Global energy minima of molecular clusters computed in polynomial time with semidefinite programming

Area of Science:

• Computational chemistry
• Quantum mechanics
• Materials science

Background:

• Determining the lowest energy configurations of molecular clusters is crucial for understanding their properties.
• Traditional methods often struggle with the combinatorial complexity of optimizing cluster structures.

Purpose of the Study:

• To develop a computationally efficient method for finding global energy minima of molecular clusters.
• To reformulate the optimization problem using the two-particle reduced density function (2-RDF).

Main Methods:

• Utilized the two-particle reduced density function (2-RDF) as the sole input.
• Derived linear matrix inequalities from N-representability constraints to ensure realistic particle configurations.
• Employed large-scale semidefinite programming for convex optimization.

Main Results:

• Successfully computed global energy minima for pure and binary molecular clusters (5-12 particles).
• Demonstrated that the 2-RDF reformulation allows for polynomial-time computation.
• Validated the approach using a semidefinite programming code.

Conclusions:

• The 2-RDF approach provides an efficient and scalable method for cluster energy minimization.
• This work bridges quantum mechanical principles with classical optimization for molecular systems.
• The method has implications for computational materials design and discovery.