Distributed multipole analysis

Distributed Multipole Analysis (DMA) is a computational technique used in the field of quantum chemistry and molecular physics to model the distribution of electrostatic potential around molecules. This method represents the electrostatic potential generated by a molecule in terms of a series of multipole moments located at specific points within the molecule. These points are not necessarily the positions of the atoms, and the moments can include charges (monopoles), dipoles, quadrupoles, and higher-order poles.

Overview

The concept of distributed multipole analysis was developed to overcome the limitations of representing molecules solely by their atomic charges when simulating molecular interactions and properties. By incorporating higher-order multipole moments, DMA provides a more accurate and detailed description of the electrostatic potential, which is crucial for understanding intermolecular forces, solvation effects, and the behavior of molecules in electric fields.

Theory

In DMA, the electrostatic potential V at a point in space due to a molecule is expressed as a sum of contributions from multiple sites within the molecule. Each site contributes a series of multipole moments, which together approximate the molecule's electrostatic potential more accurately than atomic charges alone. The potential V at a point r due to a multipole of order l located at a point r₀ is given by:

\[ V(\mathbf{r}) = \sum_{l=0}^{\infty} \frac{1}{l!} \mathbf{Q}_l \cdot \nabla^l \left( \frac{1}{|\mathbf{r} - \mathbf{r}_0|} \right) \]

where Q_l is the multipole moment of order l, and ∇^l denotes the lth derivative with respect to the position vector r.

Applications

Distributed multipole analysis has found applications in various areas of chemistry and physics, including:

• Molecular modeling and simulation, where it helps in the accurate calculation of intermolecular forces and energies.
• The study of solvation dynamics and solvent effects on molecular properties.
• The analysis of electrostatic interactions in biological molecules, contributing to the understanding of protein folding, enzyme activity, and drug design.

Implementation

Several software packages and computational chemistry tools implement DMA for the analysis of molecular electrostatic potentials. These tools typically require the user to specify the level of multipole moments to be included and the points within the molecule where these moments are to be located.

Challenges

One of the main challenges in distributed multipole analysis is determining the optimal placement of multipole sites and the appropriate level of multipole moments to accurately represent the electrostatic potential without introducing excessive computational complexity.

See Also

• Quantum chemistry
• Molecular physics
• Electrostatics
• Molecular modeling