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5.3: The dynamics of transient absorption spectrum

From the first glance, it seems that the interpretation of spectral and kinetic information of difference absorption spectra is quite simple: all the contributions to the signals (GSB, SE and IA) are proportional to the population of the excited state and all decay in unison. Indeed, in the most primitive cases, this is what we will observe. After the excitation of the molecule, a difference absorption spectrum will appear and uniformly decay with a characteristic time, equal to the lifetime of the excited state, analogously to the Eq. . In real life, however, the molecules are more complex than this: they jiggle around, interact with their environment (protein, solvent, solid state matrix, etc.). All sorts of processes may occur after the excitation and they all influence the difference absorption spectrum one way or another.

Let us discuss some of these processes.

  1. Internal conversion and vibrational relaxation. The molecules have a number of electronic states, each of which, in turn, has its vibrational sublevels. When the molecule is excited to the higher vibrational sublevels of an electronic state, it seeks to establish the Boltzman distribution (kBT is roughly 25 meV at 300 K, which is comparable to the typical energy spacing between vibrational sublevels) and the molecule will relax to the lower vibrational sublevels. Since the energy of the excited states is decreasing during such relaxation, the transient absorption spectrum will reflect this relaxation. For example, the wavelength of SE at each time instance depends on the energy gap between the excited state occupied at that particular instance and the ground state. Vibrational relaxation can also be observed in the IA signal, because the wavelength of the IA matches the energy gap between the excited state occupied at that particular instance and the higher excited state. Therfore, when we put the molecule, say in S2 electronic state, we will observe the IA corresponding to transitions , and when the molecule relaxes to S1, this IA signal will disappear and the absorption corresponding to  transitions will appear. Additionally, if the ensemble of molecules (in macroscopic samples we always work with an ensemble) is distributed in a number of different vibrational states, SE and IS spectra become broader. When vibrational realaxation takes place, all the molecules of the ensemble gather in their lowest vibrational states, and the broadening decrases. The particular realization depeneds on the molecule, but it is safe to say that SE and IA spectra are sensitive to the energy redistribution among the vibrational degrees of freedom in the molecule.
  2. Solvation and the relaxation of the environment. Each molecule has a certain charge distribution in the ground state, corresponding to the spatial configuration of its nuclei and electrons. The charges of the environment (solvent, protein, etc.) adjust to the molecular configuration in such a way that the overall energy of the system is at its minimum. After the excitation of the molecule, the configuration of its electrons (hence the charge distribution) is instantly changed. The environment charges ‘feel’ this and readjust first their electrons, and, subsequently, their nuclei to match the charge distribution of the excited molecule. Besides dielectric relaxation (redistribution of electron orbitals) this may include the shifts of solvent nuclei and reorientation of solvent molecules as dipoles. Dielectric relaxation is near-instantaneous, faster than 10 fs. The rearrangement of environment molecules is called solvation; its rate depends on the mobility of solvent molecules and their dipole moments. Typically, they are in the range of picoseconds and tens of picoseconds.[1] Obviously, the energy of the excited state must decrease when solvation takes place. What happens to the ground state energy? Well, it is easy to answer this if we keep in mind that the environment is now adjusted to the excited state. Were we to suddenly place the molecule back in the ground state with its charge distribution, the environment ‘would not like it’, i.e. the energy of the ground state would be higher than that of a relaxed ground state. To summarize, solvation reduces the energy of the excited state and increases that of the ground state (Fig. 28A). The energy gap between these states is directly measured by the stimulated emission spectrum. Therefore, SE maximum will shift towards the red upon solvation (Fig. 28B). Note that GSB spectrum will not be sensitive to solvation; it will stay in place, because it represents the absorption that disappeared upon excitation. This absorption disappears at the time instant of excitation and is recovered when the molecule returns to the lowest energy ground state.

 

Fig. 1) A. Potential energy surfaces for solvation: when the molecule is excited, the environment reorients to fit the new electronic configuration of the solute. This leads to the decrease of the excited state energy and the increase of ground state energy. As a result, SE spectrum observed in a transient absorption experiment, shifts to the red (B). The GSB spectrum remains unaffected.

 

 

 

  1. Conformational change of the molecule. Another biologically relevant reaction is the light-induced change in molecular structure. Biological example of this is the photoisomerization of retinal (discussed in section 4.3), from which the photosynthetic process of halophilic bacteria starts. Similar conformational change occurs in rhodopsin – protein residing in the animal retina and responsible for the vision process. There are many types of conformational change and trans-cis isomerization is just one of them. Molecules able to undergo conformational changes under light excitation are interesting because of their potential applications in nanotechnology, optoelectronics, information storage, etc. Let us discuss the changes of the transient absorption spectrum resulting from the isomerization of the molecule, similar to the scheme shown in Fig. 24A. Obviously, the ground and excited state energies will follow the same general trend as in the case of solvation (compare the potential energy schemes in Figs. 24A and 28A). This means, one can expect the shift of SE towards the red. After the completion of isomerization and return to a new ground state, SE signal will disappear, because there will be no more excited state able to emit photons. However, the ground state will be different from the originally excited state. Therefore, we can expect that some GSB will still persist and there will be new IA contribution matching the energy gap between the new ground state and its excited state. This means that PP spectroscopy allows us to oserve not only the course of photoisomerization, but also the absorption of the product being formed.
  2. Formation of a triplet state. Other photoinduced transformations of a molecule, such as triplet state formation, can be analyzed similarly to a conformational change. Triplets hardly emit any light (at least compared to the singlet excited states), therefore, after intersystem crossing, SE signal in transient absorption spectrum will disappear, and the induced absorption of triplet state (corresponding to transitions from T1 to T2) will become visible. The GSB signal will persist until the formed triplet state decays.
  3. Excitation energy transfer. We have already discussed excitation energy transfer. It can be monitored by using both fluorescence and PP spectroscopy. When donor molecule transfers the excitation energy to the acceptor molecule, PP signatures (GSB, SE and IA) will disappear and be replaced by the difference absorption spectrum of excited acceptor. This makes PP spectroscopy and excellent tool to monitor energy transfer between molecules with femtosecond time resolution. Compared to time-resolved fluorescence (where femtosecond resolution is only available in fluorescence upconversion experiments), PP is not just more sensitive (provides better signal-to-noise ratio), but also more flexible, because donor and acceptor populations can be observed at different wavelengths, e.g. at donor excited state absorption and acceptor bleach wavelengths. By selecting the spectral bands appropriately, experiment sensitivity and selectivity can be increased.
  4. Proton or electron transfer. Another very important class of photoinduced reactions relates to the photoinduced charge transfer events. Proton transfer occurs in molecules called photoacids and photobases. These are molecules with easily protonating groups (e.g. –OH), the pKa of which changes upon excitation. Two types of proton transfer are possible: intramolecular, when the proton leaves one group of the molecule and attaches to another group, and proton dissociation, when the proton goes to the environment leaving behind a molecular anion. Electron transfer occurs between electron donor (the molecule that receives excitation) and acceptor, and leads to the formation to two radicals of both molecules. The physical basis of proton transfer is always the same: the excited molecule can reduce its energy by releasing (or capturing) proton or electron. When this charge carrier is caught and stabilized by the molecules in the environment (which could be solvent or acceptor molecules), the donor molecule returns to the ground state, but the charge is not available any more – it is bound to the environment molecules. Therefore, at least for some time, the system remains in the charge-separated state, including radical, ion or isomer. All these reactions are inevitably accompanied by structural changes in the molecule; often, the molecules acquire a net electric charge. This is necessarily reflected by the change in the absorption spectrum. Following the general logic of analyzing the PP signals, we may expect that initially (at short delay times) we will observe the spectrum of the excited donor (excited states are easy to discern by their SE signals). In a while, this signal will decay and be replaced by new absorption bands, corresponding to the acceptor radical. Note that the GSB of the donor will also remain, because the donor will have become a radical too, rather than returning to its original ground state. In summary, when charge transfer is complete, we can expect to observe: a) donor GSB; b) donor radical (or ion) IA; c) acceptor GSB; d) acceptor radical (or ion) IA. Of course, some of these signals may be weak or lie outside the spectral window of the experiment, in which case they will not be observed.
  5. Photoionization. Another group of photoinduced events visible in PP experiments are related to photoionization. If the energy of absorbed light quantum is higher than the ionization potential of the molecule, the photon will rip off an electron from the molecule; this electron will be ejected into the environment. This process is instantaneous, and we will not be able to observe the excited state of the molecule. Instead, the excitation will immediately result in the spectrum composed molecular GSB and radical IA. If the molecule is dissolved in liquid or embedded in solid-state matrix, we will also observe the IA spectrum of solvated electron (electron surrounded by oriented solvent molecles). In water, this IA band is very broad (its width is around 0.84 eV) and has a maximum at roughly 720 nm [22]. Note that in ultrafast experiments, when the peak power of excitation pulse is high, photoionization may also be induced by multi-photon absorption, the phenomenon when two or more pump photons are absorbed by the molecule at once. In this case, the wavelength of the pump pulse may be longer than the photoionization threshold of the molecule, because the energy of two photons is combined to ionize the molecule. [2]

 

 


[1] A notable exception to this is water solvation, the major part of which occurs within 50 fs.

[2] To answer if the photoionization is one- or two-photon induced, we can measure the pump intensity dependence of radical/electron signals. In the case of single photon ionization, this dependence will be linear, in the case of two-photons -  quadratic.