Exhaustive Spatial Sampling for Complete Topology of the Electrostatic Potential

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.