We present a complex-scaling generalized pseudospectral method for accurate and efficient treatment of resonance states in two-center molecular systems, involving optimal nonuniform grid discretization of the Hamiltonian in prolate spheroidal coordinates. The procedure is applied to the first converged non-Hermitian Floquet study of multiphoton ionization of molecular ions in intense low-frequency (1064 nm) laser fields. We explore the underlying mechanism responsible for the ionization enhancement of ${\mathrm{H}}_2^{+}$ at some critical internuclear distances. Several features of the complex quasienergy states are observed. A detailed analysis of the nature and dynamical behavior of these quasienergy states reveals that the ionization enhancement is mainly due to the effect of charge-resonance-enhanced multiphoton resonances of the $1{\sigma }_g$ and $1{\sigma }_u$ states with excited electronic states at some particular internuclear distances. These “critical” distances depend on the details of molecular electronic structure and the laser frequency and intensity used in the study.

• Received 22 April 2000

DOI:https://doi.org/10.1103/PhysRevA.63.013414