Frontier orbital theory principle

The formation of Thiele s ester 6.217 is a remarkable example of several of the kinds of selectivity that we have been seeing in the last few sections, all of which can be explained by frontier orbital theory. The particular pair of cyclopenta-dienes which do actually react together 6.215 and 6.216 are not the only ones present. As a result of the rapid 1,5-sigmatropic hydrogen shifts [see (Section 6.3.1.3) page 197], all three isomeric cyclopentadiene carboxylic esters are present, and any combination of these is in principle possible. As each pair can combine in several different ways there are, in fact, 72 possible Diels-Alder adducts. 

For all their faults and limitations, frontier orbital theory and the principle of hard and soft acids and bases remain the most accessible approaches to understanding many aspects of reactivity. Since they fill a gap between the chemist s experimental results and a state of the art theoretical description of his or her observations, they will continue to be used until something better comes along. 

We are far from exhausting the subject of regioselectivity in dipolar cycloadditions with these few examples. Frontier orbital theory has been successful in accounting for most of the otherwise bewildering trends in regioselectivity. No other theory, whether based on polar or steric factors, or on the possibility of diradical intermediates, has had anything like such success. It is plain that, as so often happens in science, a very large body of data has at last been reduced to an amenable set of principles. 

The theory is presented very simply, without mathematics, stressing physical principles and assuming only that the reader is familiar with the concept of a molecular orbital as a linear combination of atomic orbitals. This book thus makes frontier orbital theory accessible for the first time to readers at every level. 

A number of concepts for general chemical reactivity exist, such as the principle of hard and soft acids and bases [17, 24], electronegativity [25-27] and frontier orbital theory [28-30]. 

The principle of hard and soft acids and bases [I] (HSAB), and the principle of electronegativity equalization [2], together with frontier orbital theory [3] have been, over the years, very useful to establish the behavior of molecules under different circumstances, their reactive sites, and possible reaction mechanisms [4]. Through these principles, and through the values of the parameters associated with them hardness, softness, and electronegativity, it has been possible to correlate and to analyze experimental information that allows one to characterize the interactions involved between different chemical species in many different situations. From this exp>erience it has been possible to establish a priori the development of a wide variety of chemical reactions. 

Dewar MJS (1989) A critique of frontier orbital theory. J Mol Struct (Theochem) 200 301-323 Doering W von E, Roth WR (1962) The overlap of two allyl radicals or a four-centered transition state in the cope rearrangement. Tetrahedron 18 67-74 Barman J (2004) Laws, symmetry, and symmetry breaking invariance, conservation principles, and objectivity. PSA 2002 Presidential Address, Philos Sci 71 1227-1241 Fisher G (2006) The autonomy of models and explanation anomalous molecular rearrangements in early twentieth-century physical organic chemistry. Stud Hist Philos Sci A 37 562-584 Gavroglu K, Simoes A (2012) Neither physics nor chemistry a history of quantum chemistry. MIT Press, Cambridge, MA... 

The chemical potential, chemical hardness and sofmess, and reactivity indices have been nsed by a number of workers to assess a priori the reactivity of chemical species from their intrinsic electronic properties. Perhaps one of the most successful and best known methods is the frontier orbital theory of Fukui [1,2]. Developed further by Parr and Yang [3], the method relates the reactivity of a molecule with respect to electrophilic or nucleophilic attack to the charge density arising from the highest occupied molecular orbital or lowest unoccupied molecular orbital, respectively. Parr and coworkers [4,5] were able to use these Fukui indices to deduce the hard and soft (Lewis) acids and bases principle from theoretical principles, providing one of the first applications of electronic structure theory to explain chemical reactivity. In essentially the same form, the Fukui functions (FFs) were used to predict the molecular chemical reactivity of a number of systems including Diels-Alder condensations [6,7], monosubstituted benzenes [8], as well as a number of model compounds [9,10]. Recent applications are too numerous to catalog here but include silylenes [11], pyridinium ions [12], and indoles [13]. 

This quantity can be viewed as a generalization of Fukui s frontier molecular orbital (MO) concept [25] and plays a key role in linking Frontier MO theory and the HSAB principle. It can be interpreted either as the sensitivity of a system s chemical potential to an external perturbation at a particular point r, or as the change of the electron density p(r) at each point r when the total number of electrons is changed. The former definition has recently been implemented to evaluate this function [26,27] but the derivative of the density with respect to the number of electrons remains by far the most widely used definition. 

We have now seen that the effort of Parr and collaborators [8-12] to put Fukui s frontier-orbital concept of chemical reactivity on sound footing in density-functional theory through the definition of the Fukui function and the local and global softness works only for extended systems. This restriction to extended systems raises a sixth issue. In both the local softness and the Fukui function, Eqs. (54) and (53a), the orbitals at the chemical potential represent both the LUMO and the HOMO in the Fukui sense. However, there is a continuum of unoccupied KS states above the chemical potential accessible even to weak chemical perturbations any linear combination of which could in principle be selected as the LUMO, and similarly for states below fi and the HOMO. This ambiguity in the frontier-orbital concept obviously applies as well to localized systems when there is more than one KS state significantly affected by a chemical perturbation. 

Li, Y, Evans, J. N. S. (1995). The fukui function a key concept linking frontier molecular orbital theory and the hard-soft-acid-base principle. J. Am. Chem. Soc. 117, 7756-7759. 

Based on the foregoing discussion, one might suppose that the Fukui function is nothing more than a DFT-inspired restatement of frontier molecular orbital (FMO) theory. This is not quite true. Because DFT is, in principle, exact, the Fukui function includes effects—notably electron correlation and orbital relaxation—that are a priori neglected in an FMO approach. This is most clear when the electron density is expressed in terms of the occupied Kohn-Sham spin-orbitals [16],... 

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. 

Klopman attempted to quantify Pearson s HSAB principle using frontier molecular orbital (FMO) theory (Klopman 1968), with the following equation ... 

In 1952, Fukui published his Frontier MO theorywhich went initially unnoticed. In 1965, Woodward and Hoffmann published their principle of conservation of orbital symmetry, and applied it to all pericyclic chemical reactions. The immense success of these rules" renewed interest in Fukui s approach and together formed a new MO-based framework of thought for chemical reactivity (called, e.g., giant steps forward in chemical theory in Morrison and Boyd, pp. 934, 939, 1201, and 1203). This success of MO theory dealt a severe blow to VB theory. In this area too, despite the early calculations of the Diels-Alder and 2-1-2 cycloaddition reactions by Evans,VB theory missed making an impact, in part at least because of its blind adherence to simple resonance theory. All the subsequent VB derivations of the rules (e.g., by Oosterhoff in Ref. 90) were after the fact and failed to reestablish the status of VB theory. 

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