Adaptive BXD in multi-dimensional CV space

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We’ve recently published a paper describing some nice extensions to the “boxed molecular dynamics” (BXD) rare event method (open-access draft available here). BXD is a method that I’ve been working on for the last few years for accelerating rare events in chemical simulations (there’s a 1-d implementation available in the CHARMM package).

The underlying BXD idea is straightforward: assuming I have a chemical transformation that I want to study, and some sense of the collective variables (CVs) that are important along the transformation pathway, I can splice the CV space into a set of ‘boxes’. A “box” is defined as a region of configuration space that lies between two boundaries; within any given box, a trajectory runs on a potential energy surface which is unmodified. If the trajectory crosses a particular box boundary, a velocity inversion operation is performed to keep it within the specified box. BXD simulations are run by locking the system within a set of adjacent ‘boxes’, and then performing statistical analysis of the time spent in the each box, and the relative number of hits at the boundaries which define the box. These quantities define box-to-box rate coefficients, which can then be used to calculate a potential of mean force, which is independent of the boundary locations. Choosing BXD boundaries is analogous to the process of specifying umbrellas (in umbrella sampling). A key difference is the fact that umbrella sampling requires two parameters per umbrella (location and force constant); whereas BXD requires only one parameter (location). With the appropriate set of boxes, it is possible to sample spaces that otherwise have a low probability of being populated.

In our recent paper, we made two useful developments to BXD. We showed that BXD can be: (1) utilized to explore multi-dimensional CV spaces, and (2) formulated in a fashion that enables adaptive exploration of minimum free energy pathways. The video shows BXD adaptively sampling reactive pathways for deuterium transfer between a Fluorine radical and deuterated acetonitrile solvent molecules.  Specifically, we told BXD to adaptively sample the free energy pathway in a 2d CV space (the D–F distance and the C–D distance).

Unlike umbrella sampling or metadynamics, BXD does not bias the underlying potential energy surface of a given system. As a result, it can be shown within certain limits that the BXD dynamics correspond to the “real” system dynamics. The philosophy that guides the adaptive BXD algorithm is therefore very simple: by ‘listening’ to the system dynamics, we get an idea of where the system is trying to go, and are therefore able to adaptively locate box boundaries which nudge the system along so that it does not become trapped. The video in fact shows the box boundaries which BXD places as it ‘listens’ to the system dynamics.