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Detailed balance relation

The frequency (number per second) of /transitions from all g. degenerate initial internal states and from the p. d E. initial external translational states is equal to tire reverse frequency from the g degenerate final internal states and the pyd final external translational states. The detailed balance relation between the forward and reverse frequencies is therefore... [Pg.2013]

Wlien cast in temis of cross sections, the detailed balance relation in section B2.2.4.2 is... [Pg.2015]

Collision strengths Q exploit this detailed balance relation by being defined as... [Pg.2015]

As an example, Fig. 6.20 below compares the Ai AL = 0001 and 2023 line profiles at 195 K which were computed with and without (solid and dashed curves, respectively) accounting for the vibrational dependences of the interaction potential. The correct profiles (solid curves) are more intense in the blue wing, and less intense in the red wing by up to 25% relative to the approximation (dashed), over the range of frequencies shown. Whereas the dashed profiles satisfy the detailed balance relation, Eq. 6.59, if a> is taken to be the frequency shift relative to the line center, the exact profiles deviate by up to a factor of 2 from that equation over the range of frequencies shown. In a comparison of theory and measurement the different symmetries are quite striking use of the correct symmetry clearly improves the quality of the fits attainable. [Pg.321]

Remark. The detailed balance relation (4.2) or (6.1) asserts that the matrix W is virtually symmetric and will be seen in the next section to guarantee that W can be diagonalized. The relation (6.14) is also a property of W but does not by itself guarantee diagonalizability, and wil be referred to as extended detailed balance . The relations (6.12) and (6.13) are not properties of W but relate the transition probabilities in one system to those in another system. They will therefore not be honored with the name detailed balance. The extended detailed balance property will be important in XI.4. [Pg.117]

Note the relation to the hypergeometric distribution (1.1.6). This p coincides with pi provided that a and ft are connected by the detailed balance relation (4.4), where hv is the energy gap, energy differences inside each band being neglected. [Pg.162]

Exercise. What is the equilibrium distribution Prove that (7.8) obeys the detailed balance relation (V.6.11). [Pg.455]

The rate constants of desorption (kdes) and reverse reactions (k7, kd) are calculated using the detailed balance relations. [Pg.472]

The steady state solution to this system is (using the detailed balance relation g B = B2B21 ... [Pg.63]

In obtaining the form (16.127) we have used the detailed balance relation k <)/kt) = exp(— bd/ sT) where bd = Ey — Eq is the barrier height above the donor energy, and have identified o,i and Aw+tw as the rate coefficients Ai ) i and kA N to go from the first and last bridge sites to the donor and acceptor, respectively. [Pg.599]

One issue that arises when classical correlation functions are used is that they do not satisfy the detailed-balance relation Eq. (14) (because they are even with respect to i = 0) and hence cannot produce a Redfield tensor that lets the subsystem come to thermal equilibrium. Therefore, before being introduced into Eq. (18), the classical results must be modified to satisfy detailed balance. Unfortunately, there is no unique way to accomplish this, and a handful of different approaches are found in the literature. [Pg.91]

The strength of the bath coupling to each system variable is described by the coupling constants / and, because they enter at second order, the rate constant for the dissipation process arising from each term in Eq. (38) will be proportional to f I- The only important properties of the F t) are their autocorrelation and cross-correlation functions, (FJfi)F t)) and F (0)Fi,(t)), which enter the definition of the Redfield tensor in Eq. (18). These, like the classical correlation functions discussed earlier, do not satisfy the detailed-balance relation and must be corrected in the same way. It is convenient, but not necessary, that the variables be chosen to be independent, so that the cross-correlation functions vanish. [Pg.94]

The relations connecting the rate coefficients of forward and backward collisional processes follow from the microscopic detailed balance relations for reactive collisions (8)-(9) after averaging them with the Maxwell-Boltzmann distribution over the velocity and rotational energy. Thus for the rate coefficients of forward and backward reactions we obtain... [Pg.127]

The average transition probabilities calculated from Eq. (8) and its reverse satisfy correct detailed balance relation, Pi p = Po i ... [Pg.234]

This relation is usually called detailed balance relation. The equilibrium constant may be calculated from idependent thermochemical and spectroscopic data. These calculations often utilize the following expression of statistical thermodynamics... [Pg.12]

The detailed balance relation is of great importance for kinetics. First of all, it permits the calculation of k if k is measured. Second, in many cases, the accuracy of thermodynamical data is superior to that obtained from kinetics, and Eq. (3.3) may be used to check the consistency of the independently measured values of k and k. For instance, in the case of the reaction... [Pg.12]

Up to now simple reactions involving one elementary reaction have been considered. It was mentioned in the previous section that any complex reaction can be described by a set of elementary reactions. It foUows from the general theory of chemical equilibrium [383] that when several simultaneous reactions proceed in a system, Eq. (3.1) holds for any equilibrium (Kc is given by Eq. (34.)). Now, since the rates of all elementary reactions at equilibrium are zero, the detailed balance relation (3.3) applies to each elementary step of the complex reactions. [Pg.13]

Detailed balance relations for probabilities (Eq. (8.8)), cross sections (Eq. (8.12)) and microscopic rate constants (Eq. (8.24)) yield a certain relation between partially averaged rate constants for forward and reverse reactions at any detailization. [Pg.33]

The following detailed balance relations will be assumed to be held... [Pg.50]

It is important to emphasize that the averaged detailed balance relations (8.2.20)-(8.2.22) have more wide range of validity than (8.2.17)-(8.2.19) since the adsorbate is a thermodynamical (not fuDy detemiined) system. Therefore the further considerations will be restricted to the evaluation of quasiequilibrium distributions tf°(a) vanishing operators M, M, AD , and X,. [Pg.50]

Detailed balance relates the rates of a particular activation and deactivation energy transfer process. Detailed balance thus provides a quantitative exact relation between rate constants that correspond to the same gap. This is unlike the principle of exponential gap tiiat provides an estimate of how the rate constants vary when the gap changes. The quahtative implication of detailed balance is that on a quantum state-to-quantum state basis, the rate constant for the activation process is always smaller than the rate constant for the reverse deactivation process. Take as an example the V—T process that we started this section with, A -I- BC(v = 0) A -I- BC(v = 1) and the reverse deactivation process, A -I- BC(v = 1) A -I- BC(v = 0). Detailed balance states that at equilibrium the rates of these two detailed ways of transferring populations between BC(v = 1) and BC(v = 0) must be equal. This is to be so even though there may be other processes that can transfer populations, such as transitions in the IR. Therefore, using the subscript eq to designate concentrations at equilibrium,... [Pg.377]


See other pages where Detailed balance relation is mentioned: [Pg.2016]    [Pg.2018]    [Pg.2026]    [Pg.242]    [Pg.245]    [Pg.148]    [Pg.313]    [Pg.317]    [Pg.284]    [Pg.382]    [Pg.227]    [Pg.230]    [Pg.372]    [Pg.378]    [Pg.474]    [Pg.296]    [Pg.388]    [Pg.571]    [Pg.171]    [Pg.2016]    [Pg.2018]    [Pg.2026]    [Pg.53]    [Pg.134]    [Pg.11]   
See also in sourсe #XX -- [ Pg.237 , Pg.240 ]

See also in sourсe #XX -- [ Pg.237 , Pg.240 ]




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Detailed balance

Detailed balancing

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