Valleys in the Potential

FIGURE 8.3 The collective potential energy surface of 108 and calculated within the two-center shell model by J. Maruhn et ai, shows clearly the cold valleys which reach up to the barrier and beyond. Here R is the distance between the fragments and t] = denotes the 

FIGURE 8.4 Typical structure of the fullerene The double bindings are illustrated by double lines. In the nuclear case the Carbon atoms are replaced by a particles and the double bindings by the additional neutrons. Such a structure would immediately explain the semi-hollowness of that superheavy nucleus, which is revealed in the mean-field calculations within meson-field theories. For a colour reproduction of this figure see the colour plate section, near the end of this book. 

FIGURE 8.5 The fusion of element 112 with °Zn as projectile and ° Pb as target nucleus has been accomplished for the first time in 1995/96 by S. Hofmann, G. Munzenberg and their collaborators. 

FIGURE 8.7 Potential energy surface as a function of reduced elongation (R — R/)/(Rt — R ) and mass asymmetry jj for the double magic nucleus ° l20i84. 

FIGURE 8.8 The collective potential as a function of the mass asymmetry jj =.  

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Reaction rates are macroscopic averages of the number of microscopical molecules that pass from the reactant to the product valley in the potential hypersurface. An estimation of this rate can be obtained from the energy of the highest point in the reaction path, the transition state. This approach will however fail when the reaction proceeds without an enthalpic barrier or when there are many low frequency modes. The study of these cases will require the analysis of the trajectory of the molecule on the potential hypersurface. This idea constitutes the basis of molecular dynamics (MD) [96]. Molecular dynamics were traditionally too computationally demanding for transition metal complexes, but things seem now to be changing with the use of the Car-Parrinello (CP) method [97]. This approach has in fact been already succesfully applied to the study of the catalyzed polymerization of olefins [98]. 

Table 6.14 contains a current summary of the nature of the complexes of the various amines, coupled with each of the HX acids, as determined by ab initio calculations. HF does not form ion pairs at all, whereas HI forms ion pairs with all (with the exception of the shallow valley in the potential with NHj). In the case of HBr and HCl, one can see the transition from neutral to ion pair as the amine becomes more basic. 

Energies corresponding to two valleys in the potential energy hyperspace are plotted as a function of R in Fig. 2. One of these pathways represents the energy minimization view of the rectangle-square-rectangle route, which we include for reference purposes. 

Another potentially large user of I DE is the Tennessee Valley Authority. TVA is in the final year of a three-year test of I DE at its AHen station (Memphis, Tennessee). If this faciUty begins using I DE on a production basis, and if one or two other TVA faciUties join in, the potential market for scrap tires would be enormous, consuming some or all of the tires generated in several states. 

There are three minima on this potential surface. A minimum is the bottom of a valley on the potential surface. From such a point, motion in any direction—a... 

Since these two cross sections have similar magnitudes, this would correspond to a rebound mechanism where the two molecules have to come very close together before reaction will occur. The activated complex thus lies in the exit valley and the potential energy profile has a late barrier. 

Two valleys were found in the potential surface for the reaction of triplet carbene to methane. They correspond to the modes of approach indicated in Fig. 24. The mode leading to 2 CH3 (b in the figure) is preferred with a barrier height of 3.8 kcal/mole. 

The study of alkali atom reactions with halogen-containing molecules comprises much of the history of reactive scattering in molecular beams. The broad features of the reaction dynamics and their relation to the electronic structure of the potential energy surface are well understood.2 The reaction is initiated by an electron jump transition in which the valence electron of the alkali atom M is transferred to the halogen-containing molecule RX. Subsequent interaction of the alkali ion and the molecule anion, in the exit valley of the potential surface, leads to an alkali halide product molecule MX. 

For collisions at large impact parameters, these observations have been interpreted44,45 in terms of reaction dynamics which are initiated by an electron jump in the entrance valley of the potential surface. A mutual ion dissociation reaction follows, in which the halogen molecule anion dissociates... 

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