Vibrational energy manifold

The presence of the electron acceptor site adjacent to the donor site creates an electronic perturbation. Application of time dependent perturbation theory to the system in Figure 1 gives a general result for the transition rate between the states D,A and D+,A. The rate constant is the product of three terms 1) 27rv2/fi where V is the electronic resonance energy arising from the perturbation. 2) The vibrational overlap term. 3) The density of states in the product vibrational energy manifold. 

Particles on cluster surface Particles in the vibrational energy manifold... 

FIGURE 15.12 Different electronic states have different minimum-energy internuclear distances as well as different vibrational energy manifolds within each. This complicates the electronic spectra of even the simplest, diatomic molecules. 

The important conclusions of these studies are that, even at low pressures, collisions can drastically modify fluorescence decay curves. Rotational and/or vibrational energy transfer can stabilize an initially formed predissociated state by downward relaxation and conversely can destabilize a stable state by upward energy transfer into an unstable part of the energy level manifold. 

In a second example the discrete time-reversible propagation scheme for mixed quantum-classical dynamics is applied to simulate the photoexcitation process of I2 immersed in a solid Ar matrix initiated by a femtosecond laser puls. This system serves as a prototypical model in experiment and theory for the understanding of photoinduced condensed phase chemical reactions and the accompanied phenomena like the cage effect and vibrational energy relaxation. It turns out that the energy transfer between the quantum manifolds as well as the transfer from the quantum system to the classical one (and back) can be very well described within the mixed mode frame outlined above. 

Azulene is one of the most interesting molecules from the photophysical point of view. A picosecond measurement of the vibrational energy decay in matrix isolated polyatomic molecules shows at 4K that molecular modes in a polyatomic matrix does not affect decay in the 2 vibrational manifold . The S2 Sq fluorescence of pseudoazulenes has been studies in Shpolski... 

Evidence that decay of the first excited singlet state may occur via a nonradiative process which depends on the vibrational energy and probably does not Involve the lower triplet states of the TT manifold comes from various types of experiment ... 

Here im is the effective mass of the i th vibration and Pi is the momentum conjugate to the corresponding normal vibrational coordinate Qi. The first two terms transform the electronic levels into potential energy manifolds in the coordinates of the octahedral normal modes Qi with vibrational frequencies m,- = yZ T/I/", and the complete wave functions in the Born-Oppenheimer approximation can be written as a product of the electronic and vibrational parts. The third term describes the distortions produced by the vibrations and can be interpreted in terms of a force Fi, which acts along the vibrational mode Qi associated with the electronic state E ... 

Fig. 6. Non-adiabatic contributions to the scattering process are significant when the electronic energy separation of excited states e> and Is) is comparable to the vibrational energy level separation. In this case the coordinate operator, Q, may cause transitions between the vibrational manifolds of the two electronic excited states...

Fig. 8. Schematic of a molecular motor activated by intramolecular vibration energy relaxation of manifold A towards the rotor part of the motor. The rotor is positioned on an axis connected to reservoir 1 kept at a temperature T. Vibration manifold A is represented here by a simple molecular spring that can be excited by light or by the inelastic effect of a tunneling current passing through the molecular spring. Without such an excitation, manifold A is statistically populated by reservoir 1. A specific choice of a molecular structure equivalent to the spring may avoid its complete thermalization, for example by filtering the thermal noise giving rise to a unidirectional rotary motion...

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