We propose a general method to cool the translational motion of molecules. Our method is an extension of single photon atomic cooling which was successfully implemented in our laboratory. Requiring a single event of absorption followed by a spontaneous emission, this method circumvents the need for a cycling transition and can be applied to any paramagnetic or polar molecule. In our approach, trapped molecules would be captured near their classical turning points in an optical dipole or RF-trap following an irreversible transition process.
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