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

The accurate treatment of many-unpaired-electron systems remains a central challenge in quantum chemistry, due to the exponential growth of the many-electron wave function with the number of correlated electrons. <i>Quantum Anamorphosis</i> addresses this challenge through physically motivated localization of molecular orbitals and site reordering, which yield unique block-diagonal Hamiltonian matrices and compact spin-adapted many-body wave functions. In this work, we introduce a genetic algorithm to identify optimal orbital/site orderings that enhance wave function compactness, thereby enabling the study of larger systems than previously possible. Crucially, we propose fitness functions based on approximate measures of the wave function compactness, which enable inexpensive genetic algorithm searches. We benchmark the strategy against one- and two-dimensional nearest-neighbor Heisenberg models, the one-dimensional next-nearest-neighbor Heisenberg model, and <i>selected</i> collinear ground and excited states of the nitrogenase P-cluster, employing intermediate CAS(48,40) active space ab initio Hamiltonians. In our strategy, the inclusion of nonmagnetic orbitals does not affect the fitness of the orderings, which enables the treatment of the large CAS(114,73) active space of the P-cluster without the need to search for a new optimal ordering. These results highlight the applicability and scalability of the genetic-algorithm-driven approach for systems with many unpaired electrons. The P-cluster test case is particularly relevant, as it demonstrates that wave function compression can be applied to both collinear ground and excited states, and allows the selective targeting of electronic states expressible in the given basis.