Hierarchical characterization of energy landscapes using Gaussian packet states

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Abstract
We present a new method for exploring multidimensional energy landscapes by using Gaussian packets to characterize metastable states. Focusing on spatial scaling properties of the energy function, we derive nonlinear self‐consistent packet equations which determine the parameters of these Gaussian packets. This provides a unique definition of the thermodynamic properties of metastable states and a computational prescription for their calculation. The packet equations allow bifurcation and enable us to follow the ‘‘trajectories’’ of states as functions of temperature and to determine the hierarchical relationships between states. The method is demonstrated on simple one‐dimensional models and on Lennard‐Jones six‐, seven‐, and eight‐atom microclusters. We find that the microcluster state trajectories that are connected to lowest zero‐temperature energy conformations are also connected to the lowest free‐energy trajectories up to their destabilization temperatures. That is, the global minima have a ‘‘strong scaling’’ property that can accelerate searches for global minima by scale‐dependent annealing methods.