Energy-resolved experiments

EXPERIMENTAL SET-UP FOR ANGLE AND ENERGY RESOLVED EXPERIMENTS 2.1. Experimental set-up and spectroscopic tools... 

Time-independent picture. The opposite extreme from short-pulse excitation involves the use of nearly monochromatic radiation. Practically, this means that the interaction between molecule and radiation field is of longer duration than Tnr. In this limit, the quantity measured is the absorption lineshape. It will be shown below that the linewidth observed in an energy-resolved experiment is related in a very simple way to the predissociation lifetime in the time-resolved experiment. 

This corresponds in practice to energy-resolved experiments. Two essentially different types must be distinguished, depending on the nature of the incident field. 

A second, different way for energy-resolved experiments is to use chaotic sources under steady-state working conditions. As discussed in the previous section, this corresponds to the situation where the incident beam is represented by density operator (93), as a mixture of monochromatic components averaged over the distributions fF(a) and F,( t)p. Using the results (102) and (104) for each component, one then gets in this case the expressions... 

The complementary method to time-resolved measurements is the spectroscopy in the energy domain. Energy-resolved experiments determine the Fourier transform of the exponential decay in the time domain, which yields a Lorentzian for the intrinsic spectral lineshape. As mentioned in Section 3.2.4, photoemission does not permit to separate inelastic and elastic decay processes, which both contribute to the linewidth. Because the energy resolution of inverse photoemission is usually not sufficient for a lineshape analysis, this section is devoted to photoemission of occupied states, providing an additional complementary aspect to the time-resolved measurements of transiently populated unoccupied states by 2-PPF. Occupied (initial) states can also be observed by 2-PPE spectroscopy. Their linewidth is similar to the values obtained in regular photoemission [107]. 

In these experiments, the initial ionization occurs rapidly, and the dissociation energy of AB is determined from the kinetics for its decomposition, which can be measured in a time-resolved experiment, typically within an ion trap. 

Such a rate increase at short distances has been observed also by M.E. Michel-Beyerle [12] in time resolved experiments with a photoactivated acri-dinium ion as electron acceptor. This effect can be explained by the influence of the distance on the solvent reorganization energy The solvent reorganization energy is small for charge shifts over short distances, and it increases with the distance until it reaches a plateau. In this plateau area the solvent reorganization energy remains constant and Eq. (1) can be applied ... 

The events taking place in the RCs within the timescale of ps and sub-ps ranges usually involve vibrational relaxation, internal conversion, and photo-induced electron and energy transfers. It is important to note that in order to observe such ultrafast processes, ultrashort pulse laser spectroscopic techniques are often employed. In such cases, from the uncertainty principle AEAt Ti/2, one can see that a number of states can be coherently (or simultaneously) excited. In this case, the observed time-resolved spectra contain the information of the dynamics of both populations and coherences (or phases) of the system. Due to the dynamical contribution of coherences, the quantum beat is often observed in the fs time-resolved experiments. 

From the above discussion, we can see that the purpose of this paper is to present a microscopic model that can analyze the absorption spectra, describe internal conversion, photoinduced ET, and energy transfer in the ps and sub-ps range, and construct the fs time-resolved profiles or spectra, as well as other fs time-resolved experiments. We shall show that in the sub-ps range, the system is best described by the Hamiltonian with various electronic interactions, because when the timescale is ultrashort, all the rate constants lose their meaning. Needless to say, the microscopic approach presented in this paper can be used for other ultrafast phenomena of complicated systems. In particular, we will show how one can prepare a vibronic model based on the adiabatic approximation and show how the spectroscopic properties are mapped onto the resulting model Hamiltonian. We will also show how the resulting model Hamiltonian can be used, with time-resolved spectroscopic data, to obtain internal... 

The knowledge of the internal-energy distribution is of equal interest for the practical applications indicated in the preceding paragraphs. First spectroscopic obervations of the IR emission from the molecule BC, which is related to the vibrational-state population, were reported by Karl and Polanyi13 on the system Hg + CO. These measurements were subsequently improved and extended.14-16 Recent time-resolved experiments with IR-laser absorption17- 18 and emission techniques19-21 yield more reliable results on the product-state distribution. 

The conflicting serial/parallel models for IVR/VP are not readily distinguished until time resolved experiments can be performed on the systems of interest. Both models can relate the relative intensities of the emission features to the various model parameters, but the serial process seems more in line with a simple, conventional [Fermi s Golden Rule for IVR (Avouris et al. 1977 Beswick and Jortner 1981 Jortner et al. 1988 Lin 1980 Mukamel 1985 Mukamel and Jortner 1977) and RRKM theory for VP (Forst 1973 Gilbert and Smith 1990 Kelley and Bernstein 1986 Levine and Bernstein 1987 Pritchard 1984 Robinson and Holbrook 1972 Steinfeld et al. 1989)], few parameter approach. Time resolved measurements do distinguish the models because in a serial model the rises and decays of various vibronic states should be linked, whereas in a parallel one they are, in general, unrelated. Moreover, the time dependent studies allow one to determine how the rates of the IVR and VP processes vary with excitation energy, density of states, mode properties, and isotropic substitution. 

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