From sticky-hard-sphere to Lennard-Jones-type clusters

Area of Science:

• Computational chemistry
• Statistical mechanics
• Materials science

Background:

• Understanding the relationship between simplified physical models and complex potential energy landscapes is crucial for predicting material properties.
• The Lennard-Jones potential is a widely used model for interatomic interactions, but its application to clusters can be complex.
• Sticky-hard-sphere models offer a simplified approach to cluster formation.

Purpose of the Study:

• To establish a mapping between nonisomorphic sticky-hard-sphere (SHS) clusters and local energy minima of the (m,n)-Lennard-Jones (LJ) potential.
• To investigate how the number and nature of stable clusters depend on the parameters (m,n) of the LJ potential.
• To assess the completeness of the LJ potential landscape in representing SHS cluster structures.

Main Methods:

• Establishing a mathematical relation (map) M_{SHS→LJ} between sets of clusters.
• Analyzing the injectivity and surjectivity of this map.
• Investigating cluster stability and energy minima for varying (m,n) parameters.
• Comparing results from standard LJ potentials with an extended LJ potential derived from coupled-cluster calculations.

Main Results:

• The number of nonisomorphic stable clusters depends strongly and non-trivially on m and n.
• Cluster numbers increase exponentially with size (N≳10).
• The map M_{SHS→LJ} is noninjective and nonsurjective, but few LJ structures are missing for N≤13, often corresponding to unfavorable minima.
• Even soft LJ potentials highlight coordination challenges (Gregory-Newton problem for N=13).
• An extended LJ potential significantly increases the number of nonisomorphic clusters compared to the standard (6,12)-LJ potential.

Conclusions:

• The (m,n)-Lennard-Jones potential landscape captures many, but not all, sticky-hard-sphere cluster structures.
• Cluster structure and stability are sensitive to the specific LJ potential parameters.
• More realistic potentials, like the extended LJ potential, reveal a richer and more complex energy landscape for atomic clusters.