Static reactivity theories

A theoretical study by the same author suggests that RDX forms charge transfer complexes upon crystn which are unique because their charge transfer exciton band is of lower energy than the singlet exciton band of their molecular crysts. Static reactivity indices were used to predict the likely primary dissociative products obtainable from each excited state of secondary nitramines theory predicts that the axial and equatorial nitramine groups of the polynitra-mines RDX, alpha- and beta-HMX, may possess quite novel selective decompn paths and hence give different primary dissociative products... 

Nalewajski [19-21] formulated a theory of static reactivity kernels prior to but closely related to that of Berkowitz and Parr [15] which started out from a second-order perturbative treatment of the total energy. He identified an external static potential of unspecified origin with the chemical stimulus and made the first connection between softness kernels and the total energy. His result is, in our notation,... 

The perturbation theory we consider is for the static reactivity pertaining to a perturbation of the reactor from a reference critical state. We use the general form of the transport equations with spelled-out notations and a continuous representation of the phase-space variables (r, E, 1). The subscript 0 is omitted from the parameters corresponding to the critical reactor. Instead, a bar denotes perturbed parameters. We take 7=1. 

Exact perturbation theory expressions for the static reactivity can be obtained from the pair of equations (78)-(81)and (79)-(80) [see derivation ofEq. (8)],... 

The exact perturbation theory expression for the static reactivity, Eq. (11), can be expressed in terms of the unperturbed flux and the flux perturbation as follows ... 

The quasi-static reactivity balance theory of designing for passive safety response to ATWS initiators has been applied in the design of STAR-H2. The efficacy of this design approach is confirmed by the evaluation results to be presented next. 

We can distinguish between static theories, which in essence give a description of the electron density, and dynamic theories, where an attempt is marie to measure the response of a molecule to (e.g.) an approaching N02" " ion. In recent years, the electrostatic potential has been used to give a simple representation of the more important features of molecular reactivity. It can be calculated quite easily at points in space ... 

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". 

Stability and reactivity of crown-ether complexes, 17, 279 Stereochemistry, static and dynamic, of alkyl and analogous groups, 25, 1 Stereoelectronic control, the principle of least nuclear motion and the theory of, 24, 113 Stereoselection in elementary steps of organic reactions, 6, 185 Steric isotope effects, experiments on the nature of, 10, 1... 

The quantum theory of molecular collisions in external fields described in this chapter is based on the solutions of the time-independent Schrodinger equation. The scattering formalism considered here can be used to calculate the collision properties of molecules in the presence of static electric or magnetic fields as well as in nonresonant AC fields. In the latter case, the time-dependent problem can be reduced to the time-independent one by means of the Floquet theory, discussed in the previous section. We will consider elastic or inelastic but chemically nonreac-tive collisions of molecules in an external field. The extension of the formalism to reactive scattering problems for molecules in external fields has been described in Ref. [12]. 

For problems of structure the CM model is not the first choice. The development of qualitative MO models over recent years has made an enormous impact on these questions so that, as a whole, this subject is relatively well understood. With regard to questions of reactivity, however, the situation is quite different. By its very design, qualitative MO theory is most readily applied to static problems where the interacting groups are stationary with respect to one another. There is no simple way in which motion along a reaction co-ordinate can be readily accommodated within such a framework. 

The softness kernels are relevant to the remaining cases of two or more interacting systems. However, they do not by themselves provide sufficient information to constitute a basis for a theory of chemical reactivity. Clearly, the chemical stimulus to one molecule in a bimolecular reaction is provided by the other. That being the case, an eighth issue arises. Both the perturbing system and the responding system have internal dynamics, yet the softness kernel is a static response function. Dynamic reactivities need to be defined. 

By mentioning the thermodynamic a-effect in the last section, we have again strayed from the main concern of this book—chemical reactions—into an area beyond its scope, namely the static properties of a molecule. Nevertheless, it is a large and growing area of study, and since it is in fact closely related to the general subject of frontier orbital theory, further digression on the subject will not be inappropriate. The interactions of orbitals within a molecule account for many features of chemical structure, much as the interactions of frontier orbitals account for many features of chemical reactivity. Just as frontier orbital theory is especially successful when it is used to compare the relative reactivity of two closely related systems, so its application to structural problems is most successful when the energies of two closely related molecules are to be compared. Here are two examples. 

For reactive flows the governing equations used by Lindborg et al [92] resemble those in sect 3.4.3, but the solid phase momentum equation contains several additional terms derived from kinetic theory and a frictional stress closure for slow quasi-static flow conditions based on concepts developed in soil mechanics. Moreover, to close the kinetic theory model the granular temperature is calculated from a separate transport equation. To avoid misconception the model equations are given below (in which the averaging symbols are disregarded for convenience) ... 

The physical properties and chemical reactivity of molecules may be and often are drastically changed by a surrounding medium. In many cases specific complexes are formed between the solvent and solute molecules whereas in other cases only the non-bonded intermolecular interactions are responsible for the solvational effects. By one definition, the environmental effects can be divided into two principally different types, i.e. to the static and dynamic effects. The former are caused by the coulombic, exchange, electronic polarization and correlation interactions between two or more molecular species at fixed (close) distances and relative orientation in space. The dynamic interactions are due to the orientational relaxation and atomic polarization effects, which can be accounted for rigorously only by using time-dependent quantum theory. 

The first solvent property applied to correlate reactivity data was the static dielectric constant 8 (also termed e,) in the form of dielectric functions as suggested from elementary electrostatic theories as those by Bom (l/e), Kirkwood (e-l)/(2 fl), Clausius-Mosotti (e-l)/(8+2), and (8-l)/(e+l). A successM correlation is shown in Figure 13.1.1 for the rate of the 8 2 reaction of p-nitrofluorobenzene with... 

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