A Two-Level Preconditioner for the CASSCF Linear-Response Equations

We present an efficient two-level strategy to accelerate the solution of the CASSCF linear-response eigenvalue problem using a customized Davidson algorithm. By identifying a subset of important response-vector components─the so-called P space─we compute and diagonalize full Hessian and metric matrix elements while treating the remaining Q-space components with a diagonal approximation. This approach decouples the orbital and configuration responses, enabling independent preconditioning of each component. Computational cost is further reduced through the resolution-of-the-identity approximation. We demonstrate significant performance gains across a diverse set of molecules, achieving speedups of up to 2.05 compared to the standard diagonal preconditioning. The largest efficiency gains are observed for MCTDA calculations involving many excited states and relatively small response-vector lengths. The two-level strategy is available in ORCA 6.1 and paves the way for extensions to dynamic polarizabilities, which require solving large-scale linear equations, as well as to time-dependent density functional theory and CI singles.