Robust and Efficient Spin Purification for Determinantal Configuration Interaction.

The limited precision of floating point arithmetic can lead to the qualitative and even catastrophic failure of quantum chemical algorithms, especially when high accuracy solutions are sought. For example, numerical errors accumulated while solving for determinantal configuration interaction wave functions via Davidson diagonalization may lead to spin contamination in the trial subspace. This spin contamination may cause the procedure to converge to roots with undesired ⟨Ŝ2⟩, wasting computer time in the best case and leading to incorrect conclusions in the worst. In hopes of finding a suitable remedy, we investigate five purification schemes for ensuring that the eigenvectors have the desired ⟨Ŝ2⟩. These schemes are based on projection, penalty, and iterative approaches. All of these schemes rely on a direct, graphics processing unit-accelerated algorithm for calculating the S2c matrix-vector product. We assess the computational cost and convergence behavior of these methods by application to several benchmark systems and find that the first-order spin penalty method is the optimal choice, though first-order and Löwdin projection approaches also provide fast convergence to the desired spin state. Finally, to demonstrate the utility of these approaches, we computed the lowest several excited states of an open-shell silver cluster (Ag19) using the state-averaged complete active space self-consistent field method, where spin purification was required to ensure spin stability of the CI vector coefficients. Several low-lying states with significant multiply excited character are predicted, suggesting the value of a multireference approach for modeling plasmonic nanomaterials.