Spin-Projected Divide-and-Conquer Unrestricted Self-Consistent Field: Practical Linear-Scaling Approaches for Static...

The spin-unrestricted Hartree-Fock (UHF) method effectively accounts for static electron correlation, albeit at the expense of broken spin symmetry in the wavefunction. Such broken-symmetry UHF solutions suffer from spin contamination, which degrades the accuracy of molecular properties and excited-state calculations. Spin symmetry can be fully or partially restored by various projection approaches; including Löwdin's projection method, an approximate spin-projection scheme based on the Heisenberg Hamiltonian, and the projected generator coordinate method. In this paper, the linear-scaling divide-and-conquer (DC) UHF method is combined with these spin-projection approaches to treat large strongly correlated systems. DC spin-projection calculations based on Löwdin's method are performed on a π-conjugated polyene radical cation exhibiting severe spin contamination. The resulting DC energies closely reproduced those obtained from the standard (non-DC) spin-projected calculations. Additionally, the DC-based approximate spin-projection method and projected generator coordinate method were applied to a paddlewheel-type dichromium(II) complex and poly-phenoquinodimethane, respectively, demonstrating the applicability of the proposed approaches to systems with static correlation.