Enumerating and indexing many-body intramolecular interactions: a graph theoretic approach

Area of Science:

• Computational chemistry
• Theoretical chemistry
• Molecular modeling

Background:

• Accurately describing intramolecular interactions is crucial for molecular simulations.
• Current methods for handling many-body interactions can be computationally intensive.
• Understanding molecular topology is key to developing efficient computational models.

Purpose of the Study:

• To develop a recursive method for mapping many-body intramolecular interactions.
• To generalize this method for arbitrary many-body potentials.
• To provide a complete characterization of many-body interactions.

Main Methods:

• Utilizing iterative line graph transformations for recursive mapping.
• Representing hierarchical interaction structures using directed acyclic graphs.
• Implementing algorithms for automatic enumeration and indexing of interactions.

Main Results:

• A consistent mapping of N-body intramolecular interactions to N-body terms based on molecular topology.
• Generalization of the method to arbitrary N-body potentials.
• Complete characterization of N-body interactions with efficient indexing for large systems.

Conclusions:

• The line graph transformation provides an elegant and efficient approach for handling many-body interactions.
• The developed method facilitates the study of large bio-molecular systems.
• The approach is applicable to chemically relevant models, such as bile salt potentials.