Excited state population

Figure Al.6,8 shows the experimental results of Scherer et al of excitation of I2 using pairs of phase locked pulses. By the use of heterodyne detection, those authors were able to measure just the mterference contribution to the total excited-state fluorescence (i.e. the difference in excited-state population from the two units of population which would be prepared if there were no interference). The basic qualitative dependence on time delay and phase is the same as that predicted by the hannonic model significant interference is observed only at multiples of the excited-state vibrational frequency, and the relative phase of the two pulses detennines whether that interference is constructive or destructive.

In tliese equations and are tire excited state populations of tire donor and acceptor molecules and and are tire lifetimes of tire donor and acceptor molecules in tire excited state tire notation is used to distinguish it from tire radiative constant (in otlier words for tire donor) is given by (C3.4.5) and tire... 

Standardizing the Method Equation 10.34 shows that emission intensity is proportional to the population of the excited state, N, from which the emission line originates. If the emission source is in thermal equilibrium, then the excited state population is proportional to the total population of analyte atoms, N, through the Boltzmann distribution (equation 10.35). 

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 relationship between the ground-state and excited-state populations is given by the Boltzmann 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. 

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.)...

If thermal motion on the Ti (or Si) surface leads to a quasi-equilibrium distribution of molecules between several minima, some of them are likely to provide a faster return to So than others and they will then drain the excited state population and determine which products will be formed. This is a straight-forward kinetic problem and it is clear that the process need not be dominated by the position of the lowest-energy accessible minimum in the excited hypersurface. Such minima may correspond to conformers, valence isomers, etc. Of course, it is well known that ground-state conformers may correspond to excited-state isomers, which are not in fast equilibrium. 65,72) Also, there is no reason why several separate minima in Si or Ti could not correspond to one minimum in So, and there is some evidence that this situation indeed occurs in certain polycyclic cyclohexenones. 73,74)... 

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. 

From a microscopic point of view of the absorption process, we can assume a simple two energy level quantum system for which N and N are the ground and excited state population densities (the atoms per unit volume in each state). The... 

Figure 13. Comparison of quantum (thick hues), QCL (thin lines), and SH (dashed lines) results as obtained for the one-mode two-state model IVa [205], Shown are (a) the adiabatic excited-state population P i), (b) the corresponding diabatic population probability and (c) the...

Figure 14. Statistical error of the adiabatic excited-state population at times r = 10 fs ( ), 30 fs -f), and 50 fs (X x x) for Model IVa [205], plotted as a function of the number of iterations N. The full lines represent fits to a 1 / /N dependence.

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).

It is interesting to note that the latter criterion imphes that the ground-state level density completely dominates the total level density— that is, that No E) N E). Hence the assumption (98) of complete decay into the adiabatic ground state is equivalent to the criterion that the classical and quantum total level densities should be equivalent. Furthermore, it is clear that this criterion determines an upper limit of 7. This is because larger values of the quantum correction would result in ground-state population larger than one (or negative excited-state populations). 

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).

This means that laser photons are preferentially absorbed by molecules with p // , which results in a partial polarization of the excited state population and with it the fluorescence. 

Reversal-temperature measurements of the Na and Cr lines in simple molecular gases, shock-heated to 2000-3000°K and to 0,2-2 atmospheres agree excellently with temperatures calculated from the measured shock velocity. Thus in these cases, collision processes are rapid enough to maintain effective equilibrium between ground and excited state populations despite radiatio n losses. In some shock tube work, however, the reversal temperature is initially above the equilibrium value, probably owing to delay in dissociation of the molecules, so that the temperature in translation and in internal degrees of freedom of the molecules is initially too high... 

V denoting the principal value. Henceforth, we shall concentrate on the relaxation rate as it determines the excited state population. 

We have shown that immediately after the measurement, the system and bath always heat-up, that is, get excited. Remarkably, for certain system-bath coupling spectra one can also observe a system that has lower excited-state population than the equilibrium state, that is, a purer system. This occurs despite the fact that the system has effectively recoupled with the bath and has become entangled with it. 

A theoretical description of CC of excited state dynamics using pulse trains in the perturbative regime, as carried out in experiments [63-65], is presented in Ref. [35]. Analytical expressions relating the excited state populations to the pulse train control parameters are derived in Ref. [35] we refer therein for technical details. We focus on the results here. 

---