Curve-crossing processes

Electronic transitions and curve crossing processes take place. 

It is important to clarify here that the description of PT processes by curve crossing formulations is not a new approach nor does it provide new dynamical insight. That is, the view of PT in solutions and proteins as a curve crossing process has been formulated in early realistic simulation studies [1, 2, 42] with and without quantum corrections and the phenomenological formulation of such models has already been introduced even earlier by Kuznetsov and others [47]. Furthermore, the fact that the fluctuations of the environment in enzymes and solution modulate the activation barriers of PT reactions has been demonstrated in realistic microscopic simulations of Warshel and coworkers [1, 2]. However, as clarified in these works, the time dependence of these fluctuations does not provide a useful way to determine the rate constant. That is, the electrostatic fluctuations of the environment are determined by the corresponding Boltzmann probability and do not represent a dynamical effect. In other words, the rate constant is determined by the inverse of the time it takes the system to produce a reactive trajectory, multiplied by the time it takes such trajectories to move to the TS. The time needed for generation of a reactive trajectory is determined by the corresponding Boltzmann probability, and the actual time it takes the reactive trajectory to reach the transition state (of the order of picoseconds), is more or less constant in different systems. 

If the curve crossing process is highly exothermic, the backward rate is negligible and Eq. (9.25) simplifies into... 

As a multidimensional PES for the reaction from quantum chemical calculations is not available at present, one does not know the reason for the surprismg barrier effect in excited tran.s-stilbene. One could suspect diat tran.s-stilbene possesses already a significant amount of zwitterionic character in the confomiation at the barrier top, implying a fairly Tate barrier along the reaction path towards the twisted perpendicular structure. On the other hand, it could also be possible that die effective barrier changes with viscosity as a result of a multidimensional barrier crossing process along a curved reaction path. 

Schulten, K. Curve crossing in a protein coupling of the elementary quantum process to motions of the protein. In Quantum mechanical simulation methods for studying biological systems, D. Bicout and M. Field, eds. Springer, Berlin (1996) 85-118. 

The recombination of He is a special case. We include it here because of the similarities with H3 and because it is the only known example where three-body recombination of a diatomic molecular ion dominates over the binary process. The literature on the helium afterglow is quite large and we will not be able to do justice to all aspects of this problem. Mulliken71 had predicted that fast dissociative recombination of Hej should not occur due to a lack of a suitable curve crossing between the ionic potential curve and repulsive curves of He. Afterglow experiments in pure helium, at sufficient pressure to enable formation of Hej ions, have confirmed this expectation. It does not appear that the true binary recombination... 

The curve crosses y axis at value of a. It tends towards infinity as value of t increases. This is clearly not a sustainable physiological process but could be seen in the early stages of bacterial replication where y equals number of bacteria. 

The curve crosses the y axis at a value of a. It declines exponentially as t increases. The line is asymptotic to the x axis. This curve is seen in physiological processes such as drug elimination and lung volume during passive expiration. ... 

To summarize, Jean shows that coherence can be created in a product as a result of nonadiabatic curve crossing even when none exists in the reactant [24, 25]. In addition, vibrational coherence can be preserved in the product state to a significant extent during energy relaxation within that state. In barrierless processes (e.g., an isomerization reaction) irreversible population transfer from one well to another occurs, and coherent motion can be observed in the product regardless of whether the initially excited state was prepared vibrationally coherent or not [24]. It seems likely that these ideas are crucial in interpreting the ultrafast spectroscopy of rhodopsins [17], where coherent motion in the product is directly observed. Of course there may be many systems in which relaxation and dephasing are much faster in the product than the reactant. In these cases lack of observation of product coherence does not rule out formation of the product in an essentially ballistic manner. 

In solution when iodine is excited to the bound B excited state, dissociation and recombination processes occur. The dissociation is the result of solvent-induced curve crossing to the dissociative a state, the recombination a result of momentum reversals arising from collisions with the surrounding solvent molecules. Eigenstates of the B state will decay in a continuous manner, whereas wavepackets—if the curve-crossing probability is less than unity—decay in a stepwise manner, giving rise to successive pulses of product. The B and a curves cross near the center of the B state, whereas the B state wavepacket is initially created near the left turning point thus there... 

Note that in this particular intersystem crossing process the nuclear coordinate Q is less than Q0 in both initial and final states. We call eq. (7-12) nonadiabatic intersystem crossover, since the process initiates on the E(Y) curve and ends up on the (11) curve. We call the process (7-9) an adiabatic intersystem crossover, since it follows curve E ) only. 

This reaction has been observed194 in scattering experiments and is thought to be due to a crossing or close approach of the diatomic potential curves between the reactants N+(3P) + He(1S) and the products N+(5S) + He(1S). Further examples of intersystem crossing processes will be discussed in greater detail in Sections IX-XII. 

The use of the terms adiabatic and non-adiabatic in this way leads to a source of confusion. Normally, in describing surface-crossing processes, a process which remains on the same potential curve is called adiabatic and in that sense every net electron transfer reaction is an adiabatic process. Processes which involve a transition between different states as between the two different potential curves in Figure lb are usually called non-adiabatic. Such processes have some special features and will be returned to in a later section dealing with the inverted region and excited state decay. 

These processes occur at thermal energies in the afterglow of a pulsed discharge and probably involve curve crossings. The resultant electronically excited states of Kr+ and Xe+ lead to several laser lines in the range of 512.8 to 431.9 nm and 609.5 to 486.4 nm, respectively. 

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