Recursive Taylor Series Expansion Method for Rigid-Body Molecular Dynamics

Area of Science:

• Computational Chemistry and Physics
• Biophysics

Background:

• Molecular dynamics (MD) simulations are crucial for elucidating chemical, physical, and biological mechanisms.
• The accuracy and reliability of MD simulations are critically dependent on the numerical integration schemes employed.

Purpose of the Study:

• To develop novel, computationally efficient, and robust rigid body integration schemes for MD simulations.
• To provide a numerically exact solution to the free rigid body problem without using Jacobi elliptic functions.

Main Methods:

• Developed new integration schemes based on a numerically exact solution to the free rigid body problem.
• Utilized Taylor series expansion of rotational dynamical variables and recursive solutions for higher-order derivatives.
• Extended the method to simulate canonical ensembles for constant temperature simulations.

Main Results:

• The new schemes are computationally efficient, robust, and easy to implement.
• Achieved numerically exact solutions for the free rigid body problem.
• Demonstrated long-time stability and accuracy comparable to established symplectic integrators.

Conclusions:

• The developed rigid body integration schemes offer a significant advancement in MD simulation methodology.
• These methods provide a reliable and efficient approach for studying complex molecular systems.
• The extension to canonical ensembles broadens their applicability in simulating systems at constant temperatures.