Computational Aspects of Single-Molecule Kinetics for Coupled Catalytic Cycles: A Spectral Analysis

Area of Science:

• Chemical kinetics
• Surface science
• Computational chemistry

Background:

• Catalysis at single active sites is crucial for chemical reactions.
• Understanding reaction dynamics at the molecular level is challenging.
• Existing methods often lack the precision to analyze complex catalytic networks.

Purpose of the Study:

• To develop a theoretical framework for analyzing catalysis at single active sites.
• To connect observable properties of catalytic networks to fundamental reaction parameters.
• To provide a method for identifying key reaction pathways and timescales.

Main Methods:

• Utilizing methods from single-molecule kinetics.
• Employing a stochastic Markov-state description of reaction networks.
• Applying eigenvalue decomposition of the transition matrix.
• Performing sensitivity analysis to link eigenvalues to reaction barriers and wells.
• Generalizing the energetic span theory for eigenvalue computation.

Main Results:

• Observable properties of catalytic networks are expressed via eigenvalue decomposition.
• Eigenvalues and eigenvectors are directly related to controlling energy barriers and wells.
• A generalized energetic span theory allows eigenvalue computation from activation energies.
• The formalism is validated on model systems and alkene hydrogenation on single-atom catalysts.
• Spectral analysis successfully identifies a hierarchy of timescales and relaxation modes.

Conclusions:

• The developed spectral analysis provides a powerful tool for understanding single-site catalysis.
• This approach connects macroscopic observables to microscopic reaction energetics.
• The method offers insights into the dynamics and efficiency of catalytic processes.