Finger prints based biasing for finding complex reaction pathways

Determining the pathway of a reaction/transformation
is of great importance in chemistry,
physics and materials sciences. However, due to the
indistinguishability of atoms, finding complex reaction and
transformation pathways, containing a large number of
intermediate 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 configuration
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.