Solving the eigenvalue equations of correlated vibrational structure methods: Preconditioning and targeting strategies

Various preconditioners and eigenvector targeting strategies in combination with the Davidson and Olsen methods are presented for solving eigenvalue equations encountered in vibrational configuration interaction, its response generalization, and vibrational coupled cluster response theory. The targeting methods allow significant flexibility and robustness in computing selected vibrational states, which are particularly important in the often occurring but nontrivial cases of near degeneracies. We have investigated the effect of a mode-excitation level-based generally applicable preconditioning scheme aiming to improve the robustness of the more standard diagonal preconditioning method. Although increasing convergence rates may be achieved in general through a hierarchy of these preconditioners, the strategy is not always beneficial in terms of CPU time. Features of the methods are demonstrated in calculations of the overtone vibrational states of formaldehyde and the fundamental states of vinyl fluoride, vinyl chloride, vinyl bromide, and naphthalene. (C) 2009 American Institute of Physics. [DOI: 10.1063/1.3154382]