Vibronic interactions adiabatic approximation

From the above discussion, we can see that the purpose of this paper is to present a microscopic model that can analyze the absorption spectra, describe internal conversion, photoinduced ET, and energy transfer in the ps and sub-ps range, and construct the fs time-resolved profiles or spectra, as well as other fs time-resolved experiments. We shall show that in the sub-ps range, the system is best described by the Hamiltonian with various electronic interactions, because when the timescale is ultrashort, all the rate constants lose their meaning. Needless to say, the microscopic approach presented in this paper can be used for other ultrafast phenomena of complicated systems. In particular, we will show how one can prepare a vibronic model based on the adiabatic approximation and show how the spectroscopic properties are mapped onto the resulting model Hamiltonian. We will also show how the resulting model Hamiltonian can be used, with time-resolved spectroscopic data, to obtain internal... 

We shall employ the adiabatic approximation that was shown to provide a rather good accuracy in the calculation of the magnetic susceptibility for the vibronic mixed valence systems exhibiting PJT in a wide range of parameters [9]. At the same time this approximation allows us to gain a descriptive comprehension of the physical role of the JT interaction. The full Hamiltonian of the system in the adiabatic approximation can be written as follows ... 

In order to reveal the effects of the JT vibronic interaction [74]-[76] one can employ the adiabatic approximation that was proved to provide a quite good accuracy in the description of the magnetic properties of MV clusters [77] and allowed to avoid numerical solutions of the dynamic problem. According to the adiabatic approach the magnetization can be obtained by averaging the derivatives —dUi(p, H)/dHa over the vibrational coordinates. In the case of an arbitrary p 7 0 the gap between... 

In those cases where the adiabatic approximation can be assumed to hold, the influence of vibronic coupling on the spectroscopic properties of a system can be treated within the Herzberg-Teller (perturbative) formalism (20) for vibronic interactions. This formalism is applicable when the vibronic interaction energies are small compared to the energy spacings between the... 

It has also been shown by Merrifield (52) that linear terms in appear due to displacements of nuclear equilibrium positions caused by electronic molecular excitation, whereas changes in vibration frequencies give rise to quadratic terms. By derivation of (3.181) the adiabatic approximation for isolated molecules has been applied so that (3.181) can be used for examination of vibronic states by an arbitrary intensity of resonant intermolecular interaction. 

The Born-Oppenheimer approximation (adiabatic approximation) becomes unsatisfactory when the potential energy surfaces draw closer or intersect so that the energy difference between them turns comparable with the vibrational quantum hv. In the region of the mixing of electron states, a strong interaction between the electron and the nuclear motion arises, which was termed the vibronic interaction. The narrow energy gap between the ground and the excited... 

In the non-CT radiationless transition the change in electronic charge interacts with the nuclei in a similar maimer both before and after the transition. Two types of processes can be identified internal conversion processes in which the transition is between spin states of the same multiplicity and intersystem crossing process in which the transition is between states of different spin multiplicity. For non-CT internal conversion processes the full BO (Bom—Oppenheimer) adiabatic wave-functions for the supramolecular complex are used as the zero-order basis [42-44]. The perturbations that cause the transition are the vibronic coupling between the nuclear and electron motions. These are just the terms that are neglected in the BO approximation [45]. The terms are expanded (normally to first order) in the normal vibrational coordinates of the nuclei as is customarily done for optical vibronic transitions. Thus one obtains Eq. 61b for cases when only one normal mode couples the two states... 

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