The practical description of disordered chemical reactions, where reactions
involve multiple species at multiple sites, is presently challenge using
correlated electronic structure methods. Here we describe the gradient theory
of multi-fragment density matrix embedding theory, which potentially provides a
minimal computational framework to model such processes at the correlated
electron level. We present the derivation and implementation of the gradient
theory, its validation on model systems and chemical reactions using density
matrix embedding, and its application to a molecular dynamics simulation of
proton transport in a small water cluster, a simple example of multi-site
reaction dynamics