  We report a new algorithm for constructing pathways between local minima that
involve a large number of intervening transition states on the potential energy
surface. A significant improvement in efficiency has been achieved by changing
the strategy for choosing successive pairs of local minima that serve as
endpoints for the next search. We employ Dijkstra's algorithm to identify the
`shortest' path corresponding to missing connections within an evolving
database of local minima and the transition states that connect them. The
metric employed to determine the shortest missing connection is a function of
the minimised Euclidean distance. We present applications to the formation of
buckminsterfullerene and to the folding of the B1 domain of protein G,
tryptophan zippers, and the villin headpiece subdomain. The corresponding
pathways contain up to 163 transition states, and will be used in future
discrete path sampling calculations.
