An improved algorithm to locate critical points in a 3D scalar field as implemented in the program MORPHY

Area of Science:

• Computational chemistry
• Theoretical chemistry
• Data analysis

Background:

• Topological analysis of scalar fields is crucial in computational chemistry.
• Existing methods for locating critical points often rely on specific functions like electron density.
• There is a need for more general algorithms adaptable to various scalar field functions.

Purpose of the Study:

• To develop a novel algorithm for identifying critical points in general 3D scalar fields.
• To create a versatile method that can incorporate diverse scalar field functions.
• To enhance the analysis of complex molecular systems through improved critical point detection.

Main Methods:

• A new algorithm utilizing topological information to seed critical point searches.
• Implementation of a flexible framework allowing the integration of various scalar field functions (e.g., Laplacian of electron density, Electron Localization Function).
• Retention of intermediate data, including critical point connectivity paths, and the ability to restart searches.

Main Results:

• Successful development of a new algorithm for critical point location in general 3D scalar fields.
• Demonstrated ability to integrate and analyze diverse functions beyond electron density.
• The algorithm retains connectivity information and supports search restarts, crucial for large systems.
• Identification of nine universal types of gradient paths.

Conclusions:

• The new algorithm provides a more general and flexible approach to critical point analysis in 3D scalar fields.
• Its adaptability to various functions and data retention capabilities make it suitable for analyzing complex systems.
• This method forms a core component of the new local version of the MORPHY code, advancing topological analysis.