Excited-state populations electronic excitation

It has been demonstrated that the whole photoexcitation dynamics in m-LPPP can be described considering the role of ASE in the population depletion process [33], Due to the collective stimulated emission associated with the propagation of spontaneous PL through the excited material, the exciton population decays faster than the natural lifetime, while the electronic structure of the photoexcited material remains unchanged. Based on the observation that time-integrated PL indicates the presence of ASE while SE decay corresponds to population dynamics, a numerical simulation was used to obtain a correlation of SE and PL at different excitation densities and to support the ASE model [33]. The excited state population N(R.i) at position R and time / within the photoexcited material is worked out based on the following equation ... 

The determination of the laser-generated populations rij t) is infinitely more delicate. Computer simulations can certainly be applied to study population relaxation times of different electronic states. However, such simulations are no longer completely classical. Semiclassical simulations have been invented for that purpose, and the methods such as surface hopping were proposed. Unfortunately, they have not yet been employed in the present context. Laser spectroscopic data are used instead the decay of the excited state populations is written n (t) = exp(—t/r ), where Xj is the experimentally determined population relaxation time. The laws of chemical kinetics may also be used when necessary. Proceeding in this way, the rapidly varying component of AS q, t) can be determined. 

Several characteristics of the metal beam have been studied in detail. It is well known that metal clusters and metal oxides are formed as a result of the ablation process. However, these potentially interfering species have been studied in detail130 and it has been concluded that they do not introduce any doubt as to the validity of the experimental results. Much more important than cluster or oxide formation are the atomic electronic state populations of the metal beams. For each metal reactant, these have been characterized using laser-induced fluorescence (LIF) excitation spectroscopy. For Y, only the two spin-orbit states of the ground electronic state (a Dz/2 and a D-3,/2) were observed.123... 

Further cases of non-photochemical fluorescent sensors include those where the luminophore undergoes a variation in the originally populated electronic excited state due to temperature or environmental changes (solvent, viscosity, ionic strength,...). 

Figure 8. Li + H2 Ground-state population as a function of time for a representative initial basis function (solid line) and the average over 25 (different) initial basis functions sampled (using a quasi-classical Monte Carlo procedure) from the Lit2/j) + H2(v — 0, j — 0) initial state at an impact parameter of 2 bohr. Individual nonadiabatic events for each basis function are completed in less than a femtosecond (solid line) and due to the sloped nature of the conical intersection (see Fig. 7), there is considerable up-funneling (i.e., back-transfer) of population from the ground to the excited electronic state. (Figure adapted from Ref. 140.)...

Figure 10. Excited-state population of ethylene as a function of time in femtoseconds (full line). (Results are averaged over 10 initial basis functions selected from the Wigner distribution for the ground state in the harmonic approximation.) Quenching to the ground electronic state begins approximately 50 fs after the electronic excitation, and a Gaussian fit to the AIMS data (dashed line) predicts an excited-state lifetime of 180 fs. (Figure adapted from Ref. 214.)...

One can calculate the ratio of populations of spin-up to spin-down electron orientations at room temperature (T = 300 K) from the Boltzmann formula finding that Nl / N is approximately equal to one (0.999), indicating that there is about a 0.1% net excess of spins in the more stable, spin-down orientation at room temperature. Using the same mathematical expression, this difference in populations can be shown to increase as the temperature is lowered. Actually, the EPR signal will be linearly dependent on 1/ T, and this linear dependence is called the Curie law. Because of the excited state population s temperature dependence, most EPR spectra are recorded at temperatures between 4 and 77 K. 

Figure 19. Time-dependent (a) diabatic and (b) adiabatic electronic excited-state populations and (c) vibrational mean positions as obtained for Model 1. Shown are results of the mean-field trajectory method (dotted lines), the quasi-classical mapping approach (thin full lines), and exact quantum calculations (thick full lines).

Figure 28. Time-dependent (a) adiabatic and (b) diabatic electronic excited-state populations as obtained for Model Vb describing electron transfer in solution. Quantum path-integral results [199] (big dots) are compared to mapping results for the limiting cases y = 0 (dashed lines) and Y = 1 (dotted lines) as well as ZPE-adjusted mapping results for Yi p, = 0.3 (full lines).

In the following, we will discuss two basic - and in a sense complementary [44] - physical mechanisms to exert efficient control on the strong-field-induced coherent electron dynamics. In the first scenario, SPODS is implemented by a sequence of ultrashort laser pulses (discrete temporal phase jumps), whereas the second scenario utilizes a single chirped pulse (continuous phase variations) to exert control on the dressed state populations. Both mechanisms have distinct properties with respect to multistate excitations such as those discussed in Section 6.3.3. 

The photodynamics of electronically excited indole in water is investigated by UV-visible pump-probe spectroscopy with 80 fs time resolution and compared to the behavior in other solvents. In cyclohexane population transfer from the optically excited La to the Lb state happens within 7 ps. In ethanol ultrafast state reversal is observed, followed by population transfer from the Lb to the La state within 6 ps. In water ultrafast branching occurs between the fluorescing state and the charge-transfer-to-solvent state. Presolvated electrons, formed together with indole radicals within our time resolution, solvate on a timescale of 350 fs. 

From the steady state fluorescence spectrum of indole in water a fluorescence quantum yield of about 0.09 is determined. Since the cation appears in less than 80 fs a branching of the excited state population has to occur immediately after photo excitation. We propose the model shown in Fig. 3a). A fraction of 45 % experiences photoionization, whereas the rest of the population relaxes to a fluorescing state, which can not ionize any more. A charge transfer to solvent state (CITS), that was also introduced by other authors [4,7], is created within 80 fs. The presolvated electrons, also known as wet or hot electrons, form solvated electrons with a time constant of 350 fs. Afterwards the solvated electrons show no recombination within the next 160 ps contrary to solvated electrons in pure water as is shown in Fig. 3b). 

If the system under consideration possesses non-adiabatic electronic couplings within the excited-state vibronic manifold, the latter approach no longer is applicable. Recently, we have developed a simple model which allows for the explicit calculation of RF s for electronically nonadiabatic systems coupled to a heat bath [2]. The model is based on a phenomenological dissipation ansatz which describes the major bath-induced relaxation processes excited-state population decay, optical dephasing, and vibrational relaxation. The model has been applied for the calculation of the time and frequency gated spontaneous emission spectra for model nonadiabatic electron-transfer systems. The predictions of the model have been tested against more accurate calculations performed within the Redfield formalism [2]. It is natural, therefore, to extend this... 

Here Tr means the trace over vibrational (not electronic) coordinates, pf = Z x exp(—ha/kT), and Za are the corresponding partition functions. The proposed damping operator consists of the two contributions, re and which are responsible for the electronic and vibrational relaxation, respectively. The first term in the operator (2) reflects the excited-state population decay, so that T) = l/ e is simply the excited... 

A more sophisticated version of the Tannor-Rice scheme exploits both amplitude and phase control by pump-dump pulse separation. In this case the second pulse of the sequence, whose phase is locked to that of the first one, creates amplitude in the excited electronic state that is in superposition with the initial, propagated amplitude. The intramolecular superposition of amplitudes is subject to interference whether the interference is constructive or destructive, giving rise to larger or smaller excited-state population for a given delay between pulses, depends on the optical phase difference between the two pulses and on the detailed nature of the evolution of the initial amplitude. Just as for the Brumer-Shapiro scheme, the situation described is analogous to a two-slit experiment. This more sophisticated Tannor-Rice method has been used by Scherer et al. [18] to control the population of a level of I2. The success of this experiment confirms that it is possible to control population flow with interference that is local in time. 

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