Ring polymer dynamics for rigid tops with an improved integrator.

Area of Science:

• Computational Chemistry
• Theoretical Physics
• Molecular Dynamics Simulations

Background:

• Standard Ring Polymer Molecular Dynamics (RPMD) faces challenges in curved spaces due to non-uniform metrics.
• Common integrators exhibit significant long-time energy drift in such spaces, compromising simulation accuracy.
• Curved spaces arise in systems with holonomic constraints or Lie group parameterizations.

Purpose of the Study:

• To implement and test a novel RPMD integrator adapted for curved spaces.
• To address and overcome the long-time energy drift issue in non-uniform metric environments.
• To validate the new integrator's performance using a symmetric ellipsoid and stereographic projection.

Main Methods:

• Development of a new integrator based on the variational principle.
• Adaptation of Ring Polymer Molecular Dynamics to curved spaces.
• Testing the implementation on a symmetric ellipsoid of inertia mapped by stereographic projection coordinates.
• Computation of the position-position autocorrelation function for a rigid ammonia molecule in an external field.

Main Results:

• The new RPMD integrator successfully conserves energy without long-term drift in curved spaces.
• The algorithm exhibits quadratic convergence with respect to the time step.
• Successful computation of autocorrelation functions validates the method's applicability.

Conclusions:

• The variational principle-based integrator provides an accurate and stable method for RPMD in curved spaces.
• This advancement enables reliable simulations of molecular systems with complex geometries and constraints.
• The method's efficiency and accuracy are demonstrated through benchmark tests.