title: New algorithms for iterative matrix-free eigensolvers in quantum chemistry.
abstract: New algorithms for iterative diagonalization procedures that solve for a small set of eigen-states of a large matrix are described. The performance of the algorithms is illustrated by calculations of low and high-lying ionized and electronically excited states using equation-of-motion coupled-cluster methods with single and double substitutions (EOM-IP-CCSD and EOM-EE-CCSD). We present two algorithms suitable for calculating excited states that are close to a specified energy shift (interior eigenvalues). One solver is based on the Davidson algorithm, a diagonalization procedure commonly used in quantum-chemical calculations. The second is a recently developed solver, called the "Generalized Preconditioned Locally Harmonic Residual (GPLHR) method." We also present a modification of the Davidson procedure that allows one to solve for a specific transition. The details of the algorithms, their computational scaling, and memory requirements are described. The new algorithms are implemented within the EOM-CC suite of methods in the Q-Chem electronic structure program.
authors.affiliation: Department of Chemistry, University of Southern California, Los Angeles, California, 90089-0482.
authors.forename: Dmitry
authors.initials: D
authors.lastname: Zuev
authors.forename: Eugene
authors.initials: E
authors.lastname: Vecharynski
authors.forename: Chao
authors.initials: C
authors.lastname: Yang
authors.forename: Natalie
authors.initials: N
authors.lastname: Orms
authors.forename: Anna I
authors.initials: AI
authors.lastname: Krylov
keywords: coupled-cluster; diagonalization algorithms; eigensolvers; equation-of-motion; excited states; harmonic Ritz problem; interior eigenstates