Real-space quadrature: a convenient, efficient representation for multipole expansions

Area of Science:

• Computational chemistry
• Molecular modeling
• Theoretical physics

Background:

• Multipoles are crucial for molecular electrostatics modeling.
• Current point charge representations are inefficient compared to spherical harmonics.
• Multipole rotation is a bottleneck in molecular dynamics.

Purpose of the Study:

• To develop a complete and efficient point charge representation for molecular electrostatics.
• To replace spherical harmonic basis functions with a simpler discrete point set.
• To optimize molecular dynamics simulations by addressing multipole rotation bottlenecks.

Main Methods:

• Developed a novel representation using weights associated with fixed points on a sphere.
• Replaced spherical harmonic basis functions with this discrete point set.
• Reduced spherical harmonic decomposition of Poisson's operator to pairwise summations.

Main Results:

• The new representation is space-optimal and significantly more efficient.
• Demonstrated exact quadrature-based formulas for tensor contractions.
• Showcased that multiplication of spherical harmonics translates to a direct product in this representation.

Conclusions:

• This work provides the first complete solution for efficient point charge representation in molecular electrostatics.
• The novel method drastically simplifies calculations and optimizes molecular dynamics.
• The findings offer a breakthrough in computational efficiency for electrostatic modeling.