Conceptual introduction for absolute beginners

We assume that most people interested in OpenPathSampling are familiar with the basic tools of molecular simulation: molecular dynamics and Monte Carlo sampling. [1]_ However, you might be new to path sampling methods. Furthermore, OpenPathSampling uses a rather novel perspective on path sampling in general. This introduction is aimed at users who are either new to path sampling or who want to have a better understanding of the conceptual framework that OpenPathSampling is built on.

Path sampling techniques apply, obviously, to “paths”. We will use the word “trajectory” interchangeably with “path”. Each path is made up of several “snapshots” or “frames”. Again, we often use these words interchangeably.

Collective variables are functions of a snapshot

For a system with \(N\) atoms, each snapshot on a trajectory (in 3D space) consists of \(3N\) coordinates and \(3N\) velocities — not to mention extra information about the simulation box. We can’t think in terms of what all those variables are doing, so we usually try to map the full dynamics to a smaller set of the most important variables. These are called “collective variables,” and we use them to describe the behavior of molecules in ways that we can better understand.

Of course, there are an infinite number of possible collective variable definitions, and finding the best ones to describe the process of a given transition is very difficult. When specifically referring to a collective variable which is used to describe the progress of a transition, we will sometimes call that an “order parameter” or a “reaction coordinate.” Selecting a good order parameter is a necessary first step for some of the methods implemented in OpenPathSampling.

Volumes apply to snapshots

In OpenPathSampling, we have a class of objects called volumes. These represent some sort of region in phase space, and they tell you whether a given snapshot is in that region.

The most common kind of volume is what we call a LambdaVolume. These are volumes based on some collective variable, as described above. In this case, we set a minimum and maximum value of the collective variable. Since the collective variable takes a snapshot and maps it to a single number, we can determine whether any snapshot is within that volume.

Ensembles apply to trajectories

We also have a class of objects called Ensembles. More correctly, we should call these “path ensembles” (or even more correctly, “path ensemble functions.”) The most important function this provides is the indicator function, which tells you whether or a given trajectory is in the path ensemble or not. In the same way that a volume takes a snapshot from a trajectory and tells you whether it includes it or not, an ensemble takes a whole trajectory and tells you whether it is included.

Just as configurational Monte Carlo is done by making changes to each snapshot, Monte Carlo can also be performed by making changes to trajectories. This is the idea of transition path sampling (TPS) and later methods, such as transition interface sampling (TIS), which are implemented in OpenPathSampling.

In configurational Monte Carlo, you need some function of the configuration (usually related to the energy) to decide what steps are allowed and with what probability. In path sampling Monte Carlo, you need some function of the entire trajectory. The simplest function is the ensemble indicator functions. In the same way that a Volume object can tell you whether a snapshot is in that Volume, an Ensemble object can tell you whether or not a trajectory is in that Ensemble.

A new development in OpenPathSampling is the concept of the “can-extend” functions, can_append and can_prepend. A given ensemble’s can_append function takes a trajectory, and tells you whether there is any way that trajectory could be a subtrajectory of a trajectory in the ensemble. While these existed implicitly in the stopping conditions from previous implementations, the new idea in OpenPathSampling is that they, as well as the ensembles, can be combined in predictable ways to form new and well-behaved ensembles. See the power user information on ensembles for more details.

PathMovers move in path space

Let’s further consider the analogy with configurational Monte Carlo. When doing importance sampling, you need a way to generate a new trial configuration from the old configuration. In simple Monte Carlo, this is often just a random move of one atom. There are also more advanced approaches such as cluster moves.

For path sampling, we need a similar way to move through path space. This is what path movers do: they create new trial trajectories for our ensembles. The most important path mover is probable the shooting move.

[1]	If not, we recommend that you start by reading the first four chapters of Frenkel and Smit’s “Understanding Molecular Simulation”, or find another text that provides a similar introduction.