Excitation hopping

Figure 1.14. Stationary absorption and emission spectra of p-C 1P4 in toluene. The spectral overlap is depicted in gray. Inset The scheme representing singlet-singlet excitation hopping.

The Time Scales and Mechanism of Quasi-coherent Excitation Hopping Within B850/B875 Rings. This appears to be an area where simple theory cannot apply. It will be a challenge for experimentalists and theorists to address this issue collaboratively. For example, it is not clear whether linear coupling to a harmonic bath is adequate to describe such systems. For example, it may be necessary to include multiphonon and Duschinsky effects on the dynamics in order to describe the influence of temperature on such systems. 

Time-resolved anisotropy measurements of excitation hopping between two anthryl moieties attached to both ends of alkane molecules have been interpreted by a model based on conformational... 

An interesting problem, arising when a large number of identical chromophores is present in an artificial antenna system, is whether excitation hopping between such units can occur in a truly chaotic fashion. This problem has recently been addressed by Valeur and co-workers using a P-cyclodextrin labeled with seven naphthoyloxy chromophores on the primary face. ... 

As before, the basis states tpi and 2 for Pb represent states in which the excitation is localized on molecule 1 or 2, respectively. These are not stationary states because excitations hop back and forth between the two molecules. Setting one of the coefficients Ci or C2 to 1 and the other to zero cannot, therefore, describe the system well on time scales comparable to, or longer than the oscillation period. But we will see that it is possible to find values of the coefficients that make Ps into a stationary state. As we might expect, the values of Ci and C2 that are required depend strongly on the interaction term in the Hamiltonian, H, which is the term that mixes the two basis states (Sects. 2.3.6 and 7.2). 

Intramolecular Excitation Hopping and Time Ranges - A Different Model A... 

Figure B3.4.17. When a wavepacket comes to a crossing point, it will split into two parts (schematic Gaussians). One will remain on the same adiabat (difFerent diabat) and the other will hop to the other adiabat (same diabat). The adiabatic curves are shown by fidl lines and denoted by ground and excited die diabatic curves are shown by dashed lines and denoted 1, 2.

The simplest approach to simulating non-adiabatic dynamics is by surface hopping [175. 176]. In its simplest fomi, the approach is as follows. One carries out classical simulations of the nuclear motion on a specific adiabatic electronic state (ground or excited) and at any given instant checks whether the diabatic potential associated with that electronic state is mtersectmg the diabatic potential on another electronic state. If it is, then a decision is made as to whedier a jump to the other adiabatic electronic state should be perfomied. 

By using this approach, it is possible to calculate vibrational state-selected cross-sections from minimal END trajectories obtained with a classical description of the nuclei. We have studied vibrationally excited H2(v) molecules produced in collisions with 30-eV protons [42,43]. The relevant experiments were performed by Toennies et al. [46] with comparisons to theoretical studies using the trajectory surface hopping model [11,47] fTSHM). This system has also stimulated a quantum mechanical study [48] using diatomics-in-molecule (DIM) surfaces [49] and invoicing the infinite-onler sudden approximation (lOSA). 

A final study that must be mentioned is a study by Haitmann et al. [249] on the ultrafast spechoscopy of the Na3p2 cluster. They derived an expression for the calculation of a pump-probe signal using a Wigner-type density mahix approach, which requires a time-dependent ensemble to be calculated after the initial excitation. This ensemble was obtained using fewest switches surface hopping, with trajectories inibally sampled from the thermalized vibronic Wigner function vertically excited onto the upper surface. 

Quantum chemical methods, exemplified by CASSCF and other MCSCF methods, have now evolved to an extent where it is possible to routinely treat accurately the excited electronic states of molecules containing a number of atoms. Mixed nuclear dynamics, such as swarm of trajectory based surface hopping or Ehrenfest dynamics, or the Gaussian wavepacket based multiple spawning method, use an approximate representation of the nuclear wavepacket based on classical trajectories. They are thus able to use the infoiination from quantum chemistry calculations required for the propagation of the nuclei in the form of forces. These methods seem able to reproduce, at least qualitatively, the dynamics of non-adiabatic systems. Test calculations have now been run using duect dynamics, and these show that even a small number of trajectories is able to produce useful mechanistic infomiation about the photochemistry of a system. In some cases it is even possible to extract some quantitative information. 

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. 

Fig. 1 Schematic mechanism for the long-distance oxidation of DNA. Irradiation of the anthraquinone (AQ) and intersystem crossing (ISC) forms the triplet excited state (AQ 3), which is the species that accepts an electron from a DNA base (B) and leads to products. Electron transfer to the singlet excited state of the anthraquinone (AQ 1) leads only to back electron transfer. The anthraquinone radical anion (AQ ) formed in the electron transfer reaction is consumed by reaction with oxygen, which is reduced to superoxide. This process leaves a base radical cation (B+-, a hole ) in the DNA with no partner for annihilation, which provides time for it to hop through the DNA until it is trapped by water (usually at a GG step) to form a product, 7,8-dihydro-8-oxoguanine (8-OxoG)...

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