounds) and electrophilic reactions. 

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