Relaxation, vibrational quantum theory

The quantum theory of vibrational relaxation in low-temperature ordered solids is well develojjed, at least for weak interactions. Starting from the harmonic solid, with known normal mode energies , the anharmonic interactions between modes are introduced as an ordered perturbation and the renormalized mode energies are calculated, usually by temperature Green s function methods, for each order of jierturbation. The calculated energy shifts j — are complex. 

Consider a closed system characterized by a constant temperature T. The system is prepared in such a way that molecules in energy levels are distributed in departure from their equilibrium distribution. Transitions of molecules among energy levels take place by collisional excitation or deexcitation. The redistribution of molecular population is described by the rate equation or the Pauli master equation. The values for the microscopic transition probability kfj for transition from ith level toyth level are, in principle, calculable from quantum theory of collisions. Let the set of numbers vr be vibrational quantum numbers of the reactant molecule and vp be those of the product molecule. The collisional transitions or intermolecular relaxation processes will be described by ... 

Zhang, Y Straub, J. E., Direct evidence for mode-specific vibrational energy relaxation from quantum time-dependent perturbation theory. 11. The and v, modes of iron... 

Transient vibrational dynamics. Perturbation theory yields an intuitive picture of adsorbate relaxation the loss of a vibrational quantum and associated nodal structure in the nuclear wave function is coupled to an irreversible transfer of momentum to the metallic electrons (see Fig. 2). To obtain time-resolved information about the dynamical processes at work, it is nonetheless necessary to go beyond this simple model. In the past decades, classical molecular dynamics has been hugely successful at shedding light on the transient vibrational evolution in a variety of adsorbate-surface systems (see, e.g., ref. 54-56). The methods of choice for including non-adiabatic effects on the dynamics can be divided in two main families friction-lype... 

In conventional theories of rate processes, the temperature T is usually involved. The involvement of T implicitly assumes that vibrational relaxation is much faster than the process under consideration so that vibrational equilibrium is established before the system undergoes the rate process. For example, let us consider the photoinduced ET (see Fig. 5). From Fig. 5 we can see that for the case in which vibrational relaxation is much faster than the ET, vibrational equilibrium is established before the rate process takes place in this case the ET rate is independent of the excitation wavelength and a thermal average ET constant can be used. On the other hand, for the case in which the ET is much faster than vibrational relaxation, the ET takes place from the pumped vibronic level (or levels) and thus the ET rate depends on the excitation wavelength and often quantum beat will be observed. 

The quantum alternative for the description of the vibrational degrees of freedom has been commented by Westlund et al. (85). The comments indicate that, to get a reasonable description of the field-dependent electron spin relaxation caused by the quantum vibrations, one needs to consider the first as well as the second order coupling between the spin and the vibrational modes in the ZFS interaction, and to take into account the lifetime of a vibrational state, Tw, as well as the time constant,T2V, associated with a width of vibrational transitions. A model of nuclear spin relaxation, including the electron spin subsystem coupled to a quantum vibrational bath, has been proposed (7d5). The contributions of the T2V and Tw vibrational relaxation (associated with the linear and the quadratic term in the Taylor expansion of the ZFS tensor, respectively) to the electron spin relaxation was considered. The description of the electron spin dynamics was included in the calculations of the PRE by the SBM approach, as well as in the framework of the general slow-motion theory, with appropriate modifications. The theoretical predictions were compared once again with the experimental PRE values for the Ni(H20)g complex in aqueous solution. This work can be treated as a quantum-mechanical counterpart of the classical approach presented in the paper by Kruk and Kowalewski (161). 

In a second example the discrete time-reversible propagation scheme for mixed quantum-classical dynamics is applied to simulate the photoexcitation process of I2 immersed in a solid Ar matrix initiated by a femtosecond laser puls. This system serves as a prototypical model in experiment and theory for the understanding of photoinduced condensed phase chemical reactions and the accompanied phenomena like the cage effect and vibrational energy relaxation. It turns out that the energy transfer between the quantum manifolds as well as the transfer from the quantum system to the classical one (and back) can be very well described within the mixed mode frame outlined above. 

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