Potential energy plots

Figure 1. Potential energy plot of the reactants (precursor complex) and products (successor complex) as a function of nuclear configuration Eth is the barrier for the thermal electron transfer, Eop is the energy for the light-induced electron transfer, and 2HAB is equal to the splitting at the intersection of the surfaces, where HAB is the electronic coupling matrix element. Note that HAB << Eth in the classical model. The circles indicate the relative nuclear configurations of the two reactants of charges +2 and +5 in the precursor complex, optically excited precursor complex, activated complex, and successor complex.

Figure 1. Potential energy plots along the reaction coordinate for two dissociation reactions, one with a barrier (Eq > 8DE), and the other barrierless (Eq s BDE).

Problem 4.9 Draw a graph of potential energy plotted against angle of rotation for conformations of (a) 2.. l-dimethylbutane. (h) 2-methylbutane. Point out the factors responsible for energy differences. -4... 

For simple systems two such coordinates (characterizing two variables that change during the reaction progress from reactants to products) can be selected, and the potential energy plotted as a contour map. 

Fig. 4.40. Potential energy plots for dissociative adsorption of a molecule XX. Dxx is the dissociation energy of the free molecule, Ed is the activation energy for dissociative adsorption.

Figure 2.62. Potential energy plot of Mg-2H system as a function of displacement of the H atoms in two directions relative to the equilibrium position within the hydride. See text for further explanation (Sorensen, 2004f).

A potential energy plot for rotation about the C2-C3 bond in butane shows unique maxima and minima. There are two kinds of staggered conformations, gauche (steric strain) and anti, and two distinct eclipsed conformations (torsional and steric strain). 

Theoretical studies on the insertion of ethylene into d [MMeL2] (M = Ni, Pd, Pt) catalysts provide the relative potential energy plot in Fig. 6.5. The process consists of a coordination of the alkene perpendicular to the coordination square plane, followed by an easy alkene rotation to an in-plane coordination and a more difficult insertion. The rate-determining step of these reactions is the migratory insertion of the alkene and these calculations show that the stabilization of the system upon coordination of the alkene increases in the order Ni < Pd < Pt, whereas the insertion transition state changes very little. This explains the catalytic activity Ni > Pd > Pt generally observed, which is associated to insertion barriers in the range of 10 kcal/mol for Ni, 16 kcal/mol for Pd, and 25 kcal/mol forPt[l],... 

We now consider point A on Fig. 1. The integral o> has a positive value since the reaction has a positive activation energy. Instead of tr dng to evaluate the integral we accept that its value is the slope of Fig. 1 at the point A. The terms in 2 in gq. (3) now become important. Their sum determines the curvature of the potential energy plot. For a reaction with a small activation energy, the curvature should be as small as possible (or negative). 

The term linear in Q in Eq. (2) now vanishes, since we are at an extremum in the potential energy plot. As before, the first quadratic term is positive, and the second one is negative. Clearly at a maximum, point B, the second term is larger than the first. At a minimum, point C, the first term dominates, but the magnitude of the second term determines whether we lie in a deep potential well or a shallow one. 

Fig. 13.3 Potential energy plots for a 25° dihedral angle for ethylene + ethylene as calculated by CASSCF(4,12)/aug-cc-pVDZ in Z>2 symmetry. Surfaces 2A and 3A are aU singly excited states. Surface depicts where the Cl vectors indicate significant population of the n orbital...

Figure 11.11 I Potential energy plot for an exothermic chemical reaction. To progress from reactants to products, the molecules must collide with enough energy to pass over the activation barrier.

There is one path between reactants and products that has a lower energy maximum than any other this is the pathway that the reaction will follow. The line in a two-dimensional potential energy plot represents this lowest-energy pathway. It represents a path across an energy surface describing energy as a function of the spatial arrangement of the atoms involved in the reaction. The principle of microscopic reversibility arises directly from transition. state theory. The same pathway that is traveled in the forward direction of a reaction will be traveled in the reverse direction ... 

Figure 4.11 Molecular dynamics results for potential energy plotted against distance (in atomic units) between the centers of mass for the fragmentation of Naio into Na7 and Na.i (solid) and Na9" and Na (dashed), obtained via constrained minimization of the LSD ground-state energy of the system [10]...

Potential energy plots for the vibrational states of various hydrogen bonds. 

This is illustrated in Figs. 1 and 2. Figure 1 shows bond-length/potential energy plots for two typical trajectories. The trajectory in Fig. 1(a) went below -8.0... 

Figure A10.9 The various terms in the electron-nuclear potential energy plotted as a function of Internuclear separation for (a) H2 in the ground state, with theelectron in 1

Figures 18-20 summarize the results from both simulations. In Figure 18 we have plots of the potential energy as a function of simulation time, root mean square (RMS) deviation as a function of simulation time and the radius of gyration as a function of simulation time. The potential energy plot shows that the structures are well equilibrated and stable over the 100 ps. The root mean square deviation plot indicates that the final structures from both simulations are very similar. From the radius of gyration plot one can see that during the implicit solvent simulation the structure is similar to the explicit solvent simulation radius of gyration, then around 50 ps the structure contracts for about 40 ps before expanding back to the explicit solvent simulation structure.

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