Microreversibility principle

J.-F. Chapat, A. Finiels, J. Joffre, and C. Moreau, Synthesis of butyl-a and / -d-glucopyranosides in the presence of dealuminated H-Y faujasites Kinetic study, mechanism, stereoelectronic effects, and microreversibility principle, /. Catal., 185 (1999) 445—453. 

Michael addition, on A-2-thiazoline-5-one. with diethylazodicarboxylate, 433 with maleic anhydride, 433 4-phenyl-1,2,4-triazolin-3,5-dione, 433 Microreversibility principle, 85 Miticide, 440 Mitodepressive, 149, ISO Mn complexes, 104 Molecular orbital calculations. 17 and ambident reactivity, 61, 62 and amino-imino equilibrium, 18 and electrophilic substitution, 18 and HSAB, 1 8... 

The concerted three-center mechanism is the most common. It is exactly symmetrical to that already described for oxidative addition, according to the microreversibility principle (see section 3.1). It could indeed be shown that the reaction is intramolecular. For instance, in the following example, no cross-product was obtained ... 

Reductive elimination proceeds according to the mechanism reverse of the oxidative addition mechanism (microreversibility principle) from M (A)(B) to give M° and A-B. 

Let us finally discuss to what extent the MFT method is able to (i) obey the principle of microreversibility, (ii) account for the electronic phase coherence, and (iii) correctly describe the vibrational motion on coupled potential-energy surfaces. It is a well-known flaw of the MFT method to violate quantum microreversibility. This basic problem is most easily rationalized in the case of a scattering reaction occurring in a two-state curve-crossing system, where the initial and final state of the scattered particle may be characterized by the momenta p, and pf, respectively. We wish to calculate the probability Pi 2 that... 

The principle of microreversibility also indicates that changes involving bond rupture, molecular syntheses, or splitting are likely to occur one at a... 

The principle of microreversibility [154,155] applies to all bound states corresponding to real Hamiltonian operators. Hence the A-electron momentum density before and after time reversal are related by... 

Consider now a given Ar ArH2 reaction under rather neutral conditions. It is inferred from the preceding discussion that route a is followed for the reduction, whereas the oxidation goes through path e. At first glance, such a result seems to have to be rejected since it contradicts the principle of microreversibility, which claims that both reactions should follow the same mechanism. 

Rate constants for complex dissociation can be related to formation rate constants through the principle of microreversibility. Thus for... 

Collisional excitation can be taken as part of the larger class of the transvibronic reactions,2 all involving interconversion of translational, vibrational and electronic energy the more important processes are also listed in Table I. Several of these are related to each other by the principle of microreversibility 19 20 take, for instance, (1), excitation in a collision between two atoms if the cross section for excitation can be measured as a function of the collision energy, the cross section for collisional quenching, process (7), can be calculated from the former one. 

The one-electron momentum density for bound states of atoms and molecules always has inversion symmetry as a consequence of time-reversal symmetry or the principle of microreversibility [42,43] ... 

Onsager s approach, by definition, is valid in the vicinity of equilibrium, and deviations of Cj from c, eq are assumed to be small. The symmetry of the Onsager matrix, = Lji, follows from the principle of microreversibility (see the classical monograph by de Groot and Mazur, 1962). 

For many real chemical and biochemical processes some of the elementary reaction steps are virtually irreversible. For these processes, the microreversibility conditions (see Section 6.1.4) are not applicable directly. Nevertheless, such systems may be considered as limits of systems with detailed balance with some of the kinetic coefficients tending to zero if and only if (1) the reversible part of the system satisfies the principle of detailed balance and (2) the irreversible reactions are not included in oriented cyclic pathways. This is a weak form of detailed balance without the necessary existence of a positive equilibrium. See Yablonsky et al. (2011b) for more detailed information. 

PESs, and (iv) obey the principle of microreversibility. Section 3 describes in some detail the mean-field trajectory method and also discusses its connection to time-dependent self-consistent-field schemes. The surface-hopping method is considered in Sec. 4, which discusses various motivations of the ansatz as well as several variants of the implementation. Section 5 gives a brief account on the quantum-classical Liouville description and considers the possibility of an exact stochastic realization of its equation of motion. The mapping formalism, its relation to other formulations, and its quasi-classical implementation is introduced in Sec. 6. Section 7 is concerned with the semiclassical description of nonadiabatic quantum mechanics. Section 8 summarizes our results and concludes with some general remarks. 

On the basis of the kinetics of equilibrium reactions, we can add to this principle that of specific microreversibility . 

According to the principle of microreversibility, the dissociation of diatomic molecules A2 requires an enthalpy of activation of the order of magnitude of the enthalpy of dissociation, and can be brought about only at high temperatures. 

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