Doublet mechanism

Double Heck reaction, 42 494 Double layer interface, 30 223-225 Double nucleophilic displacement, capped cyclodextrin, 32 437 Double-pulse method, 38 31 Double recognition models, 32 451 52 Doublet mechanisms, 30 43, 45, 47 Drago parameters, 38 212 Drougard-Decrooq equation, 30 345, 356, 371 Dry evaporation, perovskite preparation, 36 246-247... 

The first mechanism proposed for the newly discovered hydrogenolysis of cyclopentane was the doublet mechanism (104), in line with the general multiplet theory of Balandin (105). According to this mechanism, cyclopentane is physically adsorbed on two metal atoms, and stands perpendicular to the surface in the vicinity of physically adsorbed hydrogen atoms (Fig. la). This mechanism, however, does not explain why cyclopentanes are hydro-genolyzed on platinum while cyclohexanes and paraffins are not. 

It was replaced later by the sextet-doublet mechanism (106), in which physically adsorbed cyclopentane lies parallel to the surface (Fig. lb) (107, 108). In the transition state, the five carbon atoms of the ring are located over the interstices of the (111) plane of platinum. The distance between two contiguous interstices allows them to accommodate two consecutive carbon atoms, but one C-C bond in cyclopentane is necessarily stretched, and this favors the hydrogenolysis of the ring. In contrast, all the carbon atoms of cyclohexane or paraffins may be brought in contact with the metal surface, which would explain the selectivity of platinum for Cj-ring hydrogenolysis. In the first presentation of the model, the relative inertness of the tertiary-secondary C-C bonds in substituted cyclopentanes was explained by some kind of steric hindrance. 

The doublet and the sextet-doublet mechanisms resemble in many respects our Mechanisms A and B discussed previously, involving it-adsorbed cyclopentene and 1,2-dicarbene complexes, respectively. Mechanism A, like the sextet-doublet mechanism, implies a quasi-planar adsorption of the molecule and is in essence nonselective. In Mechanism B, as in the doublet model, the molecule stands perpendicular to the surface and hydrogenolysis is extremely selective. 

In any event, if ring closure via 1,5 di-ff-adsorbed species occurs in the case of medium-sized ring compounds, the reverse step, C-C bond shift rupture in physically adsorbed cyclopentanes, should also take place on account of microscopic reversibility. As a matter of fact, the first mechanisms proposed for hydrogenolysis of cyclopentanes (the doublet and sextet-doublet mechanisms) involved physically adsorbed cyclopentane. 

Thus in the latter instances cyclohexane is dehydrogenated according to the doublet mechanism, in conformity with the index (1.15). 

It should be assumed that in all the cases of stepwise dehydrogenation listed above, a doublet mechanism [edgewise orientation (56)] takes place, as in the already familiar case of dehydrogenation of ethane on palladium at elevated temperatures (220). 

The analogues of these compounds with their substituents in the phenyl groups behave in a similar way. One molecule of H2 is split off and, consequently, dehydrogenation proceeds according to the doublet mechanism. Incidentally, isomerization preceding dehydrogenation is also a doublet reaction known for Pd it has the index... 

The main part of the compound (decahydroazulene) decomposes and azulene forms, evidently, by dehydrogenation by the doublet mechanism. Thus, although the aromatic nature affects catalysis to a certain degree, it cannot by itself bring about a smooth dehydrogenation such as occurs in the case of cyclohexane. In order that catalysis take place, a structural correspondence is also necessary. Bicyclo[5.3.0]decane, contrary to cyclohexane, has no elements of symmetry common with with the lattice A1 of palladium and cannot superimpose on it. 

This classification is important not only for kinetics and for the equilibrium of the heterogeneous catalytic reactions with a doublet mechanism, but for the equilibrium of homogeneous catalytic and non-catalytic reactions as well, because the equilibrium does not depend on the mechanism of the reaction. It is interesting to note that the cyclic activated 4- and 6-complexes, postulated by Syrkin 355), are nothing but doublet and triplet index groups, and consequently the multiplet classification must be proper for them as well hence it can also be applied to the kinetics of catalytic reactions that are not heterogeneous. 

To nnderstand the internal molecnlar motions, we have placed great store in classical mechanics to obtain a picture of the dynamics of the molecnle and to predict associated patterns that can be observed in quantum spectra. Of course, the classical picture is at best an imprecise image, becanse the molecnlar dynamics are intrinsically quantum mechanical. Nonetheless, the classical metaphor mnst surely possess a large kernel of truth. The classical stnichire brought out by the bifiircation analysis has accounted for real patterns seen in wavefimctions and also for patterns observed in spectra, snch as the existence of local mode doublets, and the... 

The next two temis (Lorentzians) arise from the mechanical part of the density fluctuations, the pressure fluctuations at constant entropy. These are the adiabatic sound modes (l/y)exp[-FA t ]cos[co(A) t ] with (D(k) = ck, and lead to the two spectral lines (Lorentzians) which are shifted in frequency by -ck (Stokes line) and +ck (anti-Stokes line). These are known as the Brillouin-Mandehtarn, doublet. The half-width at... 

The full quantum mechanical study of nuclear dynamics in molecules has received considerable attention in recent years. An important example of such developments is the work carried out on the prototypical systems H3 [1-5] and its isotopic variant HD2 [5-8], Li3 [9-12], Na3 [13,14], and HO2 [15-18], In particular, for the alkali metal trimers, the possibility of a conical intersection between the two lowest doublet potential energy surfaces introduces a complication that makes their theoretical study fairly challenging. Thus, alkali metal trimers have recently emerged as ideal systems to study molecular vibronic dynamics, especially the so-called geometric phase (GP) effect [13,19,20] (often referred to as the molecular Aharonov-Bohm effect [19] or Berry s phase effect [21]) for further discussion on this topic see [22-25], and references cited therein. The same features also turn out to be present in the case of HO2, and their exact treatment assumes even further complexity [18],... 

P-F 153 pm). However, the F nmr spectrum, as recorded down to — 100°C, shows only a single fluorine resonance peak (split into a doublet by P- F coupling) implying that on this longer time scale (milliseconds, as distinct from instantaneous for electron diffraction) all 5 F atoms are equivalent. This can be explained if the axial and equatorial F atoms interchange their positions more rapidly than this, a process termed pseudorotation by R. S. Berry (1960) indeed, PF5 was the first compound to show this effect. The proposed mechanism is illustrated in Fig. 12.13 and is discussed more fully in ref. 91 the barrier to notation has been calculated as 16 2kJmol". ( ... 

There are several different ways in which quantum mechanics has been applied to the problem of relating the barrier to the frequency separation of the spectroscopic doublets. These are all approximation procedures and each is especially suitable under an appropriate set of circumstances. For example one may use perturbation theory, treating either the coupling of internal and external angular momenta, the molecular asymmetry, or the potential barrier as perturbations. Some of the different treatments have regions of overlap in which they give equivalent results choice is then usually made on the basis of convenience or familiarity. Extensive numerical tabless have been prepared which simplify considerably the calculations. 

This equation, including succeeding terms, was obtained originally by Sommerfeld from relativistic considerations with the old quantum theory the first term, except for the screening constant sQ> has now been derived by Heisenberg and Jordan] with the use of the quantum mechanics and the idea of the spinning electron. The value of the screening constant is known for a number of doublets, and it is found empirically not to vary with Z. 

Dynein sidearms interact with the walls of B-microtubules of adjacent doublets by means of a sliding-filament mechanism to produce ciliary movement. The process is energized by ATP hydrolysis. Movement of the cilium occurs in two stages, termed the power stroke and the recovery stroke. 

Recently, Moskaleva et al. have proposed a new mechanism based on electronic structure calculations." Earlier experimental studies by Kasdan et al. determined that methyne (HC) has a doublet ground state and with a doublet-quartet energy splitting (AEdq) of 71.5 + O.SkJ/mol." Moskaleva et al. noted that the initially proposed mechanism (for HCN and N(" S) atom formation) is therefore spin-forbidden, and they also proposed a more favorable and spin-allowed reaction on the doublet surface. This new route on the doublet energy surface proceeds through the formation of an NCN intermediate, with concomitant formation of (doublet) hydrogen atom. 

However, if the molecular configuration is such as to bring the radical centers into close contact (say, to within some critical distance D), interaction will begin and the two doublet states will collapse since the spins of the two electrons are no longer independent of each other. Quantum mechanics tells us that under these conditions the total number of states is dependent upon the sum of the spin quantum numbers for the two electrons ... 

If the spin-spin information was being transmitted by the normal through-bond mechanism the upfield three proton signal would be expected to occur as a doublet because these protons are the only ones which can assume the required planar zig-zag conformation 77>78h Preliminary results, using the change in chemical shift method 79>, indicates that the energy barrier to rotation is of the order of 20 k.cal.mole O. As expected the silicon compound (39) shows a nine proton doublet... 

The lithium abundance, using the Li I 6707 doublet, will be used as a signature of internal mixing to confirm whether or not internal mixing is one of the mechanisms responsible for the existence of blue straggler stars. 

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