New algorithms for iterative matrix‐free eigensolvers in quantum chemistry

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. © 2014 Wiley Periodicals, Inc.