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Exhaustive Spatial Sampling for Complete Topology of the Electrostatic Potential.

Evelio Francisco1, Ángel Martín Pendás1, Dimas Suárez1

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Summary

This study introduces an efficient algorithm to find critical points in molecular electrostatic potential (MEP) landscapes. The method accurately maps molecular interactions and chemical reactivity using interpolated potentials.

Keywords:
S66 datasetmolecular electrostatic potentialquantum chemical topologyquantum theory of atoms in moleculestopology of scalar fields

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Molecular Modeling

Background:

  • The molecular electrostatic potential (MEP) is crucial for understanding chemical reactivity and noncovalent interactions.
  • Accurate determination of critical points (CPs) in the MEP is essential for topological analysis.
  • Existing methods may lack efficiency or robustness for large-scale studies.

Purpose of the Study:

  • To develop a robust and efficient algorithm for exhaustively determining all CPs of the MEP in 3D space.
  • To assess the accuracy of using tricubic interpolated MEPs compared to exact quantum-chemical MEPs.
  • To enable large-scale analyses of MEP topologies for chemical insights.

Main Methods:

  • Combined Newton's method with systematic physical space sampling.
  • Located maxima, minima, and saddle points of both exact and interpolated MEPs.
  • Validated the algorithm using a test function and applied it to diverse molecular systems (neutral, ionic, S66, IONIC-HB).

Main Results:

  • The algorithm successfully located all CPs for both exact and interpolated MEPs.
  • Tricubic interpolation closely reproduced the exact MEP topology in most regions.
  • Minor discrepancies were observed near nuclear positions or low-gradient areas.
  • Interpolated calculations were 2-7 times faster than exact calculations.

Conclusions:

  • The developed algorithm is efficient and robust for determining MEP CPs.
  • Interpolated MEPs offer a computationally advantageous approximation for topological analysis.
  • The method provides valuable insights into chemical reactivity and noncovalent interactions.