An index-resolved fixed-point homotopy and potential energy landscapes
For researchers studying chemical clusters, this method enables targeted exploration of stationary points with a desired Morse index, potentially reducing computational cost.
This work modifies the fixed-point homotopy method to directly target stationary points of a specified Morse index on potential energy landscapes, demonstrated on Lennard-Jones clusters.
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.