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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

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Seeking a Direct Optimization Method Using Distance Geometry Space for Molecular Orientation.

Kanami Sugiyama¹, Masatoshi Okada¹, Hirofumi Sato^1,2

¹Department of Molecular Engineering, Kyoto University, Kyoto, Japan.

Journal of Computational Chemistry

|June 3, 2026

Summary

This summary is machine-generated.

This study introduces a direct distance geometry method to determine molecular configuration. The approach uses constraints and slack variables to map molecular structures in 3D space.

Keywords:

CM determinant bordered Hessian distance geometry molecular orientation

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Area of Science:

Computational Chemistry
Molecular Modeling
Quantum Chemistry

Background:

Determining the relative configuration of molecules is crucial for understanding chemical reactions and properties.
Existing methods may be complex or computationally intensive.

Purpose of the Study:

To develop a direct and efficient method for determining the relative configuration of molecules.
To apply this method to various small molecular systems.

Main Methods:

Utilizing distance geometry to represent molecular structure as interatomic distances.
Employing gradient and bordered Hessian calculations with inequality and equality constraints.
Introducing slack variables for embedding structures in three-dimensional space using the Cayley-Menger determinant.

Main Results:

Successfully applied the method to water-lithium ion, hydrogen fluoride dimer, and ammonia-sodium ion systems.
Demonstrated the feasibility of determining relative molecular configurations through interatomic distances.

Conclusions:

The developed distance geometry method offers a direct route for determining molecular configuration.
This approach facilitates the exploration of potential-energy landscapes for small molecular systems.