Formic acid production from CO₂ allows the reduction of carbon dioxide emissions while synthesizing a product with a wide range of applications. CO₂ hydrogenation is challenging due to the cost of transition metal catalysts and the toxicity of the transition elements. In this work, the thermodynamic confinement effects of the metal–organic framework UiO-66 on the CO₂ hydrogenation to formic acid were studied by force field-based molecular simulations. The confinement effects of UiO-66 and the metal–organic frameworks Cu-BTC, and IRMOF-1 were compared, to assess the impact of different pore size and metal centers on the production of HCOOH. Monte Carlo simulations in the grand-canonical ensemble were performed in the frameworks, using gas phase mole fractions of CO₂, H₂, and HCOOH at chemical equilibrium, obtained from Continuous Fractional Component Monte Carlo simulations in the Reaction Ensemble. The adsorption isobars of the components in metal–organic frameworks were computed at 298.15 – 800 K, 1 – 60 bar. The enhancement of HCOOH production due to preferential adsorption of HCOOH in metal–organic frameworks was calculated for all studied conditions. UiO-66, Cu-BTC, and IRMOF-1 affect CO₂ hydrogenation reaction, shifting the thermodynamical equilibrium toward HCOOH formation. The prevailing factor is the type of metal center in the metal–organic framework. The confinement effect of Cu-BTC turns out to exceed the enhancement caused by UiO-66, and IRMOF-1. The resulting mole fraction of HCOOH increased by ca. 2000 times compared to the gas phase at 298.15 K, 60 bar. Cu-BTC can be considered as an alternative to improve the production of HCOOH due to elimination of the high-cost temperature elevation, cost reduction of downstream processing methods, and comparable final concentration of HCOOH to the reported concentrations of formate obtained using transition metal catalysts.

We present several new major features added to the Monte Carlo (MC) simulation code Brick-CFCMC for phase- and reaction equilibria calculations (https://gitlab.com/ETh_TU_Delft/Brick-CFCMC). The first one is thermodynamic integration for the computation of excess chemical potentials (μex). For this purpose, we implemented the computation of the ensemble average of the derivative of the potential energy with respect to the scaling factor for intermolecular interactions (⟨∂U∂λ⟩). Efficient bookkeeping is implemented so that the quantity ∂U∂λ is updated after every MC trial move with negligible computational cost. We demonstrate the accuracy and reliability of the calculation of μex for sodium chloride in water. Second, we implemented hybrid MC/MD translation and rotation trial moves to increase the efficiency of sampling of the configuration space. In these trial moves, short Molecular Dynamics (MD) trajectories are performed to collectively displace or rotate all molecules in the system. These trajectories are accepted or rejected based on the total energy drift. The efficiency of these trial moves can be tuned by changing the time step and the trajectory length. The new trial moves are demonstrated using MC simulations of a viscous fluid (deep eutectic solvent).

There is a growing interest in the development of routes to produce formic acid from CO2, such as the electrochemical reduction of CO2 to formic acid. The solubility of CO2 in the electrolyte influences the production rate of formic acid. Here, the dependence of the CO2 solubility in aqueous HCOOH solutions with electrolytes on the composition and the NaCl concentration was studied by Continuous Fractional Component Monte Carlo simulations at 298.15 K and 1 bar. The chemical potentials of CO2, H2O, and HCOOH were obtained directly from single simulations, enabling the calculation of Henry coefficients and subsequently considering salting in or salting out effects. As the force fields for HCOOH and H2O may not be compatible due to the presence of strong hydrogen bonds, the Gibbs-Duhem integration test was used to test this compatibility. The combination of the OPLS/AA force field with a new set of parameters, in combination with the SPC/E force field for water, was selected. It was found that the solubility of CO2 decreases with increasing NaCl concentration in the solution and increases with the increase of HCOOH concentration. This continues up to a certain concentration of HCOOH in the solution, after which the CO2 solubility is high and the NaCl concentration has no significant effect.

The series of metal–organic frameworks M-MOF-74 gained popularity in the field of capture and separation of CO₂ due to the presence of numerous, highly reactive open-metal sites. The description of effective interactions between guest molecules and open-metal sites without accounting for polarization effects is challenging but it can significantly reduce the computational cost of simulations. In this study, we propose a non-polarizable force field for CO₂, and H₂ adsorption in M-MOF-74 (M = Ni, Cu, Co, Fe, Mn, Zn) by scaling the Coulombic interactions of M-MOF-74 atoms, and Lennard-Jones interaction potentials between the center of mass of H₂ and the open-metal centers. The presented force field is based on UFF and DREIDING parameters, characterized by high transferability and efficiency. The quantum behavior of H₂ at cryogenic temperatures is considered by incorporating Feynman–Hibbs quantum corrections. To validate the force field, the experimental isotherms of CO₂ at 298 K and 10⁻¹ – 10²kPa, the isotherms of H₂ at 77 K and 10⁻⁵ – 10²kPa, the corresponding enthalpy of adsorption, and the binding geometries in the M-MOF-74 series were reproduced using Monte Carlo simulations in the grand-canonical ensemble. The computed loadings, heats of CO₂ and H₂ adsorption, and binding geometries in M-MOF-74 are in very good agreement with the experimental values. The temperature transferability of the force field from 77 K to 87 K, and 298 K was shown for adsorption of H₂. The validated force field was used to study the adsorption and separation of CO₂/H₂ mixtures at 298 K. The adsorption of H₂ practically does not occur when CO₂ is present in the mixture. As indicated from simulated breakthrough curves, the breakthrough time of CO₂ in M-MOF-74 follows the same order as the uptake and the heat of CO₂ adsorption: Ni ¿ Co ¿ Fe ¿ Mn ¿ Zn ¿ Cu. Increasing the feed mole fraction of CO₂ in the breakthrough simulations from 0.1 to 0.9 speeds up the saturation of the adsorbent, leading to a faster exit of CO₂ with the column effluent. The application of the non-polarizable force field allows full investigation of the capture and separation of CO₂ in M-MOF-74, and can be expanded to study multi-component mixtures or industrial reactions in future research.