Potential energy contour map

Murrell and co-workers290 have reported MBS and DZ calculations on the nitro-methyl anion CH2N02 in its planar and pyramidal forms. The most stable form is planar, and is expected to protonate on the oxygen, whereas the pyramidal form would protonate on C. This conclusion was not obvious from charges alone, but was evident on examination of potential energy contour maps. 

Fig. 60 Potential energy contour map of torsion angles 0i, 02 for DPP. Some pathways observed in simulations are drawn (from [51])...

Fig. 63 Potential energy contour map of torsion angles 04,05 for PDC. The intramolecular energy minima are represented by the symbol x. Some pathways observed in simulations are drawn. The end of the path indicated by the empty symbol is the starting position, and the position marked with a. filled symbol is the last simulated point (from [51])...

The energetically easiest route from reactants to products on the potential-energy contour map defines the potential-energy profile. 

Figure 3.2 Depiction of a potential energy contour map for ABC (Steinfeld et al., 1989).

Figure 3.3 Potential energy contour map for C2H5 — H + C2H4 dissociation r, H—C distance H—C—C angle w, potential energy minimum x, saddle point for H-atom migration y, barrier for H-atom addition in 2 symmetry and z, saddle point for H-atom dissociation (Hase et al., 1978).

Insight about the dynamics of a unimolecular reaction can be obtained by examining the reaction s potential energy contour map. Usually this is at best only a qualitative analysis. However, it can be made quantitative for a linear triatomic ABC molecule by using skewed and scaled coordinates (Glasstone et al., 1941 Levine and Bernstein, 1987). The significance of these coordinates becomes readily apparent by considering the internal coordinate classical Hamiltonian for the linear ABC molecule that is. 

In these equations rj and 2 are the AB and BC intemuclear separations, respectively, and M is the total mass. Because of the r,r2 coupling term in Eq. (3.5) and different values for the masses, the intramolecular motion of the linear ABC molecule cannot be studied by simply inspecting the molecule s ( 5, 2) potential energy contour map. However, if the coordinates r, and rj are transformed, so that the kinetic energy is written as... 

By using the gj and Q2 coordinate system instead of the r, and rj internal coordinates, the kinetic energy (Eq. (3.6)) can be interpreted as that of a point particle (or system point) of mass M. The motion of this particle on the potential surface Vfgi.gz) can be simulated by letting a ball of mass M roll along the surface. Thus, quantitative aspects of the reaction dynamics can be understood by simply studying the V Qi,Q2) potential energy contour map. 

Figure 20.9 Ab initio LSTH potential energy contour map for H3 in its collinear configuration. The minimum-energy...

Table 1 Partition Functions, Average Energies and Averaged Rotation Angles for the PM Chain Deduced from the Potential Energy Contour Map (Figure 1) for a Temperature of 25 °C...

Potential energy contours of the eleven surfaces are shown in Figs. 2-5. If the angle 0i (or 82) is minimized, the A, B, C, and D surface types can be characterized by their potential energy contour maps in the r], R plane. Such plots are shown in Fig. 2. In the terminology used for A 4 BC -> AB 4- C reactions, all of the surfaces have late barriers for H-C-C -> H + C=C dissociation. Potential energy contour maps of r vs, 0i for optimized R are shown in Figs. 3-5 for all eleven surfaces. These maps illustrate the... 

Fig. 2. Potential-energy contour maps of r versus R with angle minimized. Zero of energy is for the HCC equilibrium geometry (r = 1.08 A and R = 1.51 A). Solid lines represent potential-energy contours at 10 kcal/mol intervals. The dashed lines are potential-energy contours at 2 kcal/mol intervals between 40 and 50 kcal/mol. x indicates either the HCC equilibrium geometry or the geometry at the H atom dissociation barrier. (From Wolf and Hase, reference 23. Reprinted with permission of American Institute of Physics.)...

At the present time, we only have a qualitative understanding of the features that lead to intrinsic non-RRKM behavior for the A and B surfaces. In studying the potential energy contour maps in the r,R plane (Fig. 2), one sees that the C and D surfaces become strongly enharmonic with negative curvature as the HC bond is extended. This anharmonicity is expected to make trajectories which sample this part of the surface separate exponentially in time instead of linearly.Exponential separation of trajectories results in stochastic behavior which should give rise to RRKM dissociation probabilities. The absence of this anharmonicity on the A and B surfaces is an explanation for their intrinsic non-RRKM lifetime distributions. 

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