Reaction coordinate, potential energy

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

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. 

MEP (IRC, intrinsic reaction coordinate, minimum-energy path) the lowest-energy route from reactants to products in a chemical process MIM (molecules-in-molecules) a semiempirical method used for representing potential energy surfaces... 

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). 

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... 

The Sn2 reaction in solution. We saw above the application of microsolvation to Sn2 reactions ([14, 15]). Let us now look at the chloride ion-chloromethane Sn2 reaction in water, as studied by a continuum method. Figure 8.2 shows a calculated reaction profile (potential energy surface) from a continuum solvent study of the Sn2 attack of chloride ion on chloromethane (methyl chloride) in water. Calculations were by the author using B3LYP/6-31+G (plus or diffuse functions in the basis set are considered to be very important where anions are involved Section 5.3.3) with the continuum solvent method SM8 [22] as implemented in Spartan [31] some of the data for Fig. 8.2 are given in Table 8.1. Using as the reaction coordinate r the deviation from the transition state C-Cl... 

Figure 2. (a) Schematic illustration of the adiabatic (solid) and diabatic (dashed) vibrational free energy curves as functions of the solvent coordinate Zp for a symmetric single proton transfer reaction, (b) Potential energy curves as functions of the proton coordinate r, for three specific values of the solvent coordinate Zp indicated in (a). 

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 the molecule, each normal mode, including the one for the reaction coordinate, contains ZPE. However, the Eckart potential is unbound on the reactant and product side so that there is no ZPE energy in the reaction coordinate. In reconciling these two energy references, we need consider only the energy in the one-dimensional reaction coordinate. The energy in the other modes, which are perpendicular to the reaction coordinate, can continue to be referenced to the ZPE level. 

Fig. 5.8 (A) Classical parabolic free energy functions for diabatic reactant and product states of an electron-transfer reaction (DA D A ) as functions of a dimensionless reaction coordinate. The standard free energy change (AG ), reorganization energy (A), and activation free energy (AG ) are indicated vertical arrows). The two functions are assumed to have the same curvature, which will be the case if there is no change in entropy in the reaction. (B) Potential energies (solid curves) and the first few vibrational wavefunctions (dashed and dot-dashed curves) and eigenvalues (horizontal dotted lines) for two electronic states (DA and D A ), as functions of the dimensionless vibrational coordinate (u in Eq. 2.3.2) for a harmonic vibrational mode with the same frequency (v) in the two states. The quantum number (n) of each wavefunction is indicated.

Fig. 6 Diabatic solid black line) and adiabatic dashed red line) potential energy surfaces of two electronic dimer states 4>Ab) and ob) participating in the charge transfer reaction along the reaction coordinate Reorganization energies...

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