Jump /jumping between molecular states

In a molecular mechanism there is always at least one step at which the system changes its initial identity, as it were, to acquire a different one. This is called here the chemical interconversion step. Following the viewpoint developed in our paper [43], the interconversion takes place unimolecular complex where the system jumps between quantum states having different stationary Hamiltonians. A simple reaction scheme is then one having only one such interconversion step. Chemical reactions proceeding with multiple interconversion steps can be treated along lines similar to the one step process as far as the quantum aspects are concerned. 

Molecular Motions and Dynamic Structures. Molecular motions are of quite general occurrence in the solid state for molecules of high symmetry (22,23). If the motion does not introduce disorder into the crystal lattice (as, for example, the in-plane reorientation of benzene which occurs by 60° jumps between equivalent sites) it is not detected by diffraction measurements which will find a seemingly static lattice. Such molecular motions may be detected by wide-line proton NMR spectroscopy and quantified by relaxation-time measurements which yield activation barriers for the reorientation process. In addition, in some cases, the molecular reorientation may be coupled with a chemical exchange process as, for example, in the case of many fluxional organometallic molecules. ... 

The system is prepared at t=0 in the quantum state Pik> and the question is how to calculate the probability that at a later time t the system is in the state Fjn>. By construction, these quantum states are solutions of molecular Hamiltonian in absence of the radiation field, Hc->Ho Ho ik> = e k Fik> and H0 Pjn> = Sjn xPJn>. The states are orthogonal. The perturbation driving the jumps between these two states is taken to be H2(p,A)= D exp(icot), where co is the frequency of the incoherent radiation field and D will be a time independent operator. From standard quantum mechanics, the time dependent quantum state is given by ... 

We now argue that, by analogy, the frequency of molecular jumps between two rotational isomeric states of a molecule (Section 1.2.1) is given by... 

In general, jump models have been developed that permit instantaneous jumps between two or three nonequivalent molecular configurations. A more general formulation permitting jumps between several configurations is discussed in terms of lattice models. Jump models are particularly useful, in comparison to difiusion models, in that fluctuations in the intemuclear distance that may occur with the molecular motions can be accomodated easily. With the difiusion models, an avers e intemuclear distance r is used to calculate the dipolar contribution to relaxation parameters via Eq. (8). With jump models, the intemuclear distance can be explicitly specified for each jump state in this case the is removed from Eq. (8), and the distance... 

Steady-state molecular beam studies of the reaction of methylacetylene on reduced Ti02 (001) surfaces were undertaken to determine whether this reaction could be performed catalytically under UHV conditions. A representative experiment is presented in Figure 1. Prior to each experiment, the surface was sputtered and annealed to a temperature between 400 K and 550 K surfaces prepared in this manner have the highest fraction of Ti(+2) sites (ca. 30% of all surface cations) of any surface we have been able to create by initial sputtering [3]. Thus these are the surfaces most active for cyclotrimerization in TPD experiments [1]. Steady-state production of trimethylbenzene (as indicated by the m/e 105 signal detected by the mass spectrometer) was characterized by behavior typical of more traditional catalysts a jump in activity upon initial exposure of the crystal to the molecular beam, followed by a decay to a lower, constant level of activity over a longer time scale. Experiments of up to 6 hours in duration showed... 

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