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A Comparison of Three Variants of the Generalized Davidson Algorithm for the Partial Diagonalization of Large Non-Hermitian Matrices.

The solution of the equation of motion coupled cluster singles and doubles problem, that is finding the lowest lying electronic transition energies and properties, is fundamentally a large non-Hermitian matrix diagonalization problem. We implemented and compared three variants of the widely diffuse generalized Davidson algorithm, which iteratively finds the lowest eigenvalues and eigenvectors of such a matrix. Our numerical tests, based on different molecular systems, basis sets, state symmetries, and reference functions, demonstrate that the separate evaluation of the left- and right-hand eigenvectors is the most efficient strategy to solve this problem considering storage, numerical stability, and convergence rate.