Electronic relaxation of excited molecules

We will see below that the relative importance of these routes depends not only on the temperature but also on the nuclear shift parameters A, the electronic energy gap A , and the vibrational frequencies. We should also note that these two routes represent extreme cases. Intermediate mechanisms such as thermally activated tunneling also exist. Mixed situations, in which some nuclear degrees of freedom have to be activated and others, characterized by low nuclear masses and small shifts A, can tunnel, can also take place. 

A particular kind of electronic relaxation process is electron transfer. In this case (see Chapter 16) the electronic transition is associated with a large rearrangement of the charge distribution and consequently a pronounced change of the nuclear configuration, which translate into a large A. Nuclear tunneling in this case is a very low-probability event and room temperature electron transfer is usually treated as an activated 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,... 

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). 

Analysis of the fluorescence from electronically excited molecules in a conventional static gas system21 provides a way of investigating vibrational relaxation of such molecules, and is also a means of studying selection rules for rotational relaxation22. It is now well established that multiple quantum rotational jumps can occur with high probability (see Section 6). 

S. Comi, R. Cammi, B. Mennucci, J. Tomasi, Electronic excitation energies of molecules in solution within continuum solvation models Investigating the discrepancy between state-specific and linear-response methods, Formation and relaxation of excited states in solution A new time dependent polarizable continuum model based on time dependent density functional theory. J. Chem. Phys. 123, 134512 (2005)... 

A liquid scintillation counter is actually two photon counters connected in coincidence for measuring the shower or pulse of electrons resulting from the relaxation of fluorescent molecules excited by b-particle emission. In the out-of-coincidence mode, the instrument is a single photon counter, i.e., it counts single photon events. 

The following picture is emerging from this research. Core electron excited states have finite lifetimes and unique characters. The electronic and chemical relaxations are coupled and depend upon the atomic and electronic structure of the molecule, the atomic site of the core hole, and the configuration of the core hole excited state. Experiments leading to an understanding of these dependences are just beginning to be done. 

In this chapter, we have shown that electronic relaxation of vibrationally highly excited aromatic molecules is distinctly different from that of molecules with low levels of vibrational excitation. The most notable difference is in the efficiency of S, —>-S0 IC relative to St- T ISC. Thus, while S,->S0... 

Figure 3. Time dependence of different electron-transfer trajectories in molecules of pure liquid water at room temperature. The femtosecond UV excitation of water molecules (2X4 eV) triggers either an ultrafast electron photodetachment with the formation of hydronium ions and a nonadiabatic relaxation of excited p-like hydrated electrons (high photochemical channel), or concerted electron-proton transfer (low photochemical channel) (56, 72). The characteristic time of each trajectory is reported on the curve.

Considerable experimental effort has been aimed at elucidating the collision-free unimolecular dynamics of excited molecules. Processes of interest include the dynamics of highly excited vibrational states, which have been reached by multiphoton absorption, and the various electronic relaxation processes that can occur in electronically excited states of moderate to large molecules, etc. The idealized collision-free limit is approached either by extrapolating data to the limit of zero pressure or by performing experiments in molecular beams. Alternatively, estimates of expected collisional effects are made by using collision cross-sections that are computed from hard-sphere collision rates. These estimates are then utilized to determine whether the experiments are performed in the collision-free domain. 

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