We utilize magnetohydrodynamic (MHD) simulations to develop a numerical model for GMC-GMC collisions between nearly magnetically critical clouds. The goal is to determine if, and under what circumstances, cloud collisions can cause pre-existing magnetically subcritical clumps to become supercritical and undergo gravitational collapse. We first develop and implement new photodissociation region (PDR) based heating and cooling functions that span the atomic to molecular transition, creating a multiphase ISM and allowing modeling of non-equilibrium temperature structures. Then in 2D and with ideal MHD, we explore a wide parameter space of magnetic field strength, magnetic field geometry, collision velocity, and impact parameter, and compare isolated versus colliding clouds. We find factors of ~2-3 increase in mean clump density from typical collisions, with strong dependence on collision velocity and magnetic field strength, but ultimately limited by flux-freezing in 2D geometries. For geometries enabling flow along magnetic field lines, greater degrees of collapse are seen. We discuss observational diagnostics of cloud collisions, focussing on 13CO(J=2-1), 13CO(J=3-2), and 12CO(J=8-7) integrated intensity maps and spectra, which we synthesize from our simulation outputs. We find the ratio of J=8-7 to lower-J emission is a powerful diagnostic probe of GMC collisions.
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