Potential energy, profiles

Figure A2.4.8. Potential energy profile at the metal-vacuum interface. Bulk and surface contributions to Vare shown separately. From [16].

Figure A3.4.8. Potential energy profiles for reactions without barrier. Complex fomiing bimolecular reaction (left) and direct barrierless bimolecular reaction (right).

Figure A3.12.1. Schematic potential energy profiles for tluee types of iinimolecular reactions, (a) Isomerization, (b) Dissociation where there is an energy barrier for reaction in both the forward and reverse directions, (c) Dissociation where the potential energy rises monotonically as for rotational gronnd-state species, so that there is no barrier to the reverse association reaction. (Adapted from [5].)...

Example Solvation can have a profound effect on the potential energy profile for a reaction. Jorgensen s research group provided important insights into the role of solvation. Consider the nucleophilic addition of the hydroxide anion to formaldehyde ... 

A potential energy diagram for nng inversion m cyclohexane is shown m Figure 3 18 In the first step the chair conformation is converted to a skew boat which then proceeds to the inverted chair m the second step The skew boat conformation is an inter mediate in the process of ring inversion Unlike a transition state an intermediate is not a potential energy maximum but is a local minimum on the potential energy profile... 

Fig. 10.6. Various potential energy profiles for eleetrophilie aromatie substitution.

According to this very simple derivation and result, the position of the transition state along the reaction coordinate is determined solely by AG° (a thermodynamic quantity) and AG (a kinetic quantity). Of course, the potential energy profile of Fig. 5-15, upon which Eq. (5-60) is based, is very unrealistic, but, quite remarkably, it is found that the precise nature of the profile is not important to the result provided certain criteria are met, and Miller " obtained Eq. (5-60) using an arc length minimization criterion. Murdoch has analyzed Eq. (5-60) in detail. Equation (5-60) can be considered a quantitative formulation of the Hammond postulate. The transition state in Fig. 5-9 was located with the aid of Eq. (5-60). 

Fig. 2. Potential energy profile of 1,2-insertion and ring opening processes of Cp2LnH-MCP systems obtained at RPBE level...

Figure 57. Schematic potential energy profiles and the pump-dump scheme. Taken from Ref. [49].

Figure 3 UMP2/6-311G potential energy profile (a) and hyperfine coupling constants (b) of CH3 versus s. Vibrational wave functions are normalized to 5.

Scheme 7-22 Schematic proposed route obtained from the potential-energy profile of Pd(PH3)2-catalyzed addition of 99 to C2H4...

Figure 9.12. Potential energy profile along (adapted from reference 10) near the fulvene conical intersection. The branching space consists of stretching and skeletal deformation of the five-membered ring.

F ure 9.13. Potential energy profile (adapted from reference 10) for fulvene in the space spanned by Xj and the coordinate (torsion). 

Figure 2.22. Schematic potential energy profile for two types of the N—N bond formation mechanisms calculated for the 12 hosting site (BP/DNP) (after [75]).

This method was used to obtain potential energy profiles for the reaction in vacuum, in aqueous solution and in the enzyme environment [23], For the enzymatic reaction, two different choices of the quantum system were considered one where... 

Figure 2-11. ONIOM protein model (left) with QM atoms shown as spheres and MM atoms as sticks (substrate MCA atoms are shown as tubes). The graph to the right shows potential energy profiles obtained by relaxed scans along the Co—C5 bond in MCM for different computational models (see text for details) (Adapted from Kwiecien et al. [29]. Reprinted with permission. Copyright 2006 American Chemical Society.)...

Figure 11-9. CASSCF potential-energy profiles of the ground-state So (circles), the lnjr state (triangles), the Lb state (squares), and the La state (filled squares) of the 9H-adenine along the linear interpolation reaction path from the equilibrium geometry of the nit state to the CI32 (a) and CI16 (b) conical intersections. The diabatic correlation of the states is shown in (a). (From Ref. [138])...

Fig. 3 Potential energy profiles for the concerted and the stepwise mechanism in the case of a thermal reductive process. E is the electrode potential for an electrochemical reaction and the standard potential of the electron donor for a homogeneous reaction. For an oxidative process, change - into + and donor into acceptor.

Fig. 6 Passage from the stepwise to the concerted mechanism upon decreasing the driving force. Left potential energy profiles. Right reaction of 4-nitrocumyl chloride with homogeneous donors diamonds 2-nitropropanate ion, squares duroquinone anion radical, circles RNu -. E electrode potential or standard potential of a homogeneous donor.

Fig. 14 Potential energy profile for stepwise and concerted mechanisms with (solid lines) and without (dotted lines) an attractive interaction between the caged fragments in the product cluster. The case of the reduction of a neutral substrate is represented. It can be transposed for reductions of a positively charged substrate or for oxidations of neutral or negatively charged substrates.

Figure 3.86 Potential-energy profiles for XMH3 X dissociation along an adiabatic SN2-like reaction coordinate for Sift + H (M = Si, X = H circles, solid line), FSiH3 + F (M = Si, X = F squares, solid line), and FCH3 + F (M = C, X = F triangles, dashed line), showing cu-bonded equilibrium behavior in the first two cases and transition-state behavior in the last case.

Figure 4.67 The potential-energy profile for the transition-state region of the model c-metathesis reaction (4.102).

Fig. 16 (a) Comparison of potential energy profile for the formal Cope rearrangement of 3,4-difluorohexa-l,5-diyne-3-ene with that of (Z)-hexa-l,5-diyne-3-ene, (b) Rehybridization in the C(F) bond along the reaction path. EDI = 3,4-difluoro-hex- 3-ene-l,5-diyne ED2 = 1,6-di-fluoro-hex-3-ene-l,5-diyne BZY = difluoro-l,4-didehydrobenzezne TSBC = the transition state for the Bergman cyclization TSRBC = the transition state for the retro Bergman cyclization. 

Fig. 2. Potential energy profile and structure of final alkoxide for the adsorption of isobutylene on a high-silica zeolite according to Ref. (29).

Fig. 4. Potential energy profiles for the isobutane/t-butyl cation hydride transfer reaction in various media (25,64).

---