Adsorption simulations often assume a rigid framework, which can be exploited by replacing the expensive framework-adsorbate energy/force evaluation by interpolation of a precomputed energy grid. We present the implementation in RASPA3 of a triquintic interpolation algorithm by Boateng and Bradach and compare it to the tricubic algorithm of Lekien and Marsden. We extended the scheme to interpolation in fractional space to facilitate interpolation of non-rectangular frameworks and evaluated the accuracy. We find that the use of grids is advantageous for larger systems and/or large cutoffs, but generally the efficiency gains are modest (a factor of 2–5).

Porous materials such as zeolites and Metal-Organic Frameworks are widely used for molecular separations based on adsorption and enthalpy/entropy characteristics. Ideal adsorption solution theory (IAST) predicts mixture adsorption behaviour on the basis of pure component isotherms of adsorbents in porous media. Mixture data at all mole fractions are required for breakthrough simulations. The use of IAST avoids the expensive computations of mixtures with Monte Carlo methods. Matching outcomes from computational physics studies to experimentally measurable properties is the foundation of the materials design pipeline. Here, we report the regression of an Invertible Autoencoder (IAE) for the forward and backward mapping of pure and mixture isotherms. The invertible autoencoder is defined as a soft-invertible neural network, which can be used as mapping function. Pure component isotherms are modelled using a 3-site Langmuir-Freundlich model, with a broad range of equilibrium pressure and heterogeneity factors. A synthetic dataset is generated from pure component isotherms and mixture isotherms calculated with RUPTURA. The IAE predicts pure and mixture isotherms with high precision over a large fugacity range, for up to 6 components and 3-site isotherms. This work contributes to inverting the full design pipeline from physical gas separation to adsorbate design, enabling property-guided materials discovery.

In the days prior to the Thermodynamics2024 conference in Delft (The Netherlands), the annual RASPA workshop/school took place at Delft University of Technology with 55 participants (both industry and academics) from all over the world. RASPA is a popular open-source molecular simulation software package for studying adsorption and diffusion in fluids and nanoporous materials, and it is especially popular in the metal-organic frameworks and zeolite communities. The main contributors to RASPA (and organisers of the RASPA workshop/school in Delft) are David Dubbeldam, Sofia Calero, Randall Q. Snurr, and Thijs J.H. Vlugt. In this short paper, we briefly explain the history of RASPA and the RASPA workshops, as well as our strategy to teach the workshop participants how to use RASPA for their specific research projects.

Nitric oxide, NO, is a free radical that forms dimers, (NO)2, at its vapor–liquid coexisting temperatures. In this work, we developed an all-atom force field for NO and (NO)2. To assess the performance of this force field, we computed the vapor–liquid equilibrium (VLE) properties of the reactive NO–(NO)2 system, as well as those of pure NO and pure (NO)2, using Continuous Fractional Component Monte Carlo (CFCMC) simulations. We then compared the results with the available experimental data and predictions from two previously developed force fields. For the reactive NO–(NO)2 system, we performed CFCMC simulations in the reactive Gibbs ensemble in which the formation of NO dimers, 2NO ⇌ (NO)2, is considered. The predicted coexistence vapor–liquid densities, dimer mole fractions in the liquid phase, saturated vapor pressures, and heats of vaporization using our force field in the temperature range 120 K to 170 K are in excellent agreement with experimental values. In addition, we conducted a systematic parameter study to analyze the sensitivity of the new force field parameters and the isolated molecule partition functions of (NO)2 on the VLE properties of the reactive NO–(NO)2 system. The results indicate that the VLE properties of the reactive NO–(NO)2 system are affected by both the force field parameters of the involved species as well as the isolated molecule partition functions of (NO)2.

Group contribution methods (GCMs) provide a practical and computationally efficient approach for predicting thermodynamic properties of hydrocarbons, especially when experimental data are scarce. This review evaluates the evolution of GCMs from classical first-order schemes (e.g. Lydersen method, Joback method) to more advanced second-order frameworks (e.g. CG94, Sharma method), hybrid extensions, and emerging machine learning integrations. While first-order models are simple and widely used, these models struggle with branched and long-chain molecules. Second-order approaches significantly improve structural sensitivity and predictive accuracy, achieving deviations below 2–3% for critical properties and within 1 kcal/mol for formation enthalpies of branched alkanes. Nevertheless, challenges remain in extrapolating to highly complex molecules, underrepresented functional groups, and extreme conditions. Promising directions include reinforcement of second-order GCMs with molecular theory, systematic expansion of experimental and quantum-based datasets, and hybrid GCM–machine learning models that retain interpretability while improving generalisability. We recommend prioritising models that balance accuracy, robustness, simplicity, and transferability to accelerate sustainable process and product designs, particularly in applications such as fuel upgrading including hydroisomerisation, separation processes, and green chemical development.

Accurate prediction of thermodynamic properties of hydrocarbons is essential for chemical process modelling. Conventional group contribution methods often are used to predict these properties. However, these methods often require extensive parameter sets to handle structural complexities. A refined group contribution method for predicting thermodynamic properties of hydrocarbon isomers with reduced complexity and improved accuracy is presented and discussed. By combining the structural framework of Constantinou and Gani (CG94) with a sensitivity-based selection of second-order groups, a reduced yet highly effective set of twelve second-order groups is identified. This reduced set retains the predictive power comparable to more complex models while significantly reducing the number of parameters. Linear regression is applied to model enthalpies and Gibbs free energies of formation for a wide temperature range. To test broader applicability, the model is further extended to properties that require nonlinear regression, including critical temperatures, critical pressures, acentric factors, and liquid densities. For all cases, the proposed model achieves high predictive accuracy, demonstrating its robustness and generalizability. This methodology balances interpretability, efficiency, and performance, making it suitable for both research and industrial thermodynamic modelling.

Shape-selective adsorption in zeolites plays a pivotal role in catalytic hydroisomerization of long-chain alkanes, a key process in producing sustainable aviation fuels from Fischer–Tropsch products. Accurately predicting adsorption behavior for the large number of alkane isomers in different zeolite frameworks is computationally intensive. To address this, we have developed a machine learning framework that rapidly and accurately predicts Henry coefficients of linear (C1–C30) and branched (C4–C20) alkanes in one-dimensional zeolites. Using descriptors based on chain length, branching patterns, and molecular graphs, we evaluate multiple ML models, including Random Forest, XGBoost, CatBoost, TabPFN, and D-MPNN in MTT-, MTW-, MRE-, and AFI-type zeolites. TabPFN and D-MPNN offer the highest predictive accuracy. Active learning further boosts model performance by efficiently selecting diverse and structurally informative isomers. We also uncover activity cliffs, where small changes in molecular structure lead to sharp variations in adsorption, and demonstrate that targeted oversampling of these cases improves model robustness. Finally, we combine the ML-predicted Henry coefficients with gas-phase thermodynamics to compute reaction equilibrium distributions for C16 hydroisomerization. This integrated, data-driven approach enables efficient screening and design of shape-selective zeolite catalysts, thereby reducing the need for costly simulations

Experimental screening of Metal Organic Frameworks (MOFs) for separation applications can be costly and time-consuming. Computational methods can provide many benefits in this process, as expensive compounds and a wide range of operating conditions can be tested while crucial mechanistic insights are gained. TAMOF-1, a recently developed MOF, stands out for its exceptional stability, robustness and cost-effective synthesis. Its good CO2 uptake capacity makes it a promising agent for flue gas separation applications. In this work, we combine experiments with simulations at the atomistic and numerical level to investigate the adsorption and separation of CO2 and N2. Using Monte Carlo simulations, we accurately reproduce experimental adsorption isotherms and elucidate the adsorption mechanisms. TAMOF-1 effectively separates CO2 from N2 because of preferential binding sites near Cu2+ atoms. To assess separation performance in equilibrium at different conditions along the entire isotherm pressure range, adsorbed mole fractions, selectivities, and the trade-off between selectivity and uptake (TSN) are calculated. The dynamic separation performance is assessed by breakthrough experiments and numerical simulations, demonstrating efficient dynamic separation of CO2 and N2, with CO2 being retained in the column.

Heat pumps, which recycle waste heat, are a promising technology for reducing CO₂ emissions. Efficiently using low-grade waste heat remains challenging due to the limitations of standard heat exchangers and the need for more effective working fluids. This work introduces a multi-scale methodology that combines force field-based Monte Carlo simulations, quantum mechanics, and equations of state to explore the potential of formic acid as a new reactive fluid in thermodynamic cycles. Formic acid exhibits dimerization behavior, forming cyclic dimers in the gas phase, which can enhance the thermodynamic efficiency of heat recovery systems. The dimerization reaction of formic acid is crucial because it integrates chemical energy into thermodynamic processes, potentially improving the performance of heat pumps and other energy systems. The study implements umbrella sampling in Monte Carlo simulations to compute the thermodynamic properties of HCOOH dimerization, including equilibrium constants, enthalpy, and entropy. Results from two different methods to study dimer formation, namely the dimer counter method and the potential of mean force method, show strong agreement with the enthalpy of dimerization of −60.46 kJ mol⁻¹ and −62.91 kJ mol⁻¹, and entropy of −137.36 J mol⁻¹K⁻¹ and −146.98 J mol⁻¹K⁻¹, respectively. A very good agreement of the Monte Carlo results with Quantum Mechanics and experimental data validates the accuracy of the simulations. For phase equilibrium properties, the Peng–Robinson equation of state, coupled with advanced mixing rules, was applied and compared to Monte Carlo simulations in the Gibbs ensemble. This approach enabled the determination of the Global Phase Equilibrium of the system, vaporization enthalpy, phase composition, vapor and liquid densities of the coexisting phases, and entropy as a function of temperature. The agreement between the thermodynamic model and Monte Carlo simulations confirms the reliability of the methodology in capturing the phase behavior of the system. The findings demonstrate a promising approach for discovering and characterizing new reactive fluids, contributing to more efficient and sustainable energy technologies.

We present RASPA3, a molecular simulation code for computing adsorption and diffusion in nanoporous materials and thermodynamic and transport properties of fluids. It implements force field based classical Monte Carlo/molecular dynamics in various ensembles. In this article, we introduce the new additions and changes compared to RASPA2. RASPA3 is rewritten from the ground up in C++23 with speed and code readability in mind. Transition-matrix Monte Carlo is added to compute the density of states and free energies. The Monte Carlo code for rigid molecules is based on quaternions, and the atomic positions needed in the energy evaluation are recreated from the center of mass position and quaternion orientation. The expanded ensemble methodology for fractional molecules, with a scaling parameter λ between 0 and 1, now also keeps track of analytic expressions of dU/dλ, allowing independent verification of the chemical potential using thermodynamic integration. The source code is freely available under the MIT license on GitHub. Using this code, we compare four Monte Carlo (MC) insertion/deletion techniques: unbiased Metropolis MC, Configurational-Bias Monte Carlo (CBMC), Continuous Fractional Component MC (CFCMC), and CB/CFCMC. We compare particle distribution shapes, acceptance ratios, accuracy and speed of isotherm computation, enthalpies of adsorption, and chemical potentials, over a wide range of loadings and systems, for the grand canonical ensemble and for the Gibbs ensemble.

The confinement effect of porous materials on the thermodynamical equilibrium of the CO₂ hydrogenation reaction presents a cost-effective alternative to transition metal catalysts. In metal-organic frameworks, the type of metal center has a greater impact on the enhancement of formic acid production than the scale of confinement resulting from the pore size. The M-MOF-74 series enables a comprehensive study of how different metal centers affect HCOOH production, minimizing the effect of pore size. In this work, molecular simulations were used to analyze the adsorption of HCOOH and the CO₂ hydrogenation reaction in M-MOF-74, where M = Ni, Cu, Co, Fe, Mn, Zn. We combine classical simulations and density functional theory calculations to gain insights into the mechanisms that govern the low coverage adsorption of HCOOH in the surrounding of the metal centers of M-MOF-74. The impact of metal centers on the HCOOH yield was assessed by Monte Carlo simulations in the grand-canonical ensemble, using gas-phase compositions of CO₂, H₂, and HCOOH at chemical equilibrium at 298.15-800 K, 1-60 bar. The performance of M-MOF-74 in HCOOH production follows the same order as the uptake and the heat of HCOOH adsorption: Ni > Co > Fe > Mn > Zn > Cu. Ni-MOF-74 increases the mole fraction of HCOOH by ca. 10⁵ times compared to the gas phase at 298.15 K, 60 bar. Ni-MOF-74 has the potential to be more economically attractive for CO₂ conversion than transition metal catalysts, achieving HCOOH production at concentrations comparable to the highest formate levels reported for transition metal catalysts and offering a more valuable molecular form of the product.

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.

Entropies for alkane isomers longer than C10 are computed using our recently developed linear regression model for thermochemical properties which is based on second-order group contributions. The computed entropies show excellent agreement with experimental data and data from Scott’s tables which are obtained from a statistical mechanics-based correlation. Entropy production and heat input are calculated for the hydroisomerization of C7 isomers in various zeolites (FAU-, ITQ-29-, BEA-, MEL-, MFI-, MTW-, and MRE-types) at 500 K at chemical equilibrium. Small variations in these properties are observed because of the differences in reaction equilibrium distributions for these zeolites. The effect of chain length on heat input and entropy production is also studied for the hydroisomerization of C7, C8, C10, and C14 isomers in MTW-type zeolite at 500 K. For longer chains, both heat input and entropy production increase. Enthalpies and absolute entropies of C7 hydroisomerization reaction products in MTW-type zeolite increase with higher temperatures. These findings highlight the accuracy of our linear regression model in computing entropies for alkanes and provide insight for designing and optimizing zeolite-catalyzed hydroisomerization processes.

Hydrogen peroxide plays a key role in many environmental and industrial chemical processes. We performed classical Molecular Dynamics and Continuous Fractional Component Monte Carlo simulations to calculate thermodynamic properties of H₂O₂ in aqueous solutions. The quality of the available force fields for H₂O₂ developed by Orabi and English (2018) [67], and by Cordeiro (2014) [69] was systematically evaluated. To assess which water force field is suitable for predicting properties of H₂O₂ in aqueous solutions, four widely used water force fields were used, namely the TIP3P, TIP4P/2005, TIP5P-E, and a modified TIP3P force field. While the computed densities of pure H₂O₂ in the temperature range of 253 - 353 K using the force field by Orabi & English are in excellent agreement with experimental results, the densities using the force field by Cordeiro are underestimated by 3%. The TIP4P/2005 force field in combination with the H₂O₂ force field developed by Orabi & English can predict the densities of H₂O₂ aqueous solution for the whole range of H₂O₂ mole fractions in very good agreement with experimental results. The TIP4P/2005 force field in combination with either of the H₂O₂ force fields can predict the viscosities of H₂O₂ aqueous solutions for the whole range of H₂O₂ mole fractions in reasonably good agreement with experimental results. The computed diffusion coefficients for H₂O₂ and water molecules using the TIP4P/2005 force field with either of the H₂O₂ force fields are almost constant for the whole range of H₂O₂ mole fractions. Hydrogen bond analysis showed a steady increase in the number of hydrogen bonds with the solute concentrations in H₂O₂ aqueous solutions for all combinations except for the Cordeiro-TIP5P-E and Orabi-TIP5P-E systems, which showed a minimum at intermediate concentrations. The Cordeiro force field for H₂O₂ in combination with either of the water force fields can predict the Henry coefficients of H₂O₂ in water in better agreement with experimental values than the force field by Orabi & English.

We present the RUPTURA code (https://github.com/iraspa/ruptura) as a free and open-source software package (MIT license) for (1) the simulation of gas adsorption breakthrough curves, (2) mixture prediction using methods like the Ideal Adsorption Solution Theory (IAST), segregated-IAST and explicit isotherm models, and (3) fitting of isotherm models on computed or measured adsorption isotherm data. The combination with the RASPA software enables computation of breakthrough curves directly from adsorption simulations in the grand-canonical ensemble. RUPTURA and RASPA have similar input styles. IAST is implemented near machine precision but we also provide several explicit mixture prediction methods that are non-iterative and potentially faster than IAST. The code supports a wide variety of isotherm models like Langmuir, Anti-Langmuir, BET, Henry, Freundlich, Sips, Langmuir-Freundlich, Redlich-Peterson, Toth, Unilan, O'Brian & Myers, Asymptotic Temkin, and Bingel & Walton. The isotherm model parameters can easily be obtained by the fitting module. Breakthrough plots and animations of the column properties are automatically generated. In addition to highlighting the code, we also review all the developed techniques from literature for mixture prediction, breakthrough simulations, and isotherm model fitting, and provide a tutorial discussing the workflows.

Ideal Adsorbed Solution Theory (IAST) is a common method for modelling mixture adsorption isotherms based on pure component isotherms. When the adsorbent has distinct adsorption sites, the segregated version of IAST (SIAST) provides improved adsorbed loadings compared to IAST. We have adopted the concept of SIAST and applied it to an explicit isotherm model which takes into account the different sizes of the adsorbates: the so called Segregated Explicit Isotherm (SEI). The purpose of SEI is to have an explicit adsorption model that can consider both size-effects of the co-adsorbed molecules and surface heterogeneities. In sharp contrast to IAST and SIAST, no iterative scheme is required in case of SEI, which leads to much faster simulations. A comparative study has been performed to analyse the adsorption isotherms calculated using these three methods. The adsorbed loadings predicted by SEI and SIAST are in excellent agreement with the Grand-Canonical Monte Carlo (GCMC) simulation data. The loadings estimated by IAST show considerable deviations from the GCMC data at high pressures. Breakthrough curve modelling is used to compare the effects of these three models at dynamic conditions. The explicit model (SEI) leads to the fastest simulation run time, followed by SIAST.

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.

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.

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).

According to the ISO 14687-2:2019 standard, the water content of H2 fuel for transportation and stationary applications should not exceed 5 ppm (molar). To achieve this water content, zeolites can be used as a selective adsorbent for water. In this work, a computational screening study is carried out for the first time to identify potential zeolite frameworks for the drying of high-pressure H2 gas using Monte Carlo (MC) simulations. We show that the Si/Al ratio and adsorption selectivity have a negative correlation. 218 zeolites available in the database of the International Zeolite Association are considered in the screening. We computed the adsorption selectivity of each zeolite for water from the high-pressure H2 gas having water content relevant to vehicular applications and near saturation. It is shown that due to the formation of water clusters, the water content in the H2 gas has a significant effect on the selectivity of zeolites with a helium void fraction larger than 0.1. Under each operating condition, five most promising zeolites are identified based on the adsorption selectivity, the pore limiting diameter, and the volume of H2 gas that can be dried by 1 dm3 of zeolite. It is shown that at 12.3 ppm (molar) water content, structures with helium void fractions smaller than 0.07 are preferred. The structures identified for 478 ppm (molar) water content have helium void fractions larger than 0.26. The proposed zeolites can be used to dry 400-8000 times their own volume of H2 gas depending on the operating conditions. Our findings strongly indicate that zeolites are potential candidates for the drying of high-pressure H2 gas.