Vibrational relaxation mechanism

Finally, in strongly bound nonhydride molecules with large vibrational spacing (above 1500 cm ) both of the vibrational relaxation mechanisms described above may be very slow. Under these circumstances the guest relaxation is often controlled by alternative processes, for example, infrared radiation or intermolecular vibrational energy transfer. 

Perhaps the first evidence for the breakdown of the Born-Oppenheimer approximation for adsorbates at metal surfaces arose from the study of infrared reflection-absorption line-widths of adsorbates on metals, a topic that has been reviewed by Hoffmann.17 In the simplest case, one considers the mechanism of vibrational relaxation operative for a diatomic molecule that has absorbed an infrared photon exciting it to its first vibrationally-excited state. Although the interpretation of spectral line-broadening experiments is always fraught with problems associated with distinguishing... 

More recently the application of sub-picosecond, time-resolved pump-probe methods revealed the timescale for vibrational relaxation of a diatomic molecule at a metal surface directly. See for example Refs. 19-21. In comparison to vibrational relaxation on NaCl salts,22 which occurs on the millisecond timescale, another relaxation mechanism is clearly at play. Theory of vibrational relaxation based on excitation of electron-hole pairs gave agreement with observed ps timescales for CO on copper.23... 

Noncoherent mechanism and vibrational relaxations cooling off to equilibrium... 

The linear response theory [50,51] provides us with an adequate framework in order to study the dynamics of the hydrogen bond because it allows us to account for relaxational mechanisms. If one assumes that the time-dependent electrical field is weak, such that its interaction with the stretching vibration X-H Y may be treated perturbatively to first order, linearly with respect to the electrical field, then the IR spectral density may be obtained by the Fourier transform of the autocorrelation function G(t) of the dipole moment operator of the X-H bond ... 

The total Hamiltonian H should include all the vibrational modes involved in the hydrogen bond dynamics, as well as the various couplings taking place between these modes. At last, H would include the relaxation mechanisms. 

To conclude, even if there exist several processes that affect the vibrational line shape it seems probable that when most of them have been sorted out and with the good agreement between theory and experiment, the lifetime broadening for a chemisorbed CO molecule is of the order of a few cm, corresponding to a lifetime of a few ps. The main vibrational energy relaxation mechanism is creation of electron-hole pairs caused by the local charge oscillations between the metal and the 2n molecular resonance crossing the Fermi level. 

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). 

The results presented Irom vibrational relaxation calculations show that the method is numerically very feasible and that the short time approximatiorrs are welljustified as long as the energy difference between the initial and final quantum states is not too small. It is also found that the crossover from the early time quantiun regime to the rate constant regime can be due to either phase decoherence or due to the loss of correlation in the coupling between the states, or to a combination of these factors. The methodology described in Section n.C has been formulated to account for both of these mechanisms. 

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