A linear-scaling spectral-element method for computing electrostatic potentials.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Accurate calculation of the electronic Coulomb potential is crucial for understanding molecular behavior.
• Traditional methods for computing electrostatic potentials can be computationally expensive, especially for large systems.
• Developing linear-scaling methods is essential for efficient large-scale molecular simulations.

Purpose of the Study:

• To present a new, fast, linear-scaling method for evaluating the electronic Coulomb potential.
• To demonstrate the method's applicability and accuracy for molecular systems in quantum chemistry.
• To establish the spectral-element method as a competitive tool for large-scale electrostatic calculations.

Main Methods:

• A real-space partitioning of the system into cubic cells.
• A spectral-element representation of the density using high-order Chebyshev polynomials.
• Integration of the fast multipole method for non-neighboring cell interactions and exploitation of Coulomb operator separability for near-field interactions.

Main Results:

• The method achieves linear scaling for the fast numerical evaluation of the electronic Coulomb potential.
• It accurately treats arbitrary charge densities and avoids solving the Poisson equation or linear systems.
• Benchmark calculations on noble gas atoms, alkanes, and diamond fragments validate the method's performance.

Conclusions:

• The presented spectral-element method offers an accurate and efficient approach for computing electrostatic potentials.
• The adaptive resolution of the Chebyshev basis enhances the treatment of complex molecular systems.
• This method shows significant promise as a competitive tool for large-scale quantum chemistry calculations.