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Generalized Internal Coordinates for Creative Exploration of Interatomic Geometries.

Aleksandr V Marenich1, Edward N Brothers1, Hrant P Hratchian2

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|October 27, 2025
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Summary

Generalized internal coordinates (GICs) offer a flexible way to define molecular geometries. This new method simplifies complex molecular system analysis and enables novel computational chemistry approaches.

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Area of Science:

  • Computational Chemistry
  • Molecular Modeling
  • Quantum Chemistry

Background:

  • Traditional internal coordinates (bonds, angles) limit molecular system analysis.
  • Nontraditional geometric parameters are crucial for diverse molecular systems.
  • Seamless integration of custom coordinates into computational workflows is needed.

Purpose of the Study:

  • To implement generalized internal coordinates (GICs) for diverse molecular systems.
  • To enable the inclusion of nontraditional geometric parameters without additional coding.
  • To provide a flexible framework for computational chemistry analyses.

Main Methods:

  • Automatic generation of GICs from connectivity or user input.
  • Customization of GICs using symbolic algebra and mathematical operations.
  • Automatic derivation of analytical first- and second-order derivatives with respect to Cartesian coordinates.

Main Results:

  • GICs seamlessly integrate into geometry optimization, PES searching, and normal-mode analysis.
  • Users can create compound and special-purpose internal coordinates.
  • GICs support constraints to specific values, intervals, or conditional dependencies.

Conclusions:

  • The GIC implementation enhances flexibility and applicability in computational chemistry.
  • This approach opens new possibilities for analyzing complex molecular systems.
  • The method streamlines computational workflows by automating derivative calculations.