Relaxation, vibrational

6 Intramolecular Excited State Decay 1.6.1 Vibrational Relaxation 

For most practical systems (solid, liquid, and atmospheric pressure gaseous phase) vibrational relaxation occurs in the picosecond time scale. Since most of the interesting chemistry and physics that takes place in electronically excited states occurs on a much longer timescale (see below), thermally equilibrated excited states should he considered as the only relevant intermediates in photochemistry, regardless of the initial amount of vibrational excitation with which they may have been created. 

An electronically-excited species is usually associated with an excess of vibrational energy in addition to its electronic energy, unless it is formed by a transition between the zero-point vibrational levels (v = 0) of the ground state and the excited state (0 — 0 transition). Vibrational relaxation involves transitions between a vibrationally-excited state (v 0) and the v = 0 state within a given electronic state when excited molecules collide with other species such as solvent molecules, for example S2(v = 3) - Wr S2(v = 0). 

Typical timescales for the process are of the order of l(T13-l(T9s in condensed phases, and the excess vibrational energy is dissipated as heat. 

The question of the extent to which molecules behave ergodically [37, 316, 379, 513, 666] is particularly pertinent in mass spectrometry, where there are no intermolecular collisions to assist, or obscure the observation of, flow of energy among vibrations. The question in mass spectrometry is linked to and must involve the redistribution of electronic enei (Sect. 2.1.1), but there is advantage in discussing vibrational and electronic effects separately. 

In conclusion, it is worth reflecting on a classical trajectory study of neutral ethane [335] in which it was found that there were dynamical restrictions to intramolecular energy transfer among C—H motions and between these and C—C motions. It was pointed out [335] that this non-ergodicity might not produce results observable at present levels of experimental resolution. This is probably the situation in mass spectrometry. QET is a respected theory in mass spectrometry because, proceeding from clearly stated assumptions, it is mathematically tractable and is able to explain the currently available experimental data. 

It is also worth noting that tiie equivalence [317], which exists for thermal systems in terms of level of approximation and assumption between the RRKM and Slater [772] approaches, is lost in mass spectrometry. To adopt the Slater position that there is no energy flow among modes, immediately demands further information, and almost certainly further assumptions, since the form of the initial distribution of vibrational (and electronic) energy is a specific property of the ion dependent upon the ionization process. 

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We now discuss the lifetime of an excited electronic state of a molecule. To simplify the discussion we will consider a molecule in a high-pressure gas or in solution where vibrational relaxation occurs rapidly, we will assume that the molecule is in the lowest vibrational level of the upper electronic state, level uO, and we will fiirther assume that we need only consider the zero-order tenn of equation (BE 1.7). A number of radiative transitions are possible, ending on the various vibrational levels a of the lower state, usually the ground state. The total rate constant for radiative decay, which we will call, is the sum of the rate constants,... 

Figure Bl.2.5. Comparison of several light seattering proeesses. (a) Rayleigh seattering, (b) Stokes and anti-Stokes Raman seattering, (e) pre-resonanee Raman seattering, (d) resonanee Raman seattering and (e) fluoreseenee where, unlike resonanee Raman seattering, vibrational relaxation in the exeited state takes plaee. From [3], used with pennission.

Owrutsky J C, Raftery D and Hochstrasser R M 1994 Vibrational-relaxation dynamics in solutions Ann. Rev. Phys. Chem. 45 519-55... 

Okamoto H and Yoshihara K 1991 Femtosecond time-resolved coherent Raman scattering from p-carotene in solution. Ultrahigh frequency (11 THz) beating phenomenon and sub-picosecond vibrational relaxation Chem. Phys. Lett. 177 568-71... 

The dynamics of fast processes such as electron and energy transfers and vibrational and electronic deexcitations can be probed by using short-pulsed lasers. The experimental developments that have made possible the direct probing of molecular dissociation steps and other ultrafast processes in real time (in the femtosecond time range) have, in a few cases, been extended to the study of surface phenomena. For instance, two-photon photoemission has been used to study the dynamics of electrons at interfaces [ ]. Vibrational relaxation times have also been measured for a number of modes such as the 0-Fl stretching m silica and the C-0 stretching in carbon monoxide adsorbed on transition metals [ ]. Pump-probe laser experiments such as these are difficult, but the field is still in its infancy, and much is expected in this direction m the near fiitiire. 

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Figure B2.2.3. Vibrational relaxation cross sections (quantal and semiclassical) as a fiinction of collision energy E.

Similar considerations have been exploited for the systematic analysis of room-temperature and molecular-beam IR spectra in temis of intramolecular vibrational relaxation rates [33, 34, 92, 94] (see also chapter A3.13 V... 

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Figure C3.5.11. IR-Raman measurements of vibrational energy flow tlirough acetonitrile in a neat liquid at 300 K, adapted from [41], An ultrashort mid-IR pulse pumps the C-H stretch, which decays in 3 ps. Only 1% of the energy is transferred to the C N stretch, which has an 80 ps lifetime. Most of the energy is transferred to the C-H bend plus about four quanta of C-C=N bend. The daughter C-H bend vibration relaxes by exciting the C-C stretch. The build-up of energy in the C-C=N bend mirrors the build-up of energy in the bath, which continues for about 250 ps after C-H stretch pumping.

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Hill J R, Ziegler C J, Susliok K S, DIott D D, Rella C W and Payer M D 1996 Tuning the vibrational relaxation of CO bound to heme and metalloporphyrin oomplexes J. Phys. Chem. 100 18023-32... 

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Ben]amin I, Barbara P F, Gertner B J and Hynes J T 1995 Nonequilibrium free energy functions, recombination dynamics, and vibrational relaxation of tjin acetonitrile molecular dynamics of charge flow in the electronically adiabatic limit J. Phys. Chem. 99 7557-67... 

Elarris C B, Smith D E and Russell D J 1990 Vibrational relaxation of diatomic molecules in liquids Chem. Rev. 90 481-8... 

Wisdom, J. The Origin of the Kirkwood Gaps A Mapping for Asteroidal Motion Near the 3/1 Commensurability. Astron. J. 87 (1982) 577-593 Tuckerman, M., Martyna, G. J., Berne, J. Reversible Multiple Time Scale Molecular Dynamics. J. Chem. Phys. 97 (1992) 1990-2001 Tuckerman, M., Berne, J. Vibrational Relaxation in Simple Fluids Comparison of Theory and Simulation. J. Chem. Phys. 98 (1993) 7301-7318 Humphreys, D. D., Friesner, R. A., Berne, B. J. A Multiple-Time Step Molecular Dynamics Algorithm for Macromolecules. J. Chem. Phys. 98 (1994) 6885-6892... 

Energy level diagram for a molecule showing pathways for deactivation of an excited state vr Is vibrational relaxation Ic Is Internal conversion ec Is external conversion, and Isc Is Intersystem crossing. The lowest vibrational energy level for each electronic state Is Indicated by the thicker line. 

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