Apparent Kinetic Isotope Effects for Multi-Step Steady-State Reactions

Area of Science:

• Chemical kinetics
• Reaction mechanisms
• Computational chemistry

Background:

• Kinetic isotope effects (KIEs) are crucial for elucidating reaction mechanisms.
• Analyzing KIEs in multistep reactions, especially enzyme-catalyzed ones, can be complex.
• Conventional methods often rely on intrinsic KIEs, which may be difficult to determine accurately.

Purpose of the Study:

• To develop a simplified method for expressing and analyzing apparent KIEs in multistep steady-state reactions.
• To provide a more direct comparison between computed and experimental KIEs.
• To illustrate the application of the method using computational chemistry.

Main Methods:

• Formulating the apparent KIE as a sum of terms, each representing a transition state (TS).
• Each term is a product of the individual TS's KIE and its kinetic significance (weighting factor).
• Utilizing density functional theory (DFT) calculations for an S_N1 nucleophilic displacement reaction.

Main Results:

• The apparent KIE can be expressed using relative Gibbs energies of sequential TSs, avoiding intermediate information.
• A single apparent KIE value can arise from various combinations of individual KIEs and weighting factors.
• DFT calculations show the apparent KIE varies with nucleophilic species concentration, reflecting rate-limiting steps.

Conclusions:

• The proposed method offers a simpler and potentially more reliable approach to KIE analysis compared to conventional methods.
• Direct comparison of computed apparent KIEs with experimental data is recommended over using derived intrinsic KIEs.
• The study demonstrates the utility of the method for understanding rate-limiting steps in complex reactions.