  Stationary points (SPs) of the potential energy landscapes can be classified
by their Morse index, i.e., the number of negative eigenvalues of the Hessian
evaluated at the SPs. In understanding chemical clusters through their
potential energy landscapes, only SPs of a particular Morse index are needed.
We propose a modification of the "fixed-point homotopy" method which can be
used to directly target stationary points of a specified Morse index. We
demonstrate the effectiveness of our approach by applying it to the
Lennard-Jones clusters.
