Weakly non-adiabatic

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. 

Figure 4. Schematic depiction of the limits of (a) weak (non-adiabatic) and (b) strong (adiabatic) coupling. The dashed and solid lines refer to diabatic and adiabatic surfaces, respectively. The vertical bars denote the reaction zone in which D and A sites arc dose to resonance 1105).

Fig. 28.5. The effective potential surfaces for a simple gene switch are shown - h gives the binding rate, f the unbinding rate, and g and g are the synthesis rates when the gene is on or off, respectively. The different diagrams correspond with different sequences of binding/synthesis/unbinding events. The upper plot shows the typical trajectory at high non-adiabaticity. The lowest plot shows the adiabatic case. A churning process gives an enhanced rate of protein number fluctuations in the intermediate weakly non-adiabatic case B...

In other words, switches are most agile in the weakly non-adiabatic regime, corresponding to the case B, binding/growth/unbinding scenario. It is... 

Fig. 28.6. Comparison of the rate of spontaneous epigenetic switching for different values of the non-adiabaticity K. The exact numerical results are shown as a solid curve. Various approximations reflecting the mechanisms described in Fig. 28.5 are also plotted. A stochastic resonance occurs near the weakly non-adiabatic regime...

In the following section, the importance of metallic non-adiabaticity in chemical dynamics simulations will be illustrated through a few selected example applications. First, the vibrational relaxation of adsorbates at metallic surfaces will be treated in the perturbative regime. Seeond, the effect of weak non-adiabatic coupling on laser excitation simulations will be discussed. Finally, inelastic effects in scanning tunnelling mieroseopy of highly mobile species in metallic environments will be diseussed in terms of non-adiabaticity. 

A different example of non-adiabatic effects is found in the absorption spectrum of pyrazine [171,172]. In this spectrum, the, Si state is a weak structured band, whereas the S2 state is an intense broad, fairly featureless band. Importantly, the fluorescence lifetime is seen fo dramatically decrease in fhe energy region of the 82 band. There is thus an efficient nonradiative relaxation path from this state, which results in the broad spectrum. Again, this is due to vibronic coupling between the two states [109,173,174]. 

The mixed-state character of a trajectory outside a non-adiabatic region is a serious weakness of the method. As the time-dependent wave function does not... 

The functional B[(2(r)] actually depends only on the velocity dQ/dr at the moment when the non-adiabaticity region is crossed. If we take the path integral by the method of steepest descents, considering that the prefactor B[(2(r)] is much more weakly dependent on the realization of the path than Sad[Q(A]> we shall obtain the instanton trajectory for the adiabatic potential V a, then B[(2(t)] will have to be calculated for that trajectory. Since the instanton trajectory crosses the dividing surface twice, we finally have... 

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],... 

Though these are alternative models, they are both particular cases of the non-adiabatic impact theory of angular momentum relaxation in gases. Thus, we prefer to call them models of weak and strong collisions , as is usually done in analogous problems [13, 33],... 

The rotational phase shift 5, which cannot exceed a mean angle of a molecular rotation during collisional time (anc), is certainly small in the case of non-adiabatic collisions. This condition is exactly that needed for anisotropic scattering (or IR absorption) spectrum narrowing, just as vibrational dephasing must be weak for an isotropic spectrum to narrow. 

Keilson-Storer kernel 17-19 Fourier transform 18 Gaussian distribution 18 impact theory 102. /-diffusion model 199 non-adiabatic relaxation 19-23 parameter T 22, 48 Q-branch band shape 116-22 Keilson-Storer model definition of kernel 201 general kinetic equation 118 one-dimensional 15 weak collision limit 108 kinetic equations 128 appendix 273-4 Markovian simplification 96 Kubo, spectral narrowing 152... 

The general framework of the quantum mechanical rate expression for long-range electron transfer processes in the very weak or non-adiabatic regime will be presented in Sect. 2 with an emphasis on the inclusion of superexchange interactions. The relation between the simplest case of direct donor-acceptor interactions, on the one hand, and long-range electronic interactions important in proteins, on the other, is considered in terms of the elements of electron transfer theory. 

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