Reaction path zero-point energy

Transition state theory can generally be made more accurate by replacing the usual potential by an effective potential energy V(s) defined by 

---

Determine the reaction path connecting trans hydroxycarbene and H2 + CO. Predict the activation energy, referring to the values for the SCF and zero-point energies for the products and reactants summarized at the conclusion of this problem. This reaction occurs via a two step process ... 

Figure 5. Potential-energy diagram including zero-point energy for the HCC0 + 02 reaction. Energies of reactants and products ignore differences between and Intermediates species are denoted by Roman numerals, saddle points by Arabic numerals, and reactions paths are labeled A-F. Reproduced from [47] by permission of the PCCP Owner Societies.

Figure 11. The minimum energy path of the OH + CH3F reaction, not including zero-point energy. The four labeled structures are (A), the central barrier TS (B), the nearly collinear backside well complex [HOCH3 F] (C) the transition of the F atom toward the OH moiety (D) the hydrogen-bonded [CH3OH F ] structure. Reprinted from [63] with permission from the American Association for the Advancement of Science.

Figure 12 Calculated potential energy diagram for N2 dissociation on Fe(l 1 1) corrected for zero point energy [18]. (a) Shows die proposed reaction path for gas phase N2 (E = 0) adsorption and dissociation to form N (p). (b) Shows the a state and die transition state for dissociation, see text for details. Adapted from Mortensen et al. [18].

This estimate of the barrier effectively includes zero-point energy and tunneling effects since it is obtained from experimental data. In typical EVB studies of enzymatic reactions it is usually assumed that these quantum-mechanical effects do not differ significantly between the water and enzyme environments. This assumption has been verified by implementation of the path integral method [51] within the EVB framework [52,53]. 

The normal deuterium isotope effect observed in equations 110 and 111 might be caused by large zero-point energy contributions of the C—H/C—D bonds weakened substantially or broken in the transition state (with retention of configuration) of reaction paths shown in equations 116 and 117, and by some contribution to the total yield of H2 or D2... 

Thus the secondary and primary deuterium isotope effects determined in this study also indicate that entropy and zero-point energy factors associated with breaking of the C—D bond and migration in the activated complexes are important for the structural isomerization to yield butene-1 and butene-2, and reaction path B (equation 197) must be included in the mechanistic considerations concerning the cyclopropane isomerization. But the higher activation energy for isobutane formation (g = 64.3 kcal mol" ) than that for butene-2 or butene-1 (Q = 62.0 0.6 kcal mol" ) indicates also that the rupture of... 

---