Ring polymer dynamics for rigid tops with an improved integrator

Abstract

When working in curved spaces, such as those created with the introduction of holonomic constraints, or those generated from the parameters of Lie groups, the presence of a non-uniform metric significantly alters the Ring Polymer Molecular Dynamics from its Cartesian space counterpart. The presence of a nonuniform metric causes difficulties manifested in significant long-time energy drift for the common integrators, which should be absent in a good algorithm. Using a new integrator developed with the aid of the variational principle, we implement a version of Ring Polymer Molecular Dynamics adapted to curved spaces [S. Wolf and E. Curotto, J. Chem. Phys. 137, 014109 (2012)], specifically testing a symmetric ellipsoid of inertia mapped by stereographic projection coordinates. We find that the algorithm conserves the energy without long-term energy drift and converges quadratically in the time step. To test this implementation of Ring Polymer Molecular Dynamics, we compute the position-position autocorrelation function for a rigid ammonia molecule in an external field, for several values of the Trotter number.