Iterative determination of several interior eigenstates of large matrices:Application to the determination of light-induced resonances in H-2(+)

The determination of several interior eigensolutions of large non-hermitian matrices is still an open problem for research. This paper brings signific ant improvements to the perturbative iterative methods. The theory is devel oped in the framework of Bloch formalism of wave operators and effective Ha miltonians. The progresses rely on two factors. First, the full Hilbert spa ce is partitioned into three subspaces to improve the convergence and stabi lity properties of the iterative processes. Second, the quasi-quadratic alg orithms are well-defined approximations of the exact quadratic Newton-Raphs on solution. The addition of these two factors brings the computational eff iciency far beyond standard perturbation theory. An application is presente d to the determination of the Floquet resonances arising from the ten lowes t vibrational states of the molecular ion H-2(+) for laser intensities up t o 1.6x10(15) W cm(-2). These Floquet states provide the relevant basis of t he dynamics of H-2(+) submitted to intense laser pulses. (C) 2000 American Institute of Physics. [S0021-9606(00)00115-X].