Adiabatic assumption

By regrouping Equation 2.59, substituting into Equation 2.48, and maintaining the adiabatic assumption Qh = 0, Equation 2.62 is developed. 

Several explanations have been given for this result. One possibility is the failure of the adiabatic assumption in this ionization process a transition state is generated that may not be a combination of the initial and final states, but may include mixing in of an excited state structure. This idea will reappear in the following pages. 

The kinetic model developed here does not use any kind of adiabatic assumption, and thus is capable of rendering frequency dependencies of the SR characteristics. 

X 10 M" s. Although the work-term correction decreases the value of k j(calc), the effect is small at the ionic strength used (the effect increases if nonelectrostatic contributions are included). If the adiabaticity assumption is dropped and it is assumed instead that k,... 

The simplest way of taking account of vibrational effects is to assume vibrational adiabaticity during the motion up to the critical dividing surface [27]. As mentioned already in the Introduction, much of the earlier work on vibrational adiabaticity was concerned with its relationship to transition-state theory, especially as applied to the prediction of thermal rate constants [24-26]. It is pointed out in [27] that the validity of the vibrationally adiabatic assumption is supported by the results of both quasiclassical and quantum scattering calculations. The effective thresholds indicated by the latter for the D + H2(v =1) and O + H2(v =1) reactions [37,38] are similar to those found from vibrationally adiabatic transition-state theory, which is a strong evidence for the correctness of the hypothesis of vibrational adiabaticity. Similar corroboration is provided by the combined transition-state and quasiclassical trajectory calculations [39-44]. For virtrrally all the A + BC systems studied [39-44], both collinearly and in three... 

To identify bifurcations using the indicator distances, we project pB onto the curvilinear ry coordinates and look for effective energy barriers in the projected distribution. To maintain physical relevance, the projection must yield a one-dimensional Smoluchowski equation when the same transformation is applied to p(Q, t) under the adiabatic assumption that the relaxation of p toward pB is much faster in the directions transverse to ry than along ri. This assumption will be sensible when there is an effective energy barrier in this coordinate thus, the assumption can be self-consistently verified. Care is required because is a nonlinear function of 1 and we do not get an equation of the form of Eq. (3.1) by projecting onto rl itself. However, we do get such an equation by projecting onto the transformed coordinate s(ry) defined by [41]... 

The adiabatic assumption involved in equations (52-55.IV) may not be a good approximation nevertheless, it provides the possibility of simulating the non-linear collisions between the H-atoms and the H2-molecules. The importance of such a treatment will become clear in a comparison between the results of the theoretical calculations and the experimental data to be made in the next section. 

The RP dynamics is initialized at a value of s = sq where the various coupling terms vanish. A rotational adiabatic assumption [26] is made at sq, where the Hamiltonian Hrot = Hrot so) is set equal to the rotational energy of the reactant molecules (considered to be AB and CD) and the orbital energy ... 

Example 12.1 The maximum possible temperature rise in a polymerizing batch may be calculated by assuming that no heat is transferred from the system (adiabatic assumption). Estimate the adiabatic temperature rise for the bulk polymerization of styrene, given that Af/p = — 16.4kcal/mol and monomer molecular weight = 104. 

Ya or consider a channel count different from the maximum. For instance, when many channel maxima fall into regions of small q, where the adiabatic assumptions are likely to fail, one may decide to count channels as open if their potential remains below E until entering a strong coupling region defined by some q < qg. Also, the explicit inclusion of transitions between channels has been discussed as a possible variant of the SACM. ... 

Eyring adopted an ad hoc procednre that has been successful in including quantum effects in TST. First, the classical partition functions are replaced by their quantum analogues. Second, the classical rate is mnltiplied by a transmission coefficient that takes into account the qnantnm effects along the reaction coordinate. The quantum partition functions assume that the transition state can be treated as a stable system. The separate quantisation of the reaction coordinate is based on the vibrational adiabaticity assumption, that is, all the other vibrational modes of the reactive system very rapidly adjust to the reaction coordinate and maintain the continuity and smoothness of the PES. 

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