And the frontier orbital method

Most calculations on chemical systems within the scheme just mentioned are model calculations in the sense that they are performed on very simple chemical systems and are intended to serve as a model for a large class of similar systems. Consequently, it is also important to develop qualitative models of the topology and energetics of potential surfaces so that one may interpolate between experimental data that may be available, since only a small number of model situations may be explored with detailed numerical computations. Such qualitative theoretical models need to be formulated so that a numerical calculation of the characteristics of a molecular potential surface can be analysed a posteriori within a quantitative model and the results of this analysis carried forward to other systems in a qualitative way. The familiar Woodward-Hoffmann approach (based on Hiickel theory) and the frontier orbital method have the difficulty that they cannot be us to analyse the results of a molecular structure computation based upon an extensive configuration-interaction (Cl) expansion. Thus, one must begin to reformulate such qualitative models within the sophisticated models that are now routinely used to perform molecular structure computations. 

For an organic reaction, the HSAB principle can also be applied for the study of kinetics and equilibrium, and the frontier orbital method can be used to illustrate the electrophilic and nucleophilic interactions (Fig. 1) ... 

The last decade has witnessed an unprecedented strengthening of the bone between theory and experiment in organic chemistry. Much of this success may be credited to the development of widely applicable, unifying concepts, such as the symmetry rules of Woodward and Hoffmann, and the frontier orbital thee>ry of Eukui. Whereas the the ore tical emphasis had historically been on detailed structure and spectroscopy, the new methods are de signe d to solve pre)blems e>f special importance to organic chemists reactivity, stereochemistry, and mechanisms. 

This type of orientation of the newly formed bonds is called antarafacial, and the reaction would be a [ 2s + 4a] cycloaddition (a stands for antarafacial). We can easily show by the frontier-orbital method that this reaction (and consequently the reverse ring-opening reactions) are thermally forbidden and photochemically allowed. Thus in order for a reaction to proceed,... 

To circumvent problems associated with the link atoms different approaches have been developed in which localized orbitals are added to model the bond between the QM and MM regions. Warshel and Levitt [17] were the first to suggest the use of localized orbitals in QM/MM studies. In the local self-consistent field (LSCF) method the QM/MM frontier bond is described with a strictly localized orbital, also called a frozen orbital [43]. These frozen orbitals are parameterized by use of small model molecules and are kept constant in the SCF calculation. The frozen orbitals, and the localized orbital methods in general, must be parameterized for each quantum mechanical model (i.e. energy-calculation method and basis set) to achieve reliable treatment of the boundary [34]. This restriction is partly circumvented in the generalized hybrid orbital (GHO) method [44], In this method, which is an extension of the LSCF method, the boundary MM atom is described by four hybrid orbitals. The three hybrid orbitals that would be attached to other MM atoms are fixed. The remaining hybrid orbital, which represents the bond to a QM atom, participates in the SCF calculation of the QM part. In contrast with LSCF approach the added flexibility of the optimized hybrid orbital means that no specific parameterization of this orbital is needed for each new system. 

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. 

We have emphasized that the Diels-Alder reaction generally takes place rapidly and conveniently. In sharp contrast, the apparently similar dimerization of olefins to cyclobutanes (5-49) gives very poor results in most cases, except when photochemically induced. Fukui, Woodward, and Hoffmann have shown that these contrasting results can be explained by the principle of conservation of orbital symmetry,895 which predicts that certain reactions are allowed and others forbidden. The orbital-symmetry rules (also called the Woodward-Hoffmann rules) apply only to concerted reactions, e.g., mechanism a, and are based on the principle that reactions take place in such a way as to maintain maximum bonding throughout the course of the reaction. There are several ways of applying the orbital-symmetry principle to cycloaddition reactions, three of which are used more frequently than others.896 Of these three we will discuss two the frontier-orbital method and the Mobius-Huckel method. The third, called the correlation diagram method,897 is less convenient to apply than the other two. 

Method. Assume that (1) the reaction is controlled by the interaction between the radical SOMO (singly occupied MO) and the frontier orbitals of the substrates (2) the radical adds preferentially to the unsubstituted carbon of the vinyl acetate. 

Kenichi Fukui and Roald Hoffmann won the Nobel prize in 1981 (Woodward died in 1979 and so couldn t share this prize he had already won the Nobel prize in 1965 for his work on synthesis) for the application of orbital symmetry to pericyclic reactions. Theirs is an alternative description to the frontier orbital method we have used and you need to know a little about it. They considered a more fundamental correlation between the symmetry of all the orbitals in the starting materials and all the orbitals in the products. This is rather too complex for our consideration here, and we shall concentrate only on a summary of the conclusions—the Woodward-Hoffmann rules. The most important of these states ... 

In most cases, dienophile addition occurs across the 3- and 6-positions of the 1,2,4-triazine ring as shown in Scheme 56, but acetylenes can also add across the 2- and 5-positions (Scheme 57). The orientations can be explained using the frontier orbital method, or through secondary orbital interactions. 

In all of the above discussion we have assumed that a given molecule forms both the new ct bonds from the same face of the n system. This manner of bond formation, called suprafacial, is certainly most reasonable and almost always takes place. The subscript s is used to designate this geometry, and a normal Diels-Alder reaction would be called a [ 2s + 4J-cycloaddition (the subscript 71 indicates that n electrons are involved in the cycloaddition). However, we can conceive of another approach in which the newly forming bonds of the diene lie on opposite faces of the n system, that is, they point in opposite directions. This type of orientation of the newly formed bonds is called antarafacial, and the reaction would be a [ 2 + 4a]-cycloaddition (a stands for antarafacial). We can easily show by the frontier-orbital method that this reaction (and consequently the reverse ring-opening reactions) are thermally forbidden and photoche-mically allowed. Thus in order for a [fZs + -reaction to proceed, overlap between the highest occupied n orbital of the alkene and the lowest unoccupied 71 orbital of the diene would have to occur as shown in Fig. 15.10, with a + lobe... 

Calculation of the electronic distribution of 6- and 7-phenyl derivatives of (15) showed that there is only a very slight difference between the two compounds, which cannot account for the essentially different biological behavior of the two compounds <89MI 816-01 >. Quantum chemical studies have also been reported on an ylide derivative of (37) (i.e. (106)), and the frontier orbital energies have been calculated by an ab initio (STO-3G) method <87JCS(Pl)253i>. 

Hudson and Klopman proposed an equation to deseribe the effeet of orbital perturbation of two moleeules on ehemieal reaetivity. Their hypothesis is that the initial perturbation determines the eourse of a reaetion or an interaetion. They applied quantum-meehanieal method to treat the eneounter of two interaeting systems as reaetivity. Their equation for interaetion energy ean be simplified by ineluding only two terms [10.2.2] the Coulombie interaetion and the frontier orbital interaetion between HOMO and LUMO. 

Most of the theoretical methods used to correlate chemical reactivity trends implicitly (or in some cases explicitly) use a model of interacting diabatic surfaces in which the transition structure is associated with an avoided crossing of a reactant-like or a product-like diabatic surface. In the molecular-orbital correlation diagram approach of Woodward and Hoffmann or the frontier orbital method of Fukui, the molecular orbitals of the fragments are first mixed to form the MO of the supermolecule and then the electrons are assigned to various configurations of these supermolecule MO. We shall refer... 

However equally important is the availability of physically grounded models that can provide understanding of chemical reactivity. In the past, theories of reactivity have been based on empirical structure-reactivity relationships (viz. linear free energy relationships) or qualitative theoretical concepts (viz. Woodward-Hoffmann approach or the frontier orbital method)[4-ll]. However, there is a different approach, which is potentially more fruitful. In this approach one uses physically grounded models that can be obtained from the best state of the art methodology of quantum chemistry. These physically grounded models must be both quantitative and qualitative. On the one hand, any model used should reproduce the numerically computed quantities exactly, on the... 

These results are interesting because neither the frontier orbital method nor arguments based on the conservation of orbital symmetry during reactions can account for the difference between the two modes of the Cope rearrangement. According to these theories, rearrangement via boat and chair transition states should be equally allowed. 

For the acid-base interaction in solutions, in 1963, Pearson proposed the hard-soft acid-base (HSAB) principle to describe some basic rules about the kinetics and equilibrium of the reaction. In this paper, we attempt to apply the HSAB principle to solid interactions with the aid of the frontier orbital method. We shall first describe the HSAB principle as it has been evolved in recent years " and then the band structures of solids. After we demonstrate the compatibility between the HSAB principle and the band structures in the solid state, we then illustrate with several examples of adhesion and tribointeractions between metals and... 

According to the frontier orbital method,the relationship of q with the energies of LUMO and HOMO is shown in Fig. 1. Thus, from Fig. 1,... 

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