Polyatomic molecules relaxation

The electronic relaxation of the excited singlet states of benzene vapor is rather typical of polyatomic molecules. Relaxation is predominantly nonradiative, and by paths that are sensitive to the degree of vibrational excitation in the decaying electronic state. Indeed, vibrational excitation appears as perhaps the most crucial parameter in setting the course of excited state decay. 

Understanding VER in condensed phases has proven difficult. The experiments are hard. The stmcturally simple systems (diatomic molecules) involve complicated relaxation mechanisms. The stmctures of polyatomic molecules are obviously more complex, but polyatomic systems are tractable because the VER mechanisms are somewhat simpler. 

Fig. 11. (a) Diagram of energy levels for a polyatomic molecule. Optical transition occurs from the ground state Ag to the excited electronic state Ai. Aj, are the vibrational sublevels of the optically forbidden electronic state A2. Arrows indicate vibrational relaxation (VR) in the states Ai and Aj, and radiationless transition (RLT). (b) Crossing of the terms Ai and Aj. Reorganization energy E, is indicated. 

The HF results generated for representative polyatomic molecules have used the /V-derivatives estimated by finite differences, while the -derivatives have been calculated analytically, by standard methods of quantum chemistry. We have examined the effects of the electronic and nuclear relaxations on specific charge sensitivities used in the theory of chemical reactivity, e.g., the hardness, softness, and Fukui function descriptors. New concepts of the GFFs and related softnesses, which include the effects of molecular electronic and/or nuclear relaxations, have also been introduced. 

Maier JP, Seihneier A, Laubereau A, Kaiser W (1977) Ultrashort vibrational population lifetime of large polyatomic-molecules in vapor-phase. Chem Phys Lett 46 527 Shank CV, Ippen EP, Teschke O (1977) Sub-picosecond relaxation of large organic-molecules in solution. Chem Phys Lett 45 291... 

Sarkar, N., Takeuchi, S., and Tahara, T. 1999. Vibronic relaxation of polyatomic molecule in nonpolar solvent. J. Phys. Chem. A 103 4808. 

Fluorescence always occurs from the lowest singlet state even if the initial excitation is to higher energy state (Kasha s rule). Azulene and some of its derivatives are exceptions to this rule. Because of vibrational relaxation of initially excited vibronic state, the fluorescence spectrum may appear as a minor image of the absorption spectrum for large polyatomic molecules. The shape of the emission spectrum is independent of the exciting wavelength. 

It was pointed out in Section 4.2 that most polyatomic molecules show only a single relaxation process, owing to rapid intramolecular vibration-vibration transfer between modes. This corresponds to a state of affairs where Vibrational energy enters the molecule via process (a), which is rate-determining,... 

For a few polyatomic molecules, where there is a large difference between Vj and v2, the rate of the complex process (c) is much slower, and the condition P2 > P12 > Pi applies. This gives rise to a double relaxation phenomenon. Process (b) is again too slow to play any role, but process (a) is now faster than process (c). The vibrational energy of mode 2 (and any upper modes) relaxes... 

An interesting development in molecular rotational relaxation has been the microwave double-resonance method176-178. The technique permits the exploration of the fine detail of the processes which occur in collisions of polyatomic molecules, and results for a number of symmetric tops have been reported. For example, Oka has described experiments on NH3 in which inversion doublets for selected J values were pumped by high microwave power. Pumping disturbs the population of the inversion doublet, and also that of other doublets which are populated from the original pair by collision processes. By absorption measurements of other inversion doublets with steady state irradiation, Oka has shown that in NH3/NH3 collisions, transitions which are allowed by the electric dipole selection rules (A/ = 0, 1, + - —) are preferred. Oka s analysis indicates that relaxation is most favourable in collision with molecules having similar J values, which are termed rotational resonances (R-R transfer). For example the process... 

Fig. 22 shows the results of photometry of plates similar to that illustrated in Fig. 21. The relative intensities of suitable transitions were determined from the asymptotic limit at long time delays when the system attains equilibrium. (These resemble, but are not identical to, the relative/ values because of the usual instrumental effects which depend on line width.) The time variation of the relative concentrations is shown in Fig. 23 the upper four levels attain Boltzmann equilibrium amongst themselves after 100 /isec, to form a coupled (by collision) system overpopulated with respect to the 5DA state. The equilibration of the upper four levels causes the initial rise (Fig. 22) in the population of Fe(a5D3). Thus relaxation amongst the sub-levels is formally similar to vibrational relaxation in most polyatomic molecules, in which excitation to the first vibrational level is the rate determining step. In both cases, this result is due to the translational overlap term, for example, in the simple form of equation (14) of Section 3.

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