A time-dependent method is used to study the photoionization of the simplest one-electron molecule, ${\mathrm{H}}_2^{+}.$ We use the variational principle to solve the time-dependent Schrödinger equation for ${\mathrm{H}}_2^{+}$ in spherical coordinates $(r,\theta )$ centered on the center of mass of the ${\mathrm{H}}_2^{+}$ system in a time-varying electromagnetic field, in the fixed-nuclei approximation. Bound and continuum states of ${\mathrm{H}}_2^{+}$ are obtained by diagonalizing the two-dimensional Hamiltonian for ${\mathrm{H}}_2^{+}$ on a uniform lattice. Two different algorithms for the time propagation of the Schrödinger equation are described, the first an explicit time propagator involving matrix multiplication and the second an implicit time propagator involving matrix inversion. Single-photoionization cross sections for ${\mathrm{H}}_2^{+}$ are presented for the cases where the laser field is oriented both parallel and perpendicular to the internuclear axis. Excellent agreement is found between the present calculations and previous work. Two- and three-photon ionization cross sections are also presented for the cases where the laser field is oriented both parallel and perpendicular to the internuclear axis. Comparison with previous work is available only for the parallel orientation case where good agreement is found with a previous time-independent calculation.

• Received 30 June 2003

DOI:https://doi.org/10.1103/PhysRevA.68.063413