Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

Relaxation, vibrational rate calculation

Poulsen, Billing, and Steinfeld " performed semiclassical calculations based on a classical path for relative translation and rotation and an approximate coupled levels treatment of vibration. Their calculations also predict reasonable V-V,R,T fractions 149,152 Their results agree well with the experimental temperature dependence of the V = 1 relaxation they also agree with the experimental temperature dependence of the V-R,T rate coefficient for v = 2 better than the Wilkins-Kwok or Coltrin-Marcus studies. [Pg.178]

We first consider the vibrational relaxation that can be induced by aijQqiqj (three-phonon processes) or Qq qi (four-phonon processes). In the three-phonon processes there are two accepting modes, while in the four-phonon processes there are three accepting modes. To calculate the rate of vibrational relaxation, we use... [Pg.78]

A detailed description of the laser-excited vibrational fluorescence method and further results on relaxation processes in methane, including V - R transfer, have been given in reference In this paper, too, a comparison is made between the experimentally obtained F - F rates and calculations for the repulsive intermolecular potential responsible for these transitions. [Pg.28]

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. [Pg.203]

The flow of energy from the ground state can also be calculated when it is assumed that the rate of electronic dephasing is small (i.e., L%Pg = 0) and/or the rate of pure vibrational dephasing is small (i.e., L%Hg = 0). These conditions apply when the rate of relaxation to equilibrium is small relative to the rate of loss of phase coherence. Under these conditions... [Pg.240]

Figure 24. Vibrational populations of OH( = 1-6) following electron beam irradiation of a mixture of Ar (lOTorr), 02 (0.3Torr), H2 (90mTorr) and an estimated 4mTorr of 03. Relaxation rate constants were obtained from model calculations fitted to the data and shown by the solid lines. Reproduced with permission from Ref. 73. Figure 24. Vibrational populations of OH( = 1-6) following electron beam irradiation of a mixture of Ar (lOTorr), 02 (0.3Torr), H2 (90mTorr) and an estimated 4mTorr of 03. Relaxation rate constants were obtained from model calculations fitted to the data and shown by the solid lines. Reproduced with permission from Ref. 73.
ORM assumes that the atmosphere is in local thermodynamic equilibrium this means that the temperature of the Boltzmann distribution is equal to the kinetic temperature and that the source function in Eq. (4) is equal to the Planck function at the local kinetic temperature. This LTE model is expected to be valid at the lower altitudes where kinetic collisions are frequent. In the stratosphere and mesosphere excitation mechanisms such as photochemical processes and solar pumping, combined with the lower collision relaxation rates make possible that many of the vibrational levels of atmospheric constituents responsible for infrared emissions have excitation temperatures which differ from the local kinetic temperature. It has been found [18] that many C02 bands are strongly affected by non-LTE. However, since the handling of Non-LTE would severely increase the retrieval computing time, it was decided to select only microwindows that are in thermodynamic equilibrium to avoid Non-LTE calculations in the forward model. [Pg.341]

So far, one can be much more successful in calculating a rate constant when one knows in advance that it exists, than in answering the question of whether it exists. A considerable breakthrough in this area was the solution of the spin-boson problem, which, however, has only limited relevance to any problem in chemistry because it neglects the effects of intrawell dynamics (vibrational relaxation) and does not describe thermally activated transitions. A number of attempts have been made to go beyond the two-level system approximation, but the basic question of how vibrational relaxation affects the transition from coherent oscillations to exponential decay awaits a quantitative solution. Such a solution might be obtained by numerical computation of real-time path integrals for the density matrix using the influence functional technique. [Pg.338]

In this paper, the multiphonon relaxation of a local vibrational mode and the non-radiative electronic transitions in molecular systems and in solids are considered using this non-perturbative theory. Results of model calculations are presented. According to the obtained results, the rate of these processes exhibits a critical behavior it sharply increases near specific (critical) value(s) of the interaction. Also the usual increase of the non-radiative transition rate with temperature is reversed at certain value of the non-diagonal interaction and temperature. For a weak interaction, the results coincide with those of the perturbation theory. [Pg.152]


See other pages where Relaxation, vibrational rate calculation is mentioned: [Pg.217]    [Pg.205]    [Pg.887]    [Pg.133]    [Pg.301]    [Pg.450]    [Pg.112]    [Pg.243]    [Pg.852]    [Pg.66]    [Pg.81]    [Pg.89]    [Pg.107]    [Pg.107]    [Pg.166]    [Pg.185]    [Pg.203]    [Pg.507]    [Pg.40]    [Pg.231]    [Pg.12]    [Pg.559]    [Pg.40]    [Pg.283]    [Pg.54]    [Pg.88]    [Pg.148]    [Pg.261]    [Pg.330]    [Pg.185]    [Pg.199]    [Pg.203]    [Pg.187]    [Pg.224]    [Pg.265]    [Pg.296]    [Pg.152]    [Pg.97]    [Pg.157]    [Pg.233]   
See also in sourсe #XX -- [ Pg.324 ]




SEARCH



Rate, calculating

Relaxation rates

Vibrational calculations

Vibrational relaxation

Vibrational relaxational

© 2024 chempedia.info