The behavior of the high-order harmonics and output attosecond pulses from hydrogen molecule ions with various internuclear distances that are exposed to high intensity incoming pulses are investigated. The incoming pulses that are spectrally wide yield from a superposition of monochromatic beams with a constant frequency distance. Our simulations show that the most intense and shortest attosecond pulses can result from hydrogen molecular ions with large internuclear distances which are exposed to irradiation of intense pulses with a frequency width greater than 0.03 a.u.