Spin-forbidden nonadiabaticity

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... 

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. 

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... 

Spin-forbidden reactions are a subset of the broader class of electronically non-adiabatic processes, which involve more than one PES. The fundamental theory of how such processes occur is well understood (7-9), and a very large amount of research is being performed with the aim of elucidating more details in all the areas of nonadiabatic chemistry. It is not possible to present this work here, so I will instead provide an outline of the most important theoretical insights in the... 

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. 

Once the magnitude of the coupling between the two surfaces is determined, one can calculate the probability of crossing from one spin state to another at a given geometry. There are several well-established approximation methods for obtaining the crossing probability. Once obtained, it can then be incorporated into a statistical theory of rate such as the nonadiabatic version of RRKM theory to obtain rate constants for spin-forbidden processes. ... 

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

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