Unbiased rotational moves for rigid-body dynamics

Area of Science:

• Computational physics
• Molecular dynamics

Background:

• Rigid-body dynamics simulations are crucial for modeling molecular systems.
• Standard methods for rotational moves in simulations can introduce errors, especially for finite rotations.
• These errors arise from the non-commutative nature of rotational matrices when applied sequentially.

Purpose of the Study:

• To introduce an unbiased protocol for rotational moves in rigid-body dynamics simulations.
• To address and correct deficiencies in existing Brownian dynamics simulation methods.
• To provide a more accurate algorithm for rotating local coordinate frames.

Main Methods:

• Developed an approach based on the analytic solution for rotational equations of motion.
• Utilized an orthogonal coordinate system with constant angular velocity.
• Implemented an algorithm to avoid errors from applying non-commuting rotational matrices in arbitrary order.

Main Results:

• The proposed protocol provides an unbiased method for rotational moves.
• The algorithm effectively removes errors associated with finite rotations in simulations.
• Demonstrated a significant improvement over standard approaches for rotating coordinate frames.

Conclusions:

• The new protocol offers a more accurate and unbiased way to handle rotations in simulations.
• This method is recommended to replace standard approaches in Langevin and Brownian dynamics.
• Enhances the reliability of rigid-body dynamics simulations.