Observe that to generate the reactions of Fig. 9 no information was necessary on whether such a reaction is known no database of reactions is necessary. The problems in building, updating and maintaining a reaction library are thus avoided. The formal treatment of reactions as bond and electron-shifting processes allows the generation, in principle, of all conceivable reactions, and can be seen as a method to deal freely with molecular architecture. The program s result could be a known reaction, but equally a new, as yet undiscovered reaction which could be realised in the laboratory. [Pg.31]

The formal treatment is quite similar to the derivation of the principal g values as developed in Eqs. (7C) through (18C). The second-order energy term is set equal to the hyperfine term from the spin Hamiltonian, and for the z direction... [Pg.339]

The segregation or demixing is a purely kinetic effect and the magnitude depends on the cation mobility and sample thickness, and is not directly related to the thermodynamics of the system. In some specific cases, a material like a spinel may even decompose when placed in a potential gradient, although both potentials are chosen to fall inside the stability field of the spinel phase. This was first observed for Co2Si04 [39]. Formal treatments can be found in references [37] and [38],... [Pg.153]

The product cystine is presumably formed in the recombination of two thiyl radicals. This free-radical model is suitable for formal treatment of the kinetic data however, it does not account for all possible reactions of the RS radical (68). The rate constants for the reactions of this species with RS-, 02 and Cu L, (n = 2, 3) are comparable, and on the order of 109-10loM-1s-1 (70-72). Because all of these reaction partners are present in relatively high and competitive concentrations, the recombination of the thiyl radical must be a relatively minor reaction compared to the other reaction paths even though it has a diffusion controlled rate constant. It follows that the RS radical is most likely involved in a series of side reactions producing various intermediates. In order to comply with the noted chemoselectivity, at some point these transient species should produce a common intermediate leading to the formation of cystine. [Pg.430]

Counselors and therapists have to determine when the client has made sufficient progress to move into this next phase of therapy. The decision whether the client is ready to be moved from formal treatment into aftercare is determined by client progress on the treatment plan. The counselor or therapist uses clinical judgment to ascertain whether the client has made sufficient progress on the plan to warrant movement from formal treatment into aftercare and whether the client is sufficiendy stable in his or her recovery to take this next step toward autonomous recovery. The next section covers factors that counselors and therapists should consider when making the decision to graduate clients from treatment into aftercare. In addition, this chapter provides an overview of what can be expected during this final phase of treatment and therapy for professionals, and for clients and their families. [Pg.232]

The first main purpose of this book is to formalize the role of aggregate demand as a constraint on expanded reproduction. I will develop an analytical model which explores the conditions under which profits can be realized in the reproduction schema. This approach is in keeping with the spirit of Dillard s (1984 425) statement that Marx s economics would be strengthened by a more formal treatment of the theory of effective demand. ... [Pg.2]

Finally - and equally important - Jens contribution to the formal treatment of GOS based on the polarization propagator method and Bethe sum rules has been shown to provide a correct quantum description of the excitation spectra and momentum transfer in the study of the stopping cross section within the Bethe-Bloch theory. Of particular interest is the correct description of the mean excitation energy within the polarization propagator for atomic and molecular compounds. This motivated the study of the GOS in the RPA approximation and in the presence of a static electromagnetic field to ensure the validity of the sum rules. [Pg.365]

The relevant formal treatment starts from the notion that all the quantities related to electronic structure of molecules can be calculated with use of only one- and two-electron density matrices for the relevant electronic state of the system under study [36]. Taking the energy for the sake of definiteness we get ... [Pg.457]

Neither of the Is orbitals of the hydrogen atoms of the water molecule, taken separately, transform within the group of irreducible representations deduced for that molecule. The two Is orbitals must be taken together as one or the other of two group orbitals. A more formal treatment of the group orbitals which two Is orbitals may form is dealt with in Chapter 3. [Pg.26]

X being a 4/ wave function. From this expression, one estimates that the oscillator strengths should be about the same as for an ion situated in a noncentrosymmetric field (P 10 6). A rigorous formal treatment for the vibronically induced electric-dipole transitions has been developed by Satten (32-34),... [Pg.210]

Therefore, the attractive force on On will increase The attractive forces on 0 and Gn are opposite in direction and so the Ox On distance diminishes as the zero point energy level is raised. On this basis, the lower zero point energy of deuterium compared with hydrogen will produce an increase in Ox Qri distance on substituting D fox II in hydrogen bonds. A more formal treatment of this explanation will be presented at a later date. [Pg.51]

The scheme ascribed to Peaceman and Rachford provides some realization of this idea and refers to implicit alternating direction schemes. The present values y = yn and y = yn+1 of this difference scheme are put together with the intermediate value y = j/n+1 2, a formal treatment of which is the value of y at moment t = tn+]/2 = tn + r/ 2. The passage from the nth layer to the (n + 1)th layer can be done in two steps with the appropriate spacings 0.5 r ... [Pg.548]

The formal treatment of A//rxn is facilitated by a convenient general notation for chemical reactions. It is well known that a balanced chemical reaction of generic form... [Pg.102]

R. A. Marcus Prof. Fleming has shown, I gather, that apart from the behavior at very short times the harmonic oscillator approximation breaks down. Are there any implications for one current formal treatment of the liquid as a harmonic bath that interacts bilinearly with the solute Did the discrepancy merely reflect the absence of hypothetical low-frequency modes ... [Pg.181]

By justifying the independence of rate processes in the statistical limit, we have reconciled our formal treatment with the conventional discussions of isomerization reaction kinetics. In these latter treatments the quantum yield for, say, the tram to cis conversion can be simply presented185 as... [Pg.283]

This monograph deals with kinetics, not with dynamics. Dynamics, the local (coupled) motion of lattice constituents (or structure elements) due to their thermal energy is the prerequisite of solid state kinetics. Dynamics can explain the nature and magnitude of rate constants and transport coefficients from a fundamental point of view. Kinetics, on the other hand, deal with the course of processes, expressed in terms of concentration and structure, in space and time. The formal treatment of kinetics is basically phenomenological, but it often needs detailed atomistic modeling in order to construct an appropriate formal frame (e.g., the partial differential equations in space and time). [Pg.5]

Chemical diffusion has been treated phenomenologically in this section. Later, we shall discuss how chemical diffusion coefficients are related to the atomic mobilities of crystal components. However, by introducing the crystal lattice, we already abandon the strict thermodynamic basis of a formal treatment. This can be seen as follows. In the interdiffusion zone of a binary (A, B) crystal having a single sublattice, chemical diffusion proceeds via vacancies, V. The local site conservation condition requires that /a+/b+7v = 0- From the definition of the fluxes in the lattice (L), we have... [Pg.75]

Spinel formation is usually treated under some tacit assumptions which do not always hold. For example, it is tacitly assumed that the oxygen potential of the surrounding gas atmosphere prevails throughout the reaction product during reaction. In other words, it is assumed that d,u0 = 0. Although this inference reduces the number of variables by one and simplifies the formal treatment, the subsequent analysis will show that the assumption is normally not adequate. [Pg.147]

The second condition for bulk transport in AX is A > A in accordance with our assumptions. The point defects relax by a bimolecular reaction mode (see Section 5.3.3). In order to simplify the formal treatment, we linearize the recombination rate... [Pg.248]

There is one more conceptual step involved in the formal treatment. The perturbation <[> is Fourier analyzed, which means that it is constructed from the Fourier components 4>(k,t) with wavelength A = 2-n/k. 8cv is transformed in the same way. Explicitly,... [Pg.280]

For the formal treatment, we note that the divergence of the total electric current vanishes, that is, V = 0. In a closed system, the condition of (local) electro-... [Pg.285]

Periodic reactions of this kind have been mentioned before, for example, the Liese-gang type phenomena during internal oxidation. They take place in a solvent crystal by the interplay between transport in combination with supersaturation and nuclea-tion. The transport of two components, A and B, from different surfaces into the crystal eventually leads to the nucleation of a stable compound in the bulk after sufficient supersaturation. The collapse of this supersaturation subsequent to nucleation and the repeated build-up of a new supersaturation at the advancing reaction front is the characteristic feature of the Liesegang phenomenon. Its formal treatment is quite complicated, even under rather simplifying assumptions [C. Wagner (1950)]. Other non-monotonous reactions occur in driven systems, and some were mentioned in Section 10.4.2, where we discussed interface motion during phase transformations. [Pg.289]

The discussion up to this point has been concerned essentially with metal alloys in which the atoms are necessarily electrically neutral. In ionic systems, an electric diffusion potential builds up during the spinodal decomposition process. The local gradient of this potential provides an additional driving force, which acts upon the diffusing species and this has to be taken into account in the derivation of the equivalents of Eqns. (12.28) and (12.30). The formal treatment of this situation has not yet been carried out satisfactorily [A.V. Virkar, M. R. Plichta (1983)]. We can expect that the spinodal process is governed by the slower cation, for example, in a ternary AX-BX crystal. The electrical part of the driving force is generally nonlinear so that linearized kinetic equations cannot immediately be applied. [Pg.311]

TWo remarks, however, seem appropriate. 1) If the distance, a, between individual dislocations is very small on an atomic scale, diffusion coefficients obtained from macroscopic experiments can not be used in Eqn. (14.29) (as explained in Sections.1.3). 2) Since diffusional transport takes place in the stress field of dislocations, in principle, fluxes in the form of Eqn. (14.18) should be used. This, however, would complicate the formal treatment appreciably. In the zeroth order approach, one therefore neglects the influence of the stress gradient, which can partly be justified by the symmetry of the transport problem. [Pg.346]

The second part (sections H and I) is devoted to a detailed discussion of the dynamics of unimolecular reactions in the presence and the absence of a potential barrier. Section H presents a critical examination of the Kramers approach. It is stressed that the expressions of the reaction rates in the low-, intermediate-, and high-friction limits are subjected to restrictive conditions, namely, the high barrier case and the quasi-stationary regime. The dynamics related to one-dimensional diffusion in a bistable potential is analyzed, and the exactness of the time dependence of the reaction rate is emphasized. The essential results of the non-Markovian theory extending the Kramers conclusions are also discussed. The final section investigates in detail the time evolution of an unimolecular reaction in the absence of a potential barrier. The formal treatment makes evident a two-time-scale description of the dynamics. [Pg.78]

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