Isotropic periodic sum for multipole interactions and a vector relation for calculation of the Cartesian multipole...

Area of Science:

• Computational Chemistry
• Molecular Dynamics
• Statistical Mechanics

Background:

• Calculating long-range interactions in simulations is computationally intensive.
• Isotropic periodic sum (IPS) offers an efficient alternative by making interactions dependent on local conformation.
• Existing IPS methods show consistency with Particle Mesh Ewald (PME) for certain systems.

Purpose of the Study:

• To derive and implement multipole isotropic periodic sum (IPSm) potentials.
• To assess the accuracy and efficiency of multipole IPS potentials for systems with charges, dipoles, and quadrupoles.
• To compare multipole IPS potential performance against PME.

Main Methods:

• Developed multipole IPS potentials (IPSm) using a multipole homogeneous background approximation.
• Introduced a vector relation for efficient calculation of multipole interactions in Cartesian space.
• Performed simulations using model systems with varying multipolar characteristics and polarizability.

Main Results:

• Multipole interactions up to order m were accurately described by IPS potentials of order max(2, m-1).
• IPSm potentials achieved accuracy comparable to PME even with a small local region radius (6 Å).
• Simulations showed that IPSMm potentials reproduce energetic, structural, and dynamic properties similar to PME.

Conclusions:

• Multipole IPS potentials provide an efficient and accurate method for handling long-range electrostatic interactions in simulations.
• The proposed vector relation significantly enhances the computational efficiency of multipole calculations.
• IPSm potentials offer a viable and accurate alternative to PME for molecular simulations involving complex electrostatic interactions.