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We apply the Monte Carlo Wave Packet (MCWP) approach to investigate thekinetic energy release (KER) spectra of the protons following double ionizationin H$_{2}$ when interacting with laser pulses with central wavelengths rangingfrom the near-IR (800 nm) to the mid-IR (6400 nm) regions and with durations of3-21 laser cycles. We uncover the physical origins of the peaks in the nuclearKER spectra and ascribe them to mechanisms such as ionization following aresonant dipole transition, charge-resonance-enhanced ionization (CREI) andionization in the dissociative limit of large internuclear distances. Forrelatively large pulse durations, i.e., for 15 or more laser cycles at 3200 nmand 10 or more at 6400 nm, it is possible for the nuclear wave packet inH$_{2}^{+}$ to reach very large separations. Ionization of this part of thewave packet results in peaks in the KER spectra with very low energies. Thesepeaks give direct information about the dissociative energy in the$2p\sigma_{u}$ potential energy curve of H$_{2}^{+}$ at the one- andthree-photon resonances between the $2p\sigma_{u}$ and $1s\sigma_{g}$ curves inH$_{2}^{+}$. With the MCWP approach, we perform a trajectory analysis of thecontributions to the KER peaks and identify the dominant ionization pathways.Finally, we consider a pump-probe scheme by applying two delayed pulses totrack the nuclear dynamics in a time-resolved setting. Low-energy peaks appearfor large delays and these are used to obtain the $2p\sigma_{u}$ dissociativeenergy values at the one-photon resonance between the $2p\sigma_{u}$ and$1s\sigma_{g}$ curves in H$_{2}^{+}$ for different wavelengths.

Laser-induced dissociative ionization of H$_{2}$ from the near-infrared to the mid-infrared regime