Vibrational cascade

FIGURE 7.4 Modified Jablonski diagram showing transitions between excited states and the ground state. Radiative processes are shown by straight lines, radiationless processes by wavy lines. IC = internal conversion ISC = intersystem crossing, vc = vibrational cascade hvf = fluorescence hVp = phosphorescence. 

Figure 15.2. Modified Jablonski diagram A = absorption F = flourescence P = phosphorescence IC = internal conversion ISC = intersystem crossing VC = vibrational cascade.

Figure 15. Time-dependent behavior of OH(t> = 1-5) observed following production of the radical by the 0( D) + H2S reaction. The data, taken at 50- s intervals, clearly show the effects of vibrational cascade by collisional deexcitation of the initially produced inverted distribution. Reproduced with permission from Ref. 45.

Figure 21. Emission in the 1800-2800 cm-1 region following the IRMPD of CH2F2 (25 mTorr) in the presence of NO (lOOmTorr) and Ar (lOTorr). Emission from N20 (001) and C02 (001) are seen at long times following the vibrational cascade of highly excited species their presence at early times [together with CO(v = 1)] was established by cold gas filter experiments. N20 is the dominant emitter, and is believed to originate from the reaction sequence (20), (17).

Figure 3.33 (a) The two sequential steps of a non-radiative transition. 1 is the change in electronic wavefunction from state (i) to state (f) 2 is the vibrational cascade within state (f). (b) The vibrational overlap decreases rapidly with the energy gap of states Si and Sj... 

The time-scale of molecular vibrations is of the order of 10 13 s, just outside the ps range. Internal conversions and in particular vibrational cascades therefore fall into the femtosecond (10-15s) time-scale. However, the spin-forbidden processes of intersystem crossing take place in times of a few ps to several ns. The case of benzophenone is a good example of the compensation between spin and orbital angular momentum. The rise of the triplet state absorption shows that intersystem crossing is completed within some 20 ps. 

Figure 2 Vibrational energy relaxation (VER) mechanisms in polyatomic molecules, (a) A polyatomic molecule loses energy to the bath (phonons). The bath has a characteristic maximum fundamental frequency D. (b) An excited vibration 2 < D decays by exciting a phonon of frequency ph = 2. (c) An excited vibration >d decays via simultaneous emission of several phonons (multiphonon emission), (d) An excited vibration 2 decays via a ladder process, exciting lower energy vibration a> and a small number of phonons, (e) Intramolecular vibrational relaxation (IVR) where 2 simultaneously excites many lower energy vibrations, (f) A vibrational cascade consisting of many steps down the vibrational ladder. The lowest energy doorway vibration decays directly by exciting phonons. (From Ref. 96.)...

Hill and Dlott (5) illustrated the properties of vibrational cascades in model calculations of VC in crystalline naphthalene. Naphthalene (CioH8) has 48 normal modes. Forty of these vibrations (all except the eight C-H stretching vibrations) lie in the frequency range 1627-180 cm-1. In the calculation, one unit of excitation is input to the highest vibration in this range, 1627 cm-1. The ensemble-averaged population of the ith mode is determined by a master equation ... 

Figure 3 Calculated vibrational cascade in crystalline naphthalene at T = 0, for initial excitation at 1627 cm-1. The calculation uses Equation (6), which assumes that cubic anharmonic coupling dominates. From Ref. 5. 

Figure 4 Average energy of the nonequilibrium vibrational population distribution computed for the vibrational cascade in crystalline naphthalene in Fig. 3. At T = 0, the peak moves toward lower energy at a roughly constant rate, the vibrational velocity of 8.9 cm-1 ps. The initial 1627 cm-1 of vibrational energy is dissipated in 180 ps. The vibrational velocity is the same at 300 K. In the limit that cubic anharmonic coupling dominates [Equation (6)], increasing the temperature increases the rates of up- and down-conversion processes, but has no effect on the net downward motion of the population distribution. Although the lifetimes of individual vibrational levels will decrease with increasing temperature, VC is not very dependent on temperature in this limit. (From Ref. 5.)...

V = vibrational cascade (energy lost by collisional transfer)... 

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