PageRank as a collective variable to study complex chemical transformations and their energy landscapes

Area of Science:

• Computational Chemistry
• Chemical Physics
• Theoretical Chemistry

Background:

• Reduced reaction coordinates are crucial for rare event theories and energy landscape exploration in chemistry.
• Selecting appropriate collective variables becomes challenging for complex molecular systems.
• Graph-theoretical metrics like PageRank (PR) coordinates offer novel descriptions of molecular interactions.

Purpose of the Study:

• To advance the development of PageRank (PR) coordinates for describing chemical reaction paths.
• To introduce a continuous formulation of PR coordinates and their analytical derivatives.
• To demonstrate the utility of PR coordinates in analyzing molecular transformations and solvent effects.

Main Methods:

• Developed a new, continuous formulation of PageRank (PR) coordinates.
• Derived analytical derivatives of PR coordinates with respect to atomic positions.
• Combined PR coordinates with harmonic bias to compute the potential of mean force (PMF).

Main Results:

• The continuous PR formulation provides a robust reaction coordinate for complex systems.
• PR coordinate fluctuations correlate with fundamental atomic/molecular motions.
• Calculated PR-based PMFs for [Al(OH)4]-(aq) transformation and Na+⋯OH- ion pair exchange.

Conclusions:

• The enhanced PR coordinate offers a powerful tool for analyzing chemical reaction mechanisms.
• PR-based PMF calculations reveal insights into solvent rearrangement's impact on reaction pathways.
• This approach facilitates a deeper understanding of molecular dynamics in complex chemical systems.