Electronic rearrangement procedure

Oscillations in time of quantal states are usually much faster than those of the quasiclassical variables. Since both degrees of freedom are coupled, it is not efficient to solve their coupled differential equations by straightforward time step methods. Instead it is necessary to introduce propagation procedures suitable for coupled equations with very different time scales short for quantal states and long for quasiclassical motions. This situation is very similar to the one that arises when electronic and nuclear motions are coupled, in which case the nuclear positions and momenta are the quasiclassical variables, and quantal transitions lead to electronic rearrangement. The following treatment parallels the formulation introduced in our previous review on this subject [13]. Our procedure introduces a unitary transformation at every interval of a time sequence, to create a local interaction picture for propagation over time. 

With the new density matrices known up to time tj, it is possible to advance the quasiclassical positions and momenta by integrating their Hamilton equations. This completes a cycle which can be repeated to advance to a later time t2- This sequence, based on relaxing the density matrix for fixed nuclei and then correcting it to account for quasiclassical motions, has been called the relax-and-drive procedure, and has been numerically implemented in several applications involving electronic rearrangement in atomic collisions [8]. 

A modification of this method, related to the Beckmann rearrangement, entails treatment of a ketoxime with one equivalent of CDI, then four to five equivalents of a reactive halide such as allyl bromide or methyl iodide (R3X) under reflux in acetonitrile for 0.5-1.5 h. Quatemization of the imidazole ring effectively promotes the reaction by increasing the electron-withdrawing effect. The target amides then are obtained by hydrolysis. High yields, neutral conditions, and a very simple procedure make this modification of the synthesis of amides by azolides a very useful alternative. 1243... 

Clearly, the spectroscopic properties of the P clusters in the proteins do not reveal their structural nature. However, extrusion of these clusters from the protein leads to the clear identification of 3-4 Fe S clusters(13.291. Despite the uncertainties inherent in the extrusion procedure (due to possible cluster rearrangement) the extrusion result supports the Dominant Hypothesis, which designates the P centers as Fe S units, albeit highly unusual ones. The P clusters are thought to be involved in electron transfer and storage presumably providing a reservoir of low potential electrons to be used by the M center (FeMo-co) in substrate reduction. 

Methylene difluorocyclopropanes are relatively rare and their rearrangement chemistry has been reviewed recently [14]. In addition, electron deficient alkenes such as sesquiterpenoid methylene lactones may be competent substrates. Two crystal structures of compounds prepared in this way were reported recently [15,16]. Other relatively recent methods use dibromodifluoromethane, a relatively inexpensive and liquid precursor. Dolbier and co-workers described a simple zinc-mediated protocol [17], while Balcerzak and Jonczyk described a useful reproducible phase transfer catalysed procedure (Eq. 6) using bromo-form and dibromodifluoromethane [18]. The only problem here appears to be in separating cyclopropane products from alkene starting material (the authors recommend titration with bromine which is not particularly amenable for small scale use). Schlosser and co-workers have also described a mild ylide-based approach using dibromodifluoromethane [19] which reacts particularly well with highly nucleophilic alkenes such as enol ethers [20], and remarkably, with alkynes [21] to afford labile difluorocyclopropenes (Eq. 7). 

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