Forbidden transitions, nonadiabatic transition

Figure 1. Two basic elements of dynamics (l) propagation on a single adiabatic potential and (2) nonadiabatic transition. In the classically allowed case, the transition occurs at Ana- In the classically forbidden case, on the other hand, the transition region spans the interval (xi,Xf), where a , and Xf are the turning points. Taken from Ref. [9].

The formulas derived in the time-independent framework can be easily transferred into the corresponding time-dependent solutions. The formulas in the time-independent linear potential model, for example, provide the formulas in the time-dependent quadratic potential model in which the two time-dependent diabatic quadratic potentials are coupled by a constant diabatic coupling [1, 13, 147]. The classically forbidden transitions in the time-independent framework correspond to the diabatically avoided crossing case in the time-dependent framework. One more thing to note is that the nonadiabatic tunneling (NT) type of transition does not show up and only the LZ type appears in the time-dependent problems, since time is unidirectional. 

For these spin-forbidden transitions, with AS = 2, this assumption is very likely invalid and the process is nonadiabatic, i.e., k < 1. If it is assumed that the entire entropic barrier of the quintet-singlet transition is due to nonadiabaticity, a minimum value of k 10 4 is obtained. 

Considerable work has already been carried out using ab initio calculations to predict the photodissociation dynamics of gas-phase metal carbonyls (45). This is a fertile area for computational work, given the extensive experimental results available, which include the use of ultrafast methods to characterize the short time behavior in photoexcited states. There is considerable evidence that surface crossings, especially of a spin-forbidden nature, play a considerable part in the dynamics. Much of the theoretical work so far has focused on reduced-dimensionality models of the PESs, which have been used in quantum mechanical smdies of the nonadiabatic nuclear dynamics, in which spin-forbidden transitions are frequently observed (45). Here, too, the potential benefits to be derived from a proper understanding of the spin-state chemistry are considerable, due to the importance of light-induced processes in organometallic and bioinorganic systems. 

The Spin-Forbidden Reaction CH( n) -pNz — HCN -pN( S) Revisited, n. Nonadiabatic Transition State Theory and Applicatiom... 

Spin-forbidden nonadiabaticity, 32 25 transitions, 32 25-26 Spin Hamiltonian, 38 194 four-iron clusters, 38 459-460 matrix, 38 453 parameters, 38 447, 449 Spin interactions, heterobinuclear units, 43 186... 

The assumption that the entropic barrier to the spin state transition is due entirely to spin-forbidden nonadiabaticity is equivalent to assuming that the transition state has the structure of the high-spin state. This is unlikely to be the case, and insofar as the assumption is invalid, the minimum value of k is increased. There is some evidence from the volume of activation for the spin state transition that the transition state lies well along the reaction coordinate between the low-spin and high-spin states. This novel experiment was accomplished independently by two groups with use of the photoperturbation technique with the sample subjected to variable pressure 44, 115). In the two cases reported, the volume of activation places the transition state about midway between the low-spin and high-spin states. If this is correct then there will be a considerable chemical contribution to the... 

These relaxation times correspond to rates which are about 106 slower than the thermal vibrational frequency of 6 x 1012 sec 1 (kBT/h) obtained from transition state theory. The question arises how much, if any, of this free energy of activation barrier is due to the spin-forbidden nature of the AS = 2 transition. This question is equivalent to evaluating the transmission coefficient, k, that is, to assess quantitatively whether the process is adiabatic or nonadiabatic. 

After describing why there is a problem, I will briefly summarize the theoretical description of spin-forbidden reactions. It will be useful at this point to draw parallels with other types of nonadiabatic chemistry, in particular, electron transfer. Then I will review some of the typical contexts in which spin-forbidden behavior occurs in transition metal systems, to try to illustrate how widespread it is. This will be followed by a presentation of strategies used for characterizing and understanding spin-forbidden reactions, based on the use of energies and... 

Marcus and co-workers have calculated nonadiabatic transfer probabilities for a model system consisting of ellipsoidal oxidant and reductant ions, at various mutual orientations. The model is designed to apply to large molecules such as proteins, and is a simplification of earlier work. " Selection rules (i.e., transfer probabilities) have been calculated for various 3d transition metal ions embedded in oxide lattices. For example, the reaction + Mn — + Mn " " is forbidden... 

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