Adiabatic theory

From a mathematical perspective either of the two cases (correlated or non-correlated) considerably simplifies the situation [26]. Thus, it is not surprising that all non-adiabatic theories of rotational and orientational relaxation in gases are subdivided into two classes according to the type of collisions. Sack s model A [26], referred to as Langevin model in subsequent papers, falls into the first class (correlated or weak collisions process) [29, 30, 12]. The second class includes Gordon s extended diffusion model [8], [22] and Sack s model B [26], later considered as a non-correlated or strong collision process [29, 31, 32],... 

In NMR theory the analogue of the relation (1.57) connects the times of longitudinal (Ti) and transverse (T2) relaxation [39]. In the case of weak non-adiabatic interaction with a medium it turns out that T = Ti/2. This also happens in a harmonic oscillator [40, 41] and in any two-level system. However, if the system is perturbed by strong collisions then Ti = T2 as for y=0 [42], Thus in non-adiabatic theory these times differ by not more than a factor 2 regardless of the type of system, or the type of perturbation, which may be either impact or a continuous process. 

It is clear that J-diffusion is a good approximation for rotational relaxation as a whole, if the centre of equilibrium distribution over J is within the limits of non-adiabatic theory. In the opposite case m-diffusion is preferable. Consequently, the J-diffusion model is applicable, if the following inequality holds ... 

Fig. 5.6. Collisional broadening of N2 rotational components, (a) In Q-branch, calculated by purely non-adiabatic theory at 300 K (1) and with adiabatic corrections at 300 K (2) and at 100 K (3) [215]. (b) In S-branch, calculated in [191] with adiabatic corrections using the recipe of Eq. (5.56). The experimental data (+) are from [214].

As noted in Section III.C.2, the adiabatic method allows one to separate "slow" rotational motion from "fast" vibrational motion. The evaluation of vibrational distributions that has been described is based on this feature of adiabatic theory. In many cases one can also similarly ignore "slow" bending motion. However, advances in experimental methods have led to measurements of rotational distributions of photofragments (see Okabe and Jackson, this volume) and thus the evaluation of these distributions has become a timely and interesting problem. 

It turns out that it is possible to develop another version of the adiabatic theory, which can be applied in many cases. Often nuclei (ions) are located near the equilibrium geometry which leads to simplifications of the theory—the clamped adiabatic approximation. Sometimes this approach is called the "crude" approximation (46,77). 

Hence, according to the definition of HQ (see eq. A.31), the functions on the right-hand side of eq. A.33 are taken from different versions of adiabatic theory. 

The non-adiabatic theory indicates that electron - vibration (phonon) interaction, at stabilization (minimization) of the fermionic ground state... 

One expects to observe a barrier resonance associated with each vibra-tionally adiabatic barrier for a given chemical reaction. Since the adiabatic theory of reactions is closely related to the rate of reaction, it is perhaps not surprising that Truhlar and coworkers [44, 55] have demonstrated that the cumulative reaction probability, NR(E), shows the influence barrier resonances. Specifically, dNR/dE shows peaks at each resonance energy and Nr(E) itself shows a staircase structure with a unit step at each QBS energy. It is a more unexpected result that the properties of the QBS seem to also imprint on other reaction observables such as the state-to-state cross sections [1,56] and even can even influence the helicity states of the products [57-59]. This more general influence of the QBS on scattering observables makes possible the direct verification of the existence of barrier-states based on molecular beam experiments. 

R.T. Skodje, The adiabatic theory of heavy-light-heavy chemical reactions, Annu. Rev. Phys. Chem. 44 (1993) 145. 

Abdolsalami, M. and Morrison, M.A. (1987). Calculating vibrational-excitation cross sections off the energy shell A first-order adiabatic theory, Phys. Rev. A 36, 5474-5477. 

Morrison, M.A. (1986). A first-order nondegenerate adiabatic theory for calculating near-threshold cross sections for rovibrational excitation of molecules by electron impact, J. Phys. B 19, L707-L715. 

In view of the hitherto unsuccessful experimental search for eigenstates delocalized between the HCN and CNH isomers [14,22-28], the analysis of the mechanisms and spectral signatures of delocalization becomes central to theoretical studies. According to the adiabatic theory presented in Section II.A, states with excitation (vi,V3) in the perpendicular stretching coordinates are expected to remain localized even above the lowest adiabatic pseudo-potential barrier Indeed, in the adiabatic picture, these states become delocalized only if they are located close to or above the corresponding adiabatic potential barrier which can be located far above Vq q (see Fig. 3). This might... 

In contrast to the experimentally based work discussed above, in the most recent comprehensive theoretical discussion [21d], Bixon and Jortner state that the question of whether non-adiabatic or adiabatic algorithms describe electron-transfer reactions was settled in the 1960s, and that the majority of outer-sphere electron-transfer reactions are non-adiabatic. This is certainly true for the reactions that occur in the Marcus inverted region in which these authors are interested, but we think the question of whether reactions in the normal region are best treated by adiabatic theory that includes an electronic transmission coefficient or by non-adiabatic equations remains to be established. 

It should be noted that most of the Co(III)2=jCo(II) exchange reactions are unsatisfactorily described by the adiabatic theory. This may be attributed partly to the fact that the spin state of the complex depends on its oxidation state Co + ion possesses a high spin t gSl configuration, whereas Co + ion has a low-spin configuration. It is evident that one-electron transfer in this case must be accompanied by the transfer of one more electron from the eg level to the t2g level, or vice versa, i.e., either one of the initial complexes or the products must be in the excited state. As mentioned above, in some cases the correlation factor p (Eq. (101)) is employed for a quantitative evaluation of nonadiabaticity. 

Charging and discharging in adiabatic theory of Coulomb blockade... 

Hush N. S. (1961), Adiabatic theory of outer sphere electron transfer at electrodes , J. Chem. Soc. Faraday Trans. 57, 557-580. 

We have not yet implemented the fully adiabatic theory represented by Equation 5. That theory bears some resemblance to the bending-corrected rotating linear model (BCRLM)(16-18). In this model a partial wave hamiltonian is given by... 

Calculation of kopt from optical data using adiabatic theory 204... 

The hybrid or quasidassical approach is very old [1]. As the next step we go beyond the standard treatment, and we discuss using the adiabatic theory to develop a procedure for including quantum effects on reaction coordinate motion. A critical feature of this approach is that it is only necessary to make a partial adiabatic approximation, in two respeds. First, one needs to assume adiabaticity only locally, not globally. Second, even locally, although one uses an adiabatic effective potential, one does not use the adiabatic approximation for all aspects of the dynamics. 

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