Electrostatic Forces: Formulas for the First Derivatives of a Polarizable, Anisotropic Electrostatic Potential Energy...

Area of Science:

• Computational Chemistry
• Molecular Modeling
• Machine Learning

Background:

• Accurate prediction of molecular properties requires sophisticated electrostatic potential energy functions.
• Flexible molecules present challenges due to their dynamic nature and complex geometries.
• Quantum Chemical Topology (QCT) provides a robust framework for defining atomic properties.

Purpose of the Study:

• To derive analytical formulas for the first derivatives (forces) of electrostatic potential energy functions.
• To incorporate polarizable and high-rank multipolar interactions for flexible molecules.
• To enable efficient molecular dynamics and geometry optimization within the QCT framework.

Main Methods:

• Development of analytical formulas for first derivatives of electrostatic potential energy.
• Utilizing Kriging, a machine learning technique, to predict local-frame atomic multipole moments.
• Employing an interaction tensor based on spherical harmonics for multipole interactions.
• Construction of atom-centered local coordinate frames based on molecular geometry.

Main Results:

• Successful derivation of explicit analytical formulas for molecular forces.
• Integration of Kriging predictions for atomic multipole moments into the force calculation.
• The derived forces account for both geometric dependence and trained Kriging model derivatives.

Conclusions:

• The developed analytical forces are crucial for future molecular dynamics and geometry optimization.
• This work advances the QCT force field by providing accurate and efficient force calculations.
• The methodology is applicable to polarizable, high-rank multipolar electrostatic interactions in flexible molecules.