A General Model Order Reduction Scheme for the Evaluation of Spectroscopic Properties and Excited States

Due to the importance of spectroscopic methods in experimental physical chemistry, a primary directive in quantum chemistry is to be able to accurately and efficiently predict and interpret the response of molecular systems to external perturbations. Molecular response properties may be described in terns of propagators, such as the single particle Green's function and polarization propagator. Traditional methods to solve these problems, such as partial eigenvalue decompositions and direct linear system solves, become computationally intractable in cases where the spectral region of interest lies in the propagator's spectral interior. In this work is presented a novel model order reduction (MOR) technique for the rapid evaluation of molecular properties in arbitrary spectral regions. MOR accelerates the evaluation of these properties by constructing a rational Krylov subspace which spans the spectral region of interest. Numerical studies demonstrating the favorable computational cost and scaling of this method for linear response TDDFT are presented. Further, it will be demonstrated that bright eigenstates of the Hamiltonian may also be extracted from the same subspace. The proposed MOR algorithm will enable routine inquiry into previously intractable spectroscopic problems.