The study of rare events is one of the most fundamental problems in
chemistry. Chemical reactions and conformation changes of molecules are
examples of rare events. These events are rare because the system has to
overcome some barriers, which can be of energetic or entropic nature, or
both.
Transition-state theory relates the evaluation of transition rates of
rare events to the search for the so-called minimum-energy path (MEP),
i.e., the lowest-energy path for the rearrangement of a group of atoms
from one stable configuration to another. In this lecture, I will
introduce two main computational techniques for the numerical evaluation
of MEPs: the nudged-elastic-band method and the string method, including
some of their relevant variations.
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