  An analysis of the network defined by the potential energy minima of
multi-atomic systems and their connectivity via reaction pathways that go
through transition states allows to understand important characteristics like
thermodynamic, dynamic and structural properties. Unfortunately computing the
transition states and reaction pathways in addition to the significant
energetically low-lying local minima is a computationally demanding task. We
here introduce a computationally efficient method that is based on a
combination of the minima hopping global optimization method and the insight
that uphill barriers tend to increase with increasing structural distances of
the educt and product states. This method allows to replace the exact
connectivity information and transition state energies with alternative and
approximate concepts. Without adding any significant additional cost to the
minima hopping global optimization approach, this method allows to generate an
approximate network of the minima, their connectivity and a rough measure for
the energy needed for their interconversion. This can be used to obtain a first
qualitative idea on important physical and chemical properties by means of a
disconnectivity graph analysis. Besides the physical insight obtained by such
an analysis, the gained knowledge can be used to make a decision if it is
worthwhile or not to invest computational resources for an exact computation of
the transition states and the reaction pathways. Furthermore it is demonstrated
that the here presented method can be used for finding physically reasonable
interconversion pathways that are promising input pathways for methods like
transition path sampling or discrete path sampling.
