Dimer rotation

In the transition from the T to the R conformation, the two c trimers rotate slightly with respect to each other about the threefold symmetry axis, so that they come into a more eclipsed alignment (see fig. 9.17). The r dimers rotate with respect to each other about a perpendicular axis and appear to act as a lever that moves the two c trimers apart by about 12 A and opens up a cavity at the center of the entire structure (see fig. 9.18). 

The total wave function of the dimer in the ground vibrational state can be represented as a product of wave functions for dimer rotation, internal rotation, and intermolecular exchange. The last of these depends on the polar angles 6l and d2 between the dimer axis and the molecular C3 axes and has the form... 

Figure 14 The calculated LDOS (a) around the highest occupied states averaged over the trajectory (b), obtained in a simulation of 0.4ps at T — 2000 K of the Si ad-dimer on the Si(00 1) surface. The ad-dimer rotates from a B configuration (black circles) to an A configuration (white circles). The individual trajectories of four substrate atoms are shown as full lines, those of die ad-dimer atoms as strings of circles, (c) The LDOS corresponding to the quenched (T = 0) final of this trajectory. The units in the figure are 3.84 A.

In Eqn. (5), the angular brackets impley averages over the asymmetric rotor wave-function as well as the vibrational wavefunction. Rz is the component of R along the space-fixed z-axis. The final step is to relate the coupling constants in Eqn. (5) to those of the monomer. In general, the expressions depend on the complexity of the monomers and on the dimer rotational state observed. For a large number of cases, a linear type dimer in a K=0 rotational state may be assumed, and Eqn. (5) may be expressed as... 

Further examination of the ATCase-PALA complex reveals a remarkable change in quaternary structure on binding of PALA. The two catalytic trimers move 12 A farther apart and rotate approximately 10 degrees about their common threefold axis of symmetry. Moreover, the regulatory dimers rotate approximately 15 degrees to accommodate this... 

The (X 1 P 1 and (X 2 P 2 dimers rotate approximately 15 degrees with respect to one another. The dimers themselves are relatively unchanged, although localized conformational shifts do occur. Thus, the interface between the a j P j and a 2 P 2 dimers is most effected by this structural transition. 

We suppose that an attempt to cross the barrier has occurred if the dimer rotates by the angle sufficient to take the dimer from a fcc-fcc well minimum to a barrier maximum. Simple geometry shows the angle to be 16.1°, which combines with the rotation speed to yield roo(Cu2) = 7.8 x 10 s . This is in very good agreement with the observed rate. 

Table 25. Adsorbate-induced structures on Si and Ge (100) surfaces. Here doi is tbe local adsorbate height dn is the spacing between the Group IV dimer atoms and co is the Group IV dimer rotation angle.

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