Non-adiabatic interactions

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. 

The rectangular approximation (7.6) of dependence E(r) implies that ts = 0. This simplification being valid only for non-adiabatic interaction, exact knowledge of the time-dependence V(t) is not obligatory. Random walk approximation is quite acceptable. The value Ro/R is a free parameter of the model ( Ro/R < 1) and makes it possible to vary the ratio of times 0 < tc/to < oo. This interval falls into two regions one of them corresponds to impact theory (0 < tc/to < 1), and the other (1 <, tc/t0 < oo) to the fluctuating liquid cage. In the first case non-adiabaticity of the process is provided by the condition... 

T. T. Nguyen-Dang, S. Durocher, and O. Atabek, Chem. Phys., 129, 451 (1989).Direct Numerical Integration of Coupled Equations with Non-Adiabatic Interactions. 

The theory of multi-phonon electron transitions due to non-adiabatic interaction between the electron terms is expounded in this chapter. The participation of the large number of the vibration degrees of freedom in the transition is caused by the non-orthogonality of the oscillator wave function in the initial and final states. This non-orthogonality may be connected with the following factors the shift of the equilibrium positions of the oscillations, the change of the frequencies in the transition, and the change of the set of normal coordinates of the vibration system. 

Heat interactions are represented in Figure 1 by paths that follow the stable-equilibrium-state curve E AgA(j. For these interactions, and for these only, the amount aE of energy transferred is uniquely related to the amount dS of entropy transferred, namely, dE = 6Q = T dS. For end states within the cross-hatched area, neither is T definable nor can a unique dS be associated with a given amount of energy transfer dE. It follows that non-adiabatic interactions, in general, are not heat interactions. 

Wodtke, A.M., Tully, J.C., Auerbach, D.J. Electronically non-adiabatic interactions of molecules at metal surfaces Can we trust the Born-Oppenheimer approximation for surface chemistry , Int. Rev. Phys. Chem. 2004,23,513. 

As the transition probabilities depend not only on the Massey parameter but also on the value of the matrix element of the interaction causing non-adiabatic transitions, an important role in the non-adiabatic transition theory is allotted to selection rules which establish the general connection between the type of the non-adiabatic interaction and the symmetries of states between which the transition occurs. The use of these selection rules and also a specific feature of the non-adiabatic interaction, namely the localization over relatively small regions, allows to approximate in these regions the adiabatic terms and the matrix elements of non-adiabatic coupling by simple functions which permits an exact solution of equations for non-adiabatic coupling. 

Molecular predissociation is an important primary photochemical step. Predissociation as the spontaneous decomposition of an excited molecule is observed when the upper bound electronic state is coupled to a continuum via non-adiabatic interactions. These interactions can be either of an intramolecular nature (spontaneous predissociation) or an intermolecular nature (coUisionally-induced predissociation). 

Neglecting on the first step the correlations between adsorbed molecules we shall describe the relaxation processes by one-pm ticle distribution function fc(E,r,t) of molecules of chemical sort c with energy E at point r. The adsorbed molecule is deemed to be in the static potential field (r, C) (where is the vector of intramolecular coordinates), that includes both static surface potential and the self-consistent potential of interaction between molecules. Each molecule interacts with the phonon and electron subsystems of solid body (inelastic and non-adiabatic interactions respectively) uid collides with other adsorbed molecules. Thus from the... 

The charge transfer process is driven mainly by non-adiabatic interactions in the vicinity of the avoided crossings [19] and radial coupling matrix elements between all pairs of states of the same symmetry have been calculated by means of the finite difference technique ... 

Similar correlations between non-adiabatic effect and charge transfer cross sections may be established for the collision of ions on HF. However, in that case, the analysis is more complex as several non-adiabatic interactions may interfere and the concomitant evolution of several radial coupling matrix elements has to be taken into account. 

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