New algorithms for iterative matrix-free eigensolvers in quantum chemistry

D. Zuev, E. Vecharynski, C. Yang, N. Orms, and A.I. Krylov
J. Comp. Chem. 36, 273 – 284 (2015)

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 states using equation-of-motion coupled-cluster (EOM-CC) method. We present two algorithms suitable for calculating excited states that are close to specified energy shift (interior eigenvalues). One is based on the Davidson algorithm that is commonly used in quantum chemical calculations, the second one is an entirely new solver called Generalized Preconditioned Locally Minimal Residual (GPLMR) method. We also present a modification of the Davidson procedure that allows one to solve for a transition of a specific character. The details of the algorithms and their memory and CPU requirements are described. The new algorithms are implemented within the EOM-CC suite of methods in the Q-Chem electronic structure program.

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