Direct air capture of Carbon Dioxide is a technical solution that does not rely on natural processes to capture CO2 from the atmosphere. In DAC, the filter material is designed to specifically bind CO2 molecules. Hence a high-capacity filter is sought. We aim to leverage the potential of quantum computing to improve the filters used in DAC. Metal-Organic Frameworks (MOFs) have high surface area and tunable pore sizes which makes them an attractive material for gas storage and separation. Using the variational quantum eigensolver (VQE) algorithm, we find the minimum of the potential energy surface (PES) by first considering only the active site of the MOF (the metal ion). For complex systems, we employ Density Matrix Embedding Theory and use VQE as a fragment solver at the binding site. Techniques like deparameterisation are used to minimise the count of trainable parameters. We present results of ideal and noisy simulations as well as from a real hardware device. Resources are estimated for MOFs unit cell. The findings from our study demonstrates the potential of quantum computing to effectively perform quantum simulations of strongly correlated fragments.