Permutation symmetry in spin-adapted many-body wave functions

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Exchange-coupled polynuclear transition-metal (PNTM) clusters exhibit local emergent symmetries.
• These symmetries can enhance the sparsity of configuration interaction (CI) eigensolutions.
• Current methods face factorial scaling challenges when searching permutation spaces for large clusters.

Purpose of the Study:

• To reduce the factorial scaling in analyzing PNTM clusters.
• To exploit combined permutation and point group symmetries for computational efficiency.
• To develop strategies for identifying optimal site orderings and reducing redundant calculations.

Main Methods:

• Combining permutation and point group symmetry arguments.
• Utilizing commutation relations between cumulative partial spin and Hamiltonian operators.
• Developing graphical strategies for evaluating commutators and a tree search algorithm for permutation space analysis.

Main Results:

• Identified site orderings that lead to commuting operators, resulting in sparser wave functions.
• Developed methods to predict and eliminate redundant site permutations.
• Demonstrated the utility of reversal symmetry for singlet spin states to further reduce computational complexity.

Conclusions:

• The proposed methods significantly reduce the computational cost associated with CI eigensolutions for PNTM clusters.
• These strategies enable more efficient analysis of larger and more complex transition-metal systems.
• The findings pave the way for deeper understanding of the electronic structure and magnetic properties of PNTM clusters.