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.

Quest for Inexpensive Hydrogen Isotopic Fractionation: Do We Need 2D Quantum Confining in Porous Materials or Are Rough Surfaces Enough? The Case of Ammonia Nanoclusters

“…First, it seems important to develop models for amorphous ammonia ice as the ones already available for water ice ,, and with the specific intention of understanding the possible relationship between the parameters of the formation process and the structural details (e.g., site distribution, pore volume) of the solid species. Possible differences in aggregate structures due to the inclusion of quantum effects with, e.g., ring polymer molecular dynamics seem also worth investigating. With such models made available, it would be then possible to directly investigate adsorption isotherms and isotopic separation performances at finite T and p , as well as possible contributions to quantum sieving due to dynamic effects. − , Here, we specifically consider extending a recently proposed Gaussian-based time dependent Hartree dynamics .…”

Re‐weighted random series path integral simulations of molecular clusters: Applications to lithium solvated by a mixed Stockmayer cluster

“…These developments will be critical to the community when simulations of bulk electrolytes that properly include quantum effects, perhaps folded into a potential energy surface, of by other methods like the RPMD approach are used. The RPMD method is also based on the Feynman Path Integral and it has been extended for applications in curved spaces . Therefore, the massive efficiency gains discussed in the method section can be harnessed.…”

A trigonometric integrator for the constrained ring polymer Hamiltonian dynamics

“…The calculations of static equilibrium properties of a quantum mechanical system are comparatively easy by investigating the path integral representation. These methods, including the primitive path integral molecular dynamics (PIMD) [2,3], centroid molecular dynamics (CMD) [4][5][6] and ring polymer molecular dynamic (RPMD) [7][8][9][10][11], make use of the imaginary-time path integral formalism and exploit the exact equilibrium mapping between a quantum-mechanical particle and a classical ring polymer. Thus various of techniques of MD simulations can be directly implemented in PIMD simulations [3,6].…”

“…This instability may be more severe in ring polymer Hamiltonian dynamics, as the frequency of non-bond force is comparable to that of the harmonic interactions within beads. To ameliorate this problem, it's proposed to treat small covalent molecules as a set of rigid bodies [11,18], which not only significantly reduces the degrees of freedom required to represent the system, but also removes the intramolecular vibrations. The price to pay is to impose several holomonic constraints on the Hamiltonian dynamics, which needs to be preserved in the numerical integrations.…”

“…Several methods based on SHAKE are proposed to achieve better convergence [24,25]. For the holonomic constraints in more complicated geometries, the corresponding integrators are discussed in [11,26].…”