Singular value decomposition of the radial distribution function for hard sphere and square well potentials

Area of Science:

• Statistical Mechanics
• Computational Physics
• Physical Chemistry

Background:

• The radial distribution function g(r) is crucial for understanding liquid and solid structures.
• Accurate computation of g(r) is essential for predicting material properties.
• Existing methods for g(r) can be computationally intensive or limited in scope.

Purpose of the Study:

• To develop a novel, accurate, and compact representation of the radial distribution function g(r).
• To apply singular value decomposition (SVD) to g(r) for hard sphere and square well potentials.
• To provide a computational tool for this new representation.

Main Methods:

• Singular Value Decomposition (SVD) applied to g(r).
• Analysis of g(r) for hard sphere and square well potentials.
• Development of a low-order polynomial model for coefficient vectors.

Main Results:

• g(r) decomposes into a small set of basis vectors.
• This decomposition allows for highly accurate interpolation of g(r) across densities and potential strengths.
• Coefficient vectors are effectively modeled by low-order polynomials.

Conclusions:

• SVD provides an extremely accurate and compact representation of g(r).
• The polynomial description of coefficient vectors simplifies the model.
• A program is provided for calculating g(r) using this compact representation.