Energy coordinate, potential

Figure A3.12.5. A model reaction coordinate potential energy curve for a fluxional molecule. (Adapted from [30].)...

We have it on good authority (Ege, 1998) that the gauche minimum on the potential energy coordinate is about 0.9 kcal moI higher in energy than the anti conformation. This establishes a two-state energy system for the stable conformers, gauche and anti (Fig. 4-19). 

FIGURE 6.1 Parabolic model of the reaction R02 + RH in coordinates potential energy versus amplitude of vibration of the reacting bonds (for symbols, see text). 

Having successfully matched the several experimental observables available for the enolase system, Alhambra and co-workers then examine the reaction coordinate to better understand the factors discriminating H from D reactivity. They discover that the TS for the reaction of H is much later than that for reaction of D, because the rapidly increasing zero-point energy of the N-H bond compared to the N-D bond offsets the drop in reaction coordinate potential energy and moves the free-energy bottleneck for H further towards products. 

Of the three eigenvalue equations, the one of interest to us is the vibrational equation. It has a particularly simple form when normal coordinates are employed because the classical kinetic and potential energies then have no cross terms (see eqns (9-2.17) and (9-2.18)) and this fact leads to a simple form for their quantum mechanical analogues (the kinetic energy and potential energy operators). The vibrational equation is thus... 

Figure 3. Potential energy-coordinate curve as in Figure 1 but illustrating vibrational energy levels and wavefunctions, xv...

Figure S Potential energy-coordinate diagram as in Figure 1 but with E = 0...

Figure 6. Potential energy-coordinate diagrams showing the effect of increasingly favorable AG or A E. Case (a), -AG = A case (b), -AG> A case (c), excited state decay in the limit A = Stm A showing the vibrational levels in the excited and ground states...

The theory stems from the writer s work on simple electron transfer reactions of conventional reactants (5). A simple electron transfer reaction is defined as one in which no bonds are broken or formed during the redox step such a reaction might be preceded or followed by bondbreaking or bond-forming steps in a several-step reaction mechanism. Other chemical reactions involve rupture or formation of one or several chemical bonds, and only a few coordinates suffice to establish their essential features. In simple electron transfers in solution, on the other hand, numerous coordinates play a role. One cannot then use the usual two-coordinate potential energy contour diagram (4) to visualize the... 

Recent ab initio calculations of a wide series of Si-substituted 2,8,9-tricarbasilatranes (X = H, Me, H2N, HO, F, 113 S i, H2P, HS and Cl) found a single minimum corresponding to the endo form on the potential energy coordinate of the Si<—N bond deformation194. The transannular bond was shown to be very soft and sensitive to the medium. The substituent effect on this bond length and mutual weakness of the axial bonds of the TBP silicon are well described by the 3c4e bonding model. 

According to Eq. (17-69), the pure solvent refers in the computation of 8p, to the pairwise additive potential system with the solute-solvent interaction Eqm/mm (h, X). On the other hand, the solution system involves the solute-solvent interaction EqM/mm( , X) with the QM energy term of Edist(n) - E. From Eq. (17-69), the energy coordinate to formulate 8 fx, in the energy representation is associated with the instantaneous distribution p (f) through... 

It may be asked wliether the symmetry factor in Eq. 171 is identical to the symmetry factor in Eq. 7D, as we have implied in our derivation. It is not unreasonable to make this assumption, since both depend on the position of the same activated complex along the reaction coordinate, although it may be argued that the variation of the standard free energy with potential and with coverage along this coordinate is not the same, and that this leads to two different symmetry factors. Fortunately, it turns out that this does not affect the rate equations, as we shall show. 

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