CP Mode

A comparison between experimental and calculated spectroscopic parameters for various cyclopentadienyl (Cp) compounds indicated that the internal Cp modes are transferable while the skeletal modes are dependent on the nature of the metal-Cp bonds. The skeletal force constants for a number of metallocenes are given in Table 10.2. 

Switch to CP mode and increment the transmitter power of the X nucleus until the maximum signal is observed (i.e. the optimum match is obtained). 

In Figure 2 we show a space time plot of a CP mode for = 1. We note that there are collisions at ip = 0 and ip = it. The collision sites are determined by the initial conditions. This CP mode is periodic and symmetric in that the behavior at the two collision sites is the same, just 180° out of phase in time. In this mode, the hot spots enter and leave the collision essentially unchanged except for a phase shift, much like the behavior of solitons. Our computations indicate that the amplitude of the symmetric CP mode, i.e., the maximum temperature achieved at a collision, does not approach 0 as i approaches the transition point. Thus, the stable CP modes develop with finite amplitude. Our results also indicate that the mean speed V for these modes exceeds the speed for the unstable, uiuformly propagating planar solution. Thus, near the transition point finite amplitude CP modes can propagate faster than the uiuformly propagating mode. The mean propagation speed decreases as R increases. 

As R increases there is a transition to CP modes which exhibit different behavior at each of the two colhsion sites. We illustrate such a solution in Figure 2 for R = 1.2, where we plot 0/ as a function of t at the two collision sites Ip = 0 and ip = it. Each spike in the time history of 0/ corresponds to a collision. The solution is periodic, however, we note that had we chosen an angle different from one of the collision sites 0/ would exhibit two spikes per period corresponding to the two counterpropagating hot spots. In contrast to the solution for = 1 an asymmetry between the two colhsion sites has developed. Spots entering the colhsion at t/ = 0 are stronger than when they exit the colhsion and conversely for collisions at ip = it. The collisions take on the character of apparent creation/annihilation sites as the asymmetry between... 

We next consider the spin mode solution branches shown in Figure 1. The first branch we focus on corresponds to 1-headed spin modes which are traveling waves (TWl). These modes require larger radii for stability than the CP modes. Stable CP modes may be able to exist for smaller values of R as they are, in a sense, reinforced by collisions after circuiting only half the cylinder. The TWl modes also appear to enter with nonzero amplitude of the rotating hot spot. The smallest value of R for which we can find a stable TW1 mode is R=1.68. For this value of R the temperature of the hot spot is approximately 1.21. Unstable TWl modes may well exist for smaller values of R. If we decrease R further solutions with TW 1 initial data evolve to CP modes. We note that the mean axial speeds V for the TW 1 modes near onset are below those of the CP modes near onset, probably due to the fact that R is larger. 

In the "continuous path" (CP) mode the robot is allowed to operate at its programmed speed (ie the speed set by the programmer) but subject to... 

Figures 12.2 and 12.4 illustrate the activation steps for the Cp mode of III and IV, whereas Figures 12.3 and 12.5 illustrate the steps for the C mode according to Scheme 12.1. The relative energies for the optimized structures are summarized in Table 12.2. Activation step 3 is not shown for the hemilabile systems because of its...

FIGURE 12.2 Electronic energy profiles of the activation steps in the productive 1-octene metathesis using III (only the C 4 to Fjj4 structures are shown) (Cp mode). 

The calculated reaction energy for the formation of the ruthenacyclobutane intermediate (III-Dn4) from the u-complex 111-0 4 in the presence of III is endothermic (3.31 kcal/mol) for the Cp mode with activation energy of 31 kcal/mol (Figure 12.2). In contrast, the formation of Dn from the t-complex C is exothermic for both activation steps 1 (-11.95 kcal/mol) and 2 (-4.51 kcal/mol) with activation energies of 66 kcal/mol and 45 kcal/mol, respectively. The decomposition of the ruthenacyclobutane ( D, to Ej, ) is endothermic for both the heptylidene (15 kcal/ mol) and methylidene (ca. 23 kcal/mol) formation steps with activation energies of about 45 kcal/mol and 70 kcal/mol, respectively. The coordination of the 1-octene in the Cji mode has an about 2 kcal/mol-5 kcal/mol decrease in El for Dj, to Ej, ... 

Comparison of the activation steps of III and IV for the formation of the heptylidene species in the Cn mode (which is more favorable than the Cp mode) (see Figure... 

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