Reaction Rules and Predictive Theories

There have been numerous studies with the object of gaining an understanding of the factors that influence the stability, stoichiometry, and H site occupation in hydride phases. Stability has been correlated with cell volume [8] or the size of the interstitial hole in the metal lattice [13] and the free energy of the a p phase conversion. This has been widely exploited to modulate hydride phase stabihty as discussed in Section 9.2.1. 

Westlake developed a geometric model which is fairly successfril in predicting site occupation in AB5 and AB2 hydride phases [14]. It involves two structural constraints that the minimum hole size necessary to accommodate a H atom has a radius of 0.40 A and that the minimum distance between two H occupied sites is 2.10 A. The former criterion was empirically derived from a survey of known hydride structures while the latter was suggested by Switendick based on electronic [15] band structure calculations. 

A relatively simple set of rules has been found to hold for all intermetaUic hydrides useful for hydrogen storage [16]. They may be stated as follows  

1) In order for an intermetaUic compound to react directly and reversibly with hydrogen to form a distinct hydride phase it is necessary that at least one of the metal components be capable of reacting directly and reversibly with hydrogen to form a stable binary hydride. 

2) If a reaction takes place at a temperature at which the metal atoms are mobile, the system will assume its most favored thermodynamic configuration. 

Westlake developed a geometric model which is fairly successful in predicting site occupation in ABs and AB2 hydride phases [9]. It involves two structural constraints  

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From a practical point of view, it would be very desirable to have reliable rules, even if only empirical, which could provide estimates of barrier heights in the absence of experimental data. This would be of obvious use in predicting thermodynamic quantities for stable molecules and would also be most valuable in testing and applying theories of reaction rates. Furthermore, any empirical regularities observed could be helpful in the development of a theoretical treatment of barriers. 

The orbital mixing theory was developed by Inagaki and Fukui [1] to predict the direction of nonequivalent orbital extension of plane-asymmetric olefins and to understand the n facial selectivity. The orbital mixing rules were successfully apphed to understand diverse chemical phenomena [2] and to design n facial selective Diels-Alder reactions [28-34], The applications to the n facial selectivities of Diels-Alder reactions are reviewed by Ishida and Inagaki elesewhere in this volume. Ohwada [26, 27, 35, 36] proposed that the orbital phase relation between the reaction sites and the groups in their environment could control the n facial selectivities and review the orbital phase environments and the selectivities elsewhere in this volume. Here, we review applications of the orbital mixing rules to the n facial selectivities of reactions other than the Diels-Alder reactions. 

The period 1930-1980s may be the golden age for the growth of qualitative theories and conceptual models. As is well known, the frontier molecular orbital theory [1-3], Woodward-Hoffmann rules [4, 5], and the resonance theory [6] have equipped chemists well for rationalizing and predicting pericyclic reaction mechanisms or molecular properties with fundamental concepts such as orbital symmetry and hybridization. Remarkable advances in aeative synthesis and fine characterization during recent years appeal for new conceptual models. 

Having learnt about the concerted reactions, we can now undertake the theory of these reactions. The development of the theory of concerted reactions has been due chiefly to the work of R.B. Woodward and R. Hoffmann. They have taken the basic ideas of molecular orbital theory and used them, mainly in a qualitative way, to derive selection rules which predict the stereochemical course of various types of concerted reactions. These rules are best understood in terms of symmetries of interacting molecular orbitals. Here are will see some of the most important theoretical approaches and see how they are interrelated. 

This theory proves to be remarkably useful in rationalizing the whole set of general rules and mechanistic aspects described in the previous section as characteristic features of the Diels-Alder reaction. The application of perturbation molecular orbital theory as an approximate quantum mechanical method forms the theoretical basis of Fukui s FMO theory. Perturbation theory predicts a net stabilization for the intermolecular interaction between a diene and a dienophile as a consequence of the interaction of an occupied molecular orbital of one reaction partner with an unoccupied molecular orbital of the other reaction partner. 

However, despite their proven explanatory and predictive capabilities, all well-known MO models for the mechanisms of pericyclic reactions, including the Woodward-Hoffmann rules [1,2], Fukui s frontier orbital theory [3] and the Dewar-Zimmerman treatment [4-6] share an inherent limitation They are based on nothing more than the simplest MO wavefunction, in the form of a single Slater determinant, often under the additional oversimplifying assumptions characteristic of the Hiickel molecular orbital (HMO) approach. It is now well established that the accurate description of the potential surface for a pericyclic reaction requires a much more complicated ab initio wavefunction, of a quality comparable to, or even better than, that of an appropriate complete-active-space self-consistent field (CASSCF) expansion. A wavefunction of this type typically involves a large number of configurations built from orthogonal orbitals, the most important of which i.e. those in the active space) have fractional occupation numbers. Its complexity renders the re-introduction of qualitative ideas similar to the Woodward-Hoffmann rules virtually impossible. 

In this primer, Ian Fleming leads you in a more or less continuous narrative from the simple characteristics of pericyclic reactions to a reasonably full appreciation of their stereochemical idiosyncrasies. He introduces pericyclic reactions and divides them into their four classes in Chapter 1. In Chapter 2 he covers the main features of the most important class, cycloadditions—their scope, reactivity, and stereochemistry. In the heart of the book, in Chapter 3, he explains these features, using molecular orbital theory, but without the mathematics. He also introduces there the two Woodward-Hoffmann rules that will enable you to predict the stereochemical outcome for any pericyclic reaction, one rule for thermal reactions and its opposite for photochemical reactions. The remaining chapters use this theoretical framework to show how the rules work with the other three classes—electrocyclic reactions, sigmatropic rearrangements and group transfer reactions. By the end of the book, you will be able to recognize any pericyclic reaction, and predict with confidence whether it is allowed and with what stereochemistry. 

The roles and opportunities for the theoretical chemist as part of an atmospheric science investigative team have become both more defined and diverse. Since Krauss and Stevens [3], many of the topics they raised have been used, and continue to need to be used to advance our understanding of the chemistry of the atmosphere. For example, theoretical methods are used to predict and verify theories of the mechanistic pathways for the photooxidation of mercury (Ariya et al., this edition). The paper shows how heats of reaction are calculated by various methods, results which are then used to rule out reaction schemes. 

To predict the course of a copolymerization we need to be able to express the composition of a copolymer in terms of the concentrations of the monomers in the reaction mixture and some ready measure of the relative reactivities of these monomers. The utility of such a model can be tested by comparing experimental and estimated compositions of copolymers formed from given monomer concentrations. Asa general rule in science, the preferred model is the simplest one which fits the facts. For chain-growth copolymerizations, this turns out to be the simple copolymer model, which was the earliest useful theory in this connection [1,21. All other relations which have been proposed include more parameters than the simple copolymer model. We focus here on the simple copolymer theory because the basic concepts of copolymerization are most easily understood in this framework and because it is consistent with most copolymer composition and sequence distribution data. 

Liu ZP, Hu P (2003) General rules for predicting where a catalytic reaction should occur on metal surfaces A density functional theory study of C-H and C-O bond brealdng/making on flat, stepped, and kinked metal surfaces. J Am Chem Soc 125 1958... 

MO theory has been used to draw qualitative conclusions about the course of chemical reactions. The most fi-uitful applications have come from the Woodward-Hqffmemn rules, which predict the preferred path and stereochemistry for many important classes of organic reactions. As an example of the application of these rules, we consider the cyclization of a substituted 5-cis-butadiene to a substituted cyclobutene. There are two possible steric courses the reaction can take, described as con-rotatory or disrotatory, depending on whether the terminal groups rotate in the same or opposite senses as the reaction proceeds. Note the difference in products in Fig. 16.13. 

For many years, pericyclic reactions were poorly understood and unpredictable. Around 1965, Robert B. Woodward and Roald Hoffmann developed a theory for predicting the results of pericyclic reactions by considering the symmetry of the molecular orbitals of the reactants and products. Their theory, called conservation of orbital symmetry, says that the MOs of the reactants must flow smoothly into the MOs of the products without any drastic changes in symmetry. In that case, there will be bonding interactions to help stabilize the transition state. Without these bonding interactions in the transition state, the concerted cyclic reaction cannot occur. Conservation of symmetry has been used to develop rules to predict which pericyclic reactions are feasible and what products will result. These rules are often called the Woodward-Hoffinann rules. 

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