Microscopic reversibility, theory

Here, Ri f and Rf i are the rates (per moleeule) of transitions for the i ==> f and f ==> i transitions respeetively. As noted above, these rates are proportional to the intensity of the light souree (i.e., the photon intensity) at the resonant frequeney and to the square of a matrix element eonneeting the respeetive states. This matrix element square is oti fp in the former ease and otf ip in the latter. Beeause the perturbation operator whose matrix elements are ai f and af i is Hermitian (this is true through all orders of perturbation theory and for all terms in the long-wavelength expansion), these two quantities are eomplex eonjugates of one another, and, henee ai fp = af ip, from whieh it follows that Ri f = Rf i. This means that the state-to-state absorption and stimulated emission rate eoeffieients (i.e., the rate per moleeule undergoing the transition) are identieal. This result is referred to as the prineiple of microscopic reversibility. 

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. 

According to the principle of microscopic reversibility, the reverse process must follow the same path. In fact, the stereoelectronic theory was first elaborated by examining this process, i.e. the cleavage of tetrahedral... 

To invoke microscopic reversibility and obtain a rate expression for a unimolecular reaction through considering the association of its products is an idea with a long history [706] and has been taken up in recent years in mass spectrometry [486, 489]. There are a number of treatments [165, 166, 486, 489], which are similar to each other and all of which can be considered to be, in essence, reformulations of QET. There is a tendency to refer to these reformulations, either individually of collectively, as phase space theory [165, 166, 452, 485] and this term is used in a collective sense here. 

In case the collision takes place according to Newtonian mechanics, the relation (1.3) can be proved by means of Liouville s theorem. In quantum mechanics, Eq. (1.3) is practically one of the postulates of the theory, following directly from quantum mechanical calculations of transition probabilities from one state to another. For our present purpose, considering that this is an elementary discussion, we shall simply assume the correctness of relation (1.3). This relation is sometimes called the principle of microscopic reversibility. 

Magnetic moment, 153, 155, 160 Magnetic quantum number, 153 Magnetization, 160 Magnetogyric ratio, 153, 160 Main reaction, 237 Marcus equation, 227, 238, 314 Marcus plot, slope of, 227, 354 Marcus theory, applicability of, 358 reactivity-selectivity principle and, 375 Mass, reduced, 189, 294 Mass action law, 11, 60, 125, 428 Mass balance relationships, 19, 21, 34, 60, 64, 67, 89, 103, 140, 147 Maximum velocity, enzyme-catalyzed, 103 Mean, harmonic, 370 Mechanism classification of. 8 definition of, 3 study of, 6, 115 Medium effects, 385, 418, 420 physical theories of, 405 Meisenheimer eomplex, 129 Menschutkin reaction, 404, 407, 422 Mesomerism, 323 Method of residuals, 73 Michaelis constant, 103 Michaelis—Menten equation, 103 Microscopic reversibility, 125... 

The focus of this chapter is a review of the methodologies employed in a priori implementations of RRKM theory for the collisionless dissociation/ isomerization steps in gas-phase unimolecular reactions. Special attention will be paid to recent developments, particularly those that have proven their utility through substantive applications. With microscopic reversibility, RRKM treatments of the dissociation process are directly applicable to the reverse bimolecular associations. Furthermore, some of the more interesting illustrations are for bimolecular reactions and so we do not limit our discussion of RRKM theory to unimolecular reactions. However, one should bear in mind that TST was originally derived for bimolecular reactions and the specific term RRKM theory is really only applicable to the unimolecular direction. 

M is Br2 or any other gas that is present. By the principle of microscopic reversibility , the reverse processes are also pressure-dependent. A related pressure effect occurs in unimolecular decompositions which are in their pressure-dependent regions (including unimolecular initiation processes in free radical reactions). According to the simple Lindemann theory the mechanism for the unimolecular decomposition of a species A is given by the following scheme (for more detailed theories see ref. 47b, p.283)... 

Name the four types of heat flow (two reversible and two irreversible). What is one of the validity requirements for the theory of microscopic reversibility When did Onsager assume this was the case ... 

Setting the rate of formation of the outer-sphere complex equal to its rate of conversion is known as the steady-state approximation and the outer-sphere complex is a reactive intermediate under such conditions. A steady state occurs when only a single or some of the elementary reactions in a mechanism arc at equilibrium. Complete equilibrium requires that the rates of forward and reverse reactions must be equal for all the elementary reactions and that all species must be at steady state. This is the principle of detailed balancing and is a consequence of the theory of microscopic reversibility that requires that forward and reverse reactions in an elementary process follow the same path. 

Another important aspect of Onsager s theory is the principle of microscopic reversibility. This is usually discussed with respect to the detailed balancing of chemical reactions. When it is considered with respect to the phenomenological coelScients, it leads to the reciprocal relations discussed above, namely that... 

The essential nature of this relationship is clear statistical theories are based on a number of simplifying assumptions consistent with chaotic behavior. Specifically,2 any such theory must satisfy microscopic reversibility and the condition of zero relevance. The latter condition requires that the final state be independent of all initial conditions other than conserved quantities, that is, from the viewpoint of classical mechanics, that the system display the relaxation characteristic of chaotic motion. We note, for reference, that this minimal set of requirements allows for the construction of a large number of theories,3 the most prominant of which are the RRK.M theory of uni-molecular dissociation4 and the phase space theory of bimolecular reactions.5 Such theories have analogues, and in some cases their origins are in other areas such as nuclear physics.6... 

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