Quantum Kramer-Like Theory

To demonstrate the accuracy of eqn (12.26) together with eqn (12.30) and its boundary condition eqn (12.31), called the quantum Kramers-like theory, we use a symmetric spin-boson model as a concrete system. In this benchmark model, the nuclear vibrational motions are characterized by the Ohmic spectral density ... 

Before the numerical simulation, it may be interesting to know the high temperature limitation of the quantum Kramers-like theory for the purpose of comparison with other analytical approaches. At the high temperature limit, eqn (12.26) can be easily written as ... 

We have calculated the electronic coupling dependence of rate from the quantum Kramers-like theory as well as from the above mentioned methods. In the calculations, we set the parameters A = 1, = 0. In addition, J= 1 to keep... 

Nelsen and co-workers also measured the ET rates within charge-localized dinitroaromatic radical anions in several solvents.The optieal data reveal that this system has a very large electronic coupling (3000-4000 cm ). In such a case, solvent dynamics may play a significant role. Therefore, the quantum Kramers-like theory is used to estimate the rate. We use the temperature dependence of solvent relaxation time x ... 

Figure 12.7 Comparison of ESR rates with those from the quantum Kramers-like theory for a dinitroaromatic radical anion in acetonitrile (MeCN) and benzonitrile (PhCN).

We have presented several approaches to calculate the rate constants of electron transfer occurring in solvent from the weak to strong electronic couplings. In the fast solvent relaxation limit, the approach based on the nonadiabatic transition state theory can be adopted. It is related to the Marcus formula by a prefactor and referred as a modified Marcus formula. When the solvent dynamics begin to play a role, the quantum Kramers-like theory is applicable. For the case where the intramoleeular vibrational motions are much faster than the solvent motion, the extended Sumi-Mareus theory is a better ehoice. As the coherent motion of eleetron is ineorporated, such as in the organic semiconductors, the time-dependent wavepaeket diffusion approach is proposed. Several applications show that the proposed approaches, together with electronic structure calculations for the faetors eontrolling eleetron transfer, can be used to theoretically predict electron transfer rates correctly. 

To conclude this section, there is one other phenomenon we should like to discuss, viz. the Raman effect. Let it be mentioned beforehand, however, that this is not a revolutionary discovery, like, for example, the discovery of the wave nature of the electron, but an effect which was predicted by the quantum theory (Smekal (1923), Kramers-Heisenberg) some years before it was found experimentally, though it can also be explained within the framework of classical physics (Cabannes (1928), Rocard, Placzek) its great importance rests rather on the facility with which it can be applied to the study of molecules, and on the colossal amount of material relating to it which has been accumulated so quickly. The effect was discovered simultaneously (1928) by Raman in India, and by Landsberg and Mandelstam in Russia. They found that scattered light contains, in addition to the frequency of the incident light, a series of other frequencies. 

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