Fundamental Problem in the Parallel Replica Dynamics Package

Dear LAMMPS users,

We would like to inform you that we found some issues with the implementation of the Parallel Replica Dynamics (PRD) method in LAMMPS. Enrique Martínez, from LANL observed that these issues can lead to significant errors in the observed transition rates. After some exploration on the source code we found these issues:

1) As implemented in LAMMPS right now, dephasing is performed without considering the possibility that transitions could occur during dephasing. The dephasing interval should provide a set of statistically independent replicas, all corresponding to the original reference state. If one replica experiences a transition in the dephasing interval, it should be rejected, and the system on that replica should be returned to the original reference state, in order to restart the dephasing process again from scratch. This is described in the original PRD paper. This step is important because ignoring this possibility can lead to the wrong transition being accepted and to errors in the estimated transition time.

2) To compute the simulation time, we have to estimate the time at which the transition really occurred during the last block. As presently implemented in LAMMPS, if an event is detected, the transition time is taken at the end of the integration block. This leads to a systematic overestimation of the transition time of order 0.5*(block integration length)*(number of replicas) for every transition. This can be quite significant when a lot of replicas are used. A better, less biased, estimation of the time can be obtained by using a sample from the minimum of M random numbers between 0 and the block time, where M is the number of replicas that detected a transition in the last block.

We have made some modifications in the source code that correct these problems. They have been tested against theoretical calculations giving a satisfactory agreement in the transition rate. The modified files have been sent to the LAMMPS developers.

With kind regards,

Luis Sandoval
Enrique Martínez
Danny Perez
Blas Uberuaga
Art Voter

we’ll release these changes soon, likely
after the Tgiving break.

Steve