"Balancing" the Block Davidson-Liu Algorithm.

We describe a simple modification ("balancing") of the block Davidson-Liu eigenvalue algorithm which allows the norms of the Krylov search directions to decrease naturally as convergence is approached. In the context of integral-direct configuration interaction singles and time-dependent density functional theory, this provides for efficient utilization of density-based screening. Tests within the TeraChem GPGPU code exhibit speedups of ∼2× on systems with up to 1500 atoms, with negligible loss in accuracy.