Excited states, time evolution

Fmtos LM, Andruniow T, Santoro F, Ferre N, OUvucci M (2007) Tracking the excited-state time evolution of the visual pigment with multiconfigurational quantum chemistry. Proc Natl Acad Sci USA 104 7764-7769... 

Frutos, L. M., Andruniow, T., Santoro, F., Ferre, N., Olivucci, M., Tracking the Excited state Time Evolution of the Visual Pigment with Multiconfigurational Quantum Chemistry, Proc. Natl. Acad. Sci. USA 2007, 104, 7764 7769. 

Figure 1. The trajectory of ground-state D2 colliding with ground-state NHj" at 8 eV leads to abstraction with the NHsD+ ion highly vibrationally excited. The time evolution of the interatomic distances (c) and of the atomic charges (b) show which product species are generated.

In figure 4.8 only one particular type of superposition state j) and couplings are considered. With higher resolution, the individual resonances m), Eq. (4.28), in the spectrum could be excited. The time evolution for each m) state would be well-described by a single exponential with rate = y lh, where 7 , is the width of the resonance envelope. 

The pump pulse causes 74% excitation into the A state (between t = —8 and 4 fs). Afterwards the probe pulse train causes transfer of population between the A and B states, and between B and C (and X) states. Transfer of population occurs synchronous with the pulses in the pulse train, causing the step-like appearance seen in Fig. 5.35(a). The pulse train causes ionization simultaneously with population transfer among the neutral states. Time evolution of the ionized population is also seen to be step-like, with change synchronous with the pulses. Thus the electronic excitation and deexcitation seems to be a Rabi oscillation whose timing of transition is well controlled. On the other hand, the relevant nuclear vibrational motion is autonomously evolved in time during the refractory period. 

This chapter presents an ab initio description of the nature and dynamics of photoexcited states in semiconductor QDs, in the energy and time domains. By combining the bulk and molecular viewpoints, the analysis elucidates the controversies and provides a unified atomistic picture of the excited state processes. These ab initio methods are used to study excited state composition, evolution and relaxation, as well as electron phonon dephasing, all with an eye towards the incorporation of QDs in solar cells. For further reading on the work featured in this chapter see publications by the Prezhdo group. ... 

Figure Al.6.20. (Left) Level scheme and nomenclature used in (a) single time-delay CARS, (b) Two-time delay CARS ((TD) CARS). The wavepacket is excited by cOp, then transferred back to the ground state by with Raman shift oij. Its evolution is then monitored by tOp (after [44])- (Right) Relevant potential energy surfaces for the iodine molecule. The creation of the wavepacket in the excited state is done by oip. The transfer to the final state is shown by the dashed arrows according to the state one wants to populate (after [44]).

For bound state systems, eigenfunctions of the nuclear Hamiltonian can be found by diagonalization of the Hamiltonian matiix in Eq. (11). These functions are the possible nuclear states of the system, that is, the vibrational states. If these states are used as a basis set, the wave function after excitation is a superposition of these vibrational states, with expansion coefficients given by the Frank-Condon overlaps. In this picture, the dynamics in Figure 4 can be described by the time evolution of these expansion coefficients, a simple phase factor. The periodic motion in coordinate space is thus related to a discrete spectrum in energy space. 

Fig. 35). The potential energy curves and the transition dipole moment are taken from [117]. The time evolution of the populations on the ground and excited states is shown in Fig. 36 More than 86% of the initial state is excited to the B state within the period shorter than a few femtoseconds. The integrated total transition probability V given by Eq. (173) is P = 0.879, which is in good agreement with the value 0.864 obtained by numerical solution of the original coupled Schroedinger equations. This means that the population deviation from 100% is not due to the approximation, but comes from the intrinsic reason, that is, from the spread of the wavepacket. Note that the LiH molecule is one of the...

The laser intensities are taken to be the possible lowest. The intensity in case (b) is almost three times larger than the others. This is simply due to the fact that the transition dipole moment exponentially decays from the equilibrium position and also the potential energy difference increases. Note again that the coordinate-dependent level approximation works well. In order to demonstrate the selectivity the time evolution of the wave packets on the excited state are shown in Fig 41. As a measure of the selectivity, we have calculated the target yield by... 

Figure 3.13. Resonance Raman spectra of Sj excited state trans-stilbene in decane at delay times indicated. The pump wavelength was 292.9 nm and the probe wavelength was 585.8nm. The vertical dashed lines illustrated the substantial spectral evolution of the 1565 cm compared to the 1239cm band. (Reprinted with permission from reference [56]. Copyright (1993) American Chemical Society.)...

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