A Genetic Algorithm Approach for Compact Wave Function Representations in Spin-Adapted Bases

Area of Science:

• Quantum Chemistry
• Computational Physics

Background:

• Accurate treatment of many-unpaired-electron systems is computationally challenging due to exponential wave function growth.
• Existing methods struggle with the complexity of large, correlated electron systems.

Purpose of the Study:

• To develop a novel computational strategy for efficiently treating systems with numerous unpaired electrons.
• To enhance wave function compactness for studying larger and more complex molecular systems.

Main Methods:

• Introduction of a genetic algorithm (Quantum Anamorphosis) for optimizing molecular orbital and site ordering.
• Development of fitness functions based on approximate measures of wave function compactness for inexpensive searches.
• Benchmarking against Heisenberg models and ab initio calculations for the nitrogenase P-cluster.

Main Results:

• The genetic algorithm successfully identifies optimal orderings that significantly enhance wave function compactness.
• The approach enables the study of larger active spaces, such as CAS(114,73) for the P-cluster, without re-optimization.
• Demonstrated applicability to both ground and excited states of complex systems.

Conclusions:

• The genetic-algorithm-driven Quantum Anamorphosis approach is scalable and effective for systems with many unpaired electrons.
• This method significantly advances the capability to perform accurate quantum chemical calculations on previously intractable systems.
• Wave function compression is a viable strategy for targeting specific electronic states in complex molecules.