A theory of diffusion controlled reactions in polyatomic molecule system.

Area of Science:

• Chemical Physics
• Theoretical Chemistry
• Molecular Dynamics

Background:

• The Smoluchowski equation is crucial for studying diffusion-controlled reactions.
• Its application is currently limited to spherical particle systems.
• A need exists for a more versatile Smoluchowski equation applicable to complex molecular systems.

Purpose of the Study:

• To derive a novel Smoluchowski equation applicable to polyatomic molecular systems.
• To extend the applicability of Smoluchowski-type equations beyond simple spherical geometries.
• To validate the new equation against established methods and simulations.

Main Methods:

• Utilized the Zwanzig-Mori projection operator method.
• Employed Reference Interaction Site Model (RISM) theory.
• Applied the derived equation to monoatomic and diatomic molecular liquids.

Main Results:

• The new equation yields time-dependent rate constants nearly identical to the conventional Smoluchowski equation for monoatomic liquids.
• For diatomic liquids, the derived time-dependent distribution function and rate constant show good agreement with molecular dynamics simulations.
• Successfully extended Smoluchowski equation framework to polyatomic systems.

Conclusions:

• The developed Smoluchowski equation provides a robust framework for analyzing diffusion-controlled reactions in polyatomic molecular systems.
• This new theoretical approach offers a valuable tool for understanding reaction dynamics in complex liquids.
• The findings suggest broader applicability of the Zwanzig-Mori and RISM theories in chemical physics.