Finger prints based biasing for finding complex reaction pathways.

Determining the pathway of a reaction/transformation is of great importance in chem-
istry, physics and materials sciences. However, due to the indistinguishability of atoms,
finding complex reaction and transformation pathways, containing a large number of in-
termediate states, is difficult within the existing methods at the density functional theory
level.
we have resolved this issue by introducing a bias that is invariant under atomic index
permutations and that can target a single well defined configuration as the final configu-
ration of a chemical reaction or physical transformation. In this way we can overcome the
index mapping problem. The forces arising from the bias, by construction, do not depend
on the indexing of the atoms. We have thus reduced the combinatorial atomic indexing
problem, that has an exponential scaling, to a global minimization problem on a biased PES
involving an indexing invariant penalty function. The later problem can be solved easily in
practice. The penalty function we propose is universal and can be applied to any reaction
or transformation. We expect that this method will give atomistic insight into complex
reaction pathways i.e. in catalysis as well as complex phase and shape transformations.