For curbing the global temperature increase, effective approaches for carbon capture are needed. By utilizing amine-based liquid sorbents, current methods suffer from a high-energy cost for the thermal desorption step that is responsible for 60-80% of the total operating costs. The use of solid sorbent materials for carbon capture has been proposed as an alternative to amine-based liquid sorbents due to their lower desorption energy requirement, which can potentially boost the commercial viability of point-source carbon capture. Among various porous solids for gas separation and purification, metal organic frameworks (MOFs) are promising materials that potentially combine high $CO_2$ uptake and $CO_2/N_2$ selectivity. So far, within the hundreds of thousands of MOF structures known today, it remains a challenge to computationally identify the best suited species. First principle-based simulations of $CO_2$ adsorption in MOFs (particularly, the ones with open metal sites) would provide the necessary accuracy, however, they are impractical due to the high computational cost. Classical force field-based simulations would be computationally feasible but they do not provide sufficient accuracy. Thus, the entropy contribution that requires both accurate force fields and sufficiently long computing time for sampling is difficult to obtain in simulation. The effect of chemisorption on an open metal site manifests itself more prominently at lower pressures, precisely where the desorption step happens and, therefore, is of utmost importance for the regeneration cost. Here, we report the quantum-informed machine-learning force fields (QMLFF) for atomistic simulations of $CO_2$ in MOFs. We demonstrate that the method has a much higher computational efficiency (~1000x) than the first-principle one while maintaining quantum-level accuracy. As a proof of concept, we show that the QMLFF-based molecular dynamics simulations of $CO_2$ in Mg-MOF-74 can predict the binding free energy landscape and the diffusion coefficient similar to experimental values. The combination of machine learning and atomistic simulation paves the way for more accurate and efficient in silico evaluations of chemisorption and diffusion.