New alternatives to the Lennard-Jones potential

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Accurate interatomic potentials are crucial for simulating material properties.
• Ab initio calculations provide high-fidelity data but are computationally expensive.
• Existing methods for potential approximation can be limited in accuracy or efficiency.

Purpose of the Study:

• To develop a novel, computationally efficient method for approximating two-body interatomic potentials.
• To represent unknown potentials using analytic continued fractions and Dirichlet polynomials.
• To validate the method against ab initio data for noble gases.

Main Methods:

• Representing interatomic potentials as analytic continued fractions.
• Utilizing Dirichlet polynomials for potential approximation.
• Fitting the models to ab initio data for Xenon, Krypton, Argon, Neon, and Helium.
• Investigating non-linear optimization challenges and parallelization opportunities.

Main Results:

• Achieved close and computationally efficient approximations of ab initio data for Xe, Kr, Ar, and Ne using truncated continued fractions.
• Found a simple, accurate approximation for Helium using a single-variable function and a truncated continued fraction.
• Identified a Dirichlet polynomial providing a good fit for Helium in both attractive and repulsive regions.
• Demonstrated the method's effectiveness across various noble gases.

Conclusions:

• Analytic continued fractions offer a powerful tool for approximating interatomic potentials from ab initio data.
• The proposed method provides a computationally efficient and accurate alternative to existing approaches.
• The findings have implications for materials modeling and simulations involving noble gases.