Molecular orbitals frontier orbital method

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. 

Professors Kenichi Fukui (Kyoto University) and Roald Hoffmann (Cornell University) received the 1981 Nobel Prize in Chemistry for their quantum mechanical studies of chemical reactivity. Their applied theoretical chemistry research is certainly at the core of computational chemistry by today s yardstick. Professor Fukui s name is associated with frontier electrons, which govern the transition states in reactions, while that of Hoffmann is often hyphenated to R. B. Woodward s name in regard to their orbital symmetry rules. In addition, Professor Hoffmann s name is strongly identified with the extended Hiickel molecular orbital method. Not only was he a pioneer in the development of the method, he has continued to use it in almost all of his over 300 papers. 

Another acronym for this approach is FO (frontier orbital) theory. The acronym FMO is also used for the fragment molecular orbital method. See, for example, Fedorov, D. G. Kitaura, K. J. Phys. Chem. A 2007, 111, 6904. 

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. 

From 1933 85>, several theoretical approaches to the problem of the chemical reactivity of planar conjugated molecules began to appear, mainly by the Huckel molecular orbital theory. These were roughly divided into two groups 36>. The one was called the "static approach 35,37-40)j and the other, the "localization approach 41,42). in 1952, another method which was referred to as the "frontier-electron method was proposed 43> and was conventionally grouped 44> together with other related methods 45 48> as the "delocalization approach". 

Each reaction species must have molecular orbitals available and with the correct symmetry to allow bonding. These will be called frontier orbitals composed of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). In addition to their involvement in bonding between species, these orbitals are of considerable interest in that they are largely responsible for many of the chemical and spectroscopic characteristics of molecules and species and are thus important in analytical procedures and spectroscopic methods of analysis [5-7],... 

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 highest-energy occupied molecular orbital (HOMO) and the lowest-energy unoccupied molecular orbital (LUMO) of a particular molecular entity. The HOMO can be completely or partially filled whereas the LUMO can be completely or partially vacant. The frontier orbital method allows one to interpret reaction behavior by studying HOMO and LUMO overlaps between reacting entities. 

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. 

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