What is BXDE?
To understand BXDE, it is important to have in mind what a potential energy surface is. Potential energy surfaces are a way of representing how the potential energy of a system varies with a particular coordinate.
The image above is a contour plot of a potential energy surface for a 2D particle. It shows how the potential energy of the particle changes as the x and y coordinates are varied. For example, at position 1 the particle has a lower potential energy than at position 2.
In general, having lower potential energy is better. So, if we run a dynamic simulation, the particle would spend more time in one of the two darker purple areas (see video below).
However, it would be good if we could explore the other side of the potential energy surface. We could let the simulation run unbiased for ages, and hope that eventually the particle finds a way of escaping the well it is currently in. But this may take a very long time.
Another other approach is to bias the simulation. BXDE is a way of doing this. The principle is that the particle is constrained in a region of a certain potential energy. It is not allowed to go to regions of the surface where the energy is higher than a certain value and lower than another value. Once the particle has explored this region enough, it is allowed to proceed to the next region. Progressively, the particle explores more and more regions (see video below).
You may be asking yourself why this is interesting at all? In chemistry, finding new low energy regions in potential energy surfaces is very important. For example, in atmospheric chemistry the isoprene peroxy radical is a key intermediate of the isoprene atmospheric oxidation sequence. This molecule can react in many different ways and in order to find all the possible reaction pathways, exploring the potential energy surface is vital. You can find more details on this application in the paper.
Final note: The code used to generate all the images of the 2D particle on the Müller Brown potential can be found on my github.