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. Quantum Anamorphosis 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 selected 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.