A Benchmark Open-Source Implementation of COSMO-SAC

Atomistic molecular dynamics simulation and COSMO-SAC approach for enhanced 1,3-propanediol extraction with imidazolium-based ionic liquids

CONTEXT

1,3-Propanediol (1,3-PDO) is a key chemical in various industries, including pharmaceuticals and material sciences, and is projected to see significant market growth. However, the current challenges in its downstream processing, particularly in terms of cost and efficiency, highlight the need for innovative solutions. Our study delves into using ionic liquids (ILs) as a potential alternative, aiming to address these critical separation challenges more sustainably and efficiently. In this study, we utilized molecular dynamics (MD) simulations and the COSMO-SAC to examine 1,3-propanediol (1,3-PDO) extraction using four imidazolium-based ionic liquids with 1-butyl-3-methylimidazolium [Bmim] cation and with different anions bis(pentafluoroethanesulfonyl)imide [NPF2]-, bis(trifluoromethylsulfonyl)imide [NTF2]-, thiocyanate [SCN]-, and trifluoromethanesulfonate [TFO]-. Molecular dynamics simulations, incorporating analysis of radial distribution functions (RDF) and spatial distribution functions (SDF), revealed that [Bmim][SCN] and [Bmim][TFO] exhibit enhanced interactions with 1,3-PDO. Notably, [Bmim][SCN] formed the most hydrogen bonds, averaging 1.639 per molecule, due to its coordinating [SCN]- anion. This was in contrast to the fewer hydrogen bonds formed by non-coordinating anions in [Bmim][NPF2] and [Bmim][NTF2]. In ternary systems, [Bmim][SCN] and [Bmim][TFO] demonstrated superior selectivity for 1,3-PDO extraction compared to the other ionic liquids, with selectivity values around 29. These findings, supported by COSMO-SAC predictive modeling, highlight the potential of [Bmim][SCN] as a promising candidate for 1,3-PDO extraction, emphasizing the importance of anion selection in optimizing ionic liquid properties for this application.

METHODS

In our study, we employed MD simulations, incorporating the OPLS-AA force field, and COSMO-SAC to investigate the extraction of 1,3-PDO using imidazolium-based ionic liquids: [Bmim][NTF2], [Bmim][NPF2], [Bmim][SCN], and [Bmim][TFO]. The MD simulations were conducted using LAMMPS software, focusing on elucidating the RDF, SDF, and hydrogen bonding. Analysis of the distribution coefficient (β) and selectivity (S) for the ternary mixture was also conducted. These aspects of the simulation were analyzed using TRAVIS and VMD software. Additionally, the COSMO-SAC model was employed to determine the activity coefficients of 1,3-PDO in the ionic liquids, with molecular optimization conducted using Gaussian16 and sigma profile calculations performed using COSMO-SAC.

Molecular insights into dicationic versus monocationic ionic liquids as a high hydrophobic alternative for the separation of phenol from waters

The hydrophobic nature of an extractant is particularly critical in the treatment of wastewater. Considering that dicationic ionic liquids (DILs) are likely to be more hydrophobic, a comparative study of the separation of phenol from waters using [NTf2]- based monocationic ionic liquids (MILs) and DILs is carried out both from experimental and theoretical analysis perspectives. Experimental results revealed that DILs exhibited superior extraction ability compared to MILs, with extraction efficiencies of 93.7% and 97.4% using [BMIM][NTf2] and [C6(MIM)2][NTf2]2 as extractants, respectively. The microscopic examination through theoretical calculations elucidated the higher hydrophobicity and extraction efficiency of DILs over MILs. The results indicated that the DIL showed stronger hydrophobicity than the MIL because the hydrogen bond strength between the DIL and water was lower than that of the MIL. Although the hydrogen bond strength between the DIL and phenol was lower than that of the MIL, the stronger van der Waals forces existed between DIL and phenol, so DIL was more efficient in extracting phenol. In addition, the experimental parameters were optimized to provide basic data for application, such as mass ratio of ILs to water, extraction time and temperature, pH, and initial phenol content. Finally, the DILs were recovered using rotary evaporation apparatus, and the results demonstrated that DILs had good recovery and reuse performance. In brief, this work could provide an effective method for the treatment of phenol-containing wastewater. And the revelation of molecular mechanism is expected to positively impact the design of high-performance task-specific ILs.

Quantum Cluster Equilibrium Theory for Multicomponent Liquids

In this work, we present a new theory to treat multicomponent liquids based on quantum-chemically calculated clusters. The starting point is the binary quantum cluster equilibrium theory, which is able to treat binary systems. The theory provides one equation with two unknowns. In order to obtain another linearly independent equation, the conservation of mass is used. However, increasing the number of components leads to more unknowns, and this requires linearly independent equations. We address this challenge by introducing a generalization of the conservation of arbitrary quantities accompanied by a comprehensive mathematical proof. Furthermore, a case study for the application of the new theory to ternary mixtures of chloroform, methanol, and water is presented. Calculated enthalpies of vaporization for the whole composition range are given, and the populations or weights of the different clusters are visualized.

Can Pure Predictions of Activity Coefficients from PC-SAFT Assist Drug-Polymer Compatibility Screening?

The bioavailability of poorly water-soluble active pharmaceutical ingredients (APIs) can be improved via the formulation of an amorphous solid dispersion (ASD), where the API is incorporated into a suitable polymeric carrier. Optimal carriers that exhibit good compatibility (i.e., solubility and miscibility) with given APIs are typically identified through experimental means, which are routinely labor- and cost-inefficient. Therefore, the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state, a popular thermodynamic model in pharmaceutical applications, is examined in terms of its performance regarding the computational pure prediction of API-polymer compatibility based on activity coefficients (API fusion properties were taken from experiments) without any binary interaction parameters fitted to API-polymer experimental data (that is, kij = 0 in all cases). This kind of prediction does not need any experimental binary information and has been underreported in the literature so far, as the routine modeling strategy used in the majority of the existing PC-SAFT applications to ASDs comprised the use of nonzero kij values. The predictive performance of PC-SAFT was systematically and thoroughly evaluated against reliable experimental data for almost 40 API-polymer combinations. We also examined the effect of different sets of PC-SAFT parameters for APIs on compatibility predictions. Quantitatively, the total average error calculated over all systems was approximately 50% in the weight fraction solubility of APIs in polymers, regardless of the specific API parametrization. The magnitude of the error for individual systems was found to vary significantly from one system to another. Interestingly, the poorest results were obtained for systems with self-associating polymers such as poly(vinyl alcohol). Such polymers can form intramolecular hydrogen bonds, which are not accounted for in the PC-SAFT variant routinely applied to ASDs (i.e., that used in this work). However, the qualitative ranking of polymers with respect to their compatibility with a given API was reasonably predicted in many cases. It was also predicted correctly that some polymers always have better compatibility with the APIs than others. Finally, possible future routes to improve the cost-performance ratio of PC-SAFT in terms of parametrization are discussed.

Solv: An Alternative Continuum Model Implementation Based on Fixed Atomic Charges, Scaled Particle Theory, and the Atom-Atom Potential Method

An alternative continuum model implementation is reported. The electrostatic contribution to the solvation Gibbs free energy utilizes the noniterative conductor-like screening model of Vyboishchikov and Voityuk (DOI: 10.1002/jcc.26531) based on the fixed partial atomic charges. The nonelectrostatic solute-solvent dispersion-repulsion energy is calculated through the Caillet-Claverie atom-atom potential method employing the grid-based approach. The nonelectrostatic cavitation energy is computed within the scaled particle theory (SPT) formalism with the solute hard-sphere radius obtained via the Pierotti-Claverie (PC) scheme, from the solute molecular surface (SPT-S) or volume (SPT-V). The solvent hard-sphere radius is derived through the fitting to the experimental total solvation free energies of 2530 neutral species in 92 solvents. Application of the model to reproduce both the absolute and relative (reaction net) solvation free energies indicates that the SPT-V approach based on the CM5 charges is the best performer. The method is suggested for the solvation free energy calculation in the nonaqueous solvents.

Molecular modelling of the thermophysical properties of fluids: expectations, limitations, gaps and opportunities

This manuscript provides an overview of the current state of the art in terms of the molecular modelling of the thermophysical properties of fluids. It is intended to manage the expectations and serve as guidance to practising physical chemists, chemical physicists and engineers in terms of the scope and accuracy of the more commonly available intermolecular potentials along with the peculiarities of the software and methods employed in molecular simulations while providing insights on the gaps and opportunities available in this field. The discussion is focused around case studies which showcase both the precision and the limitations of frequently used workflows.

VOCs absorption from gas streams using deep eutectic solvents - A review

Volatile organic compounds (VOCs) are one of the most severe atmospheric pollutants. They are mainly emitted into the atmosphere from anthropogenic sources such as automobile exhaust, incomplete fuel combustion, and various industrial processes. VOCs not only cause hazards to human health or the environment but also adversely affect industrial installation components due to their specific properties, i.e., corrosive and reactivity. Therefore, much attention is being paid to developing new methods for capturing VOCs from gaseous streams, i.e., air, process streams, waste streams, or gaseous fuels. Among the available technologies, absorption based on deep eutectic solvents (DES) is widely studied as a green alternative to other commercial processes. This literature review presents a critical summary of the achievements in capturing individual VOCs using DES. The types of used DES and their physicochemical properties affecting absorption efficiency, available methods for evaluating the effectiveness of new technologies, and the possibility of regeneration of DES are described. In addition, critical comments on the new gas purification methods and future perspectives are included.

Solid–Liquid Equilibrium in Co-Amorphous Systems: Experiment and Prediction

In this work, the solid–liquid equilibrium (SLE) of four binary systems combining two active pharmaceutical ingredients (APIs) capable of forming co-amorphous systems (CAMs) was investigated. The binary systems studied were naproxen-indomethacin, naproxen-ibuprofen, naproxen-probucol, and indomethacin-paracetamol. The SLE was experimentally determined by differential scanning calorimetry. The thermograms obtained revealed that all binary mixtures investigated form eutectic systems. Melting of the initial binary crystalline mixtures and subsequent quenching lead to the formation of CAM for all binary systems and most of the compositions studied. The experimentally obtained liquidus and eutectic temperatures were compared to theoretical predictions using the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state and conductor-like screening model for real solvents (COSMO-RS), as implemented in the Amsterdam Modeling Suite (COSMO-RS-AMS). On the basis of the obtained results, the ability of these models to predict the phase diagrams for the investigated API–API binary systems was evaluated. Furthermore, the glass transition temperature (Tg) of naproxen (NAP), a compound with a high tendency to recrystallize, whose literature values are considerably scattered, was newly determined by measuring and modeling the Tg values of binary mixtures in which amorphous NAP was stabilized. Based on this analysis, erroneous literature values were identified.

Solubility of palbociclib in supercritical carbon dioxide from experimental measurement and Peng-Robinson equation of state

Palbociclib is a poorly water-soluble medicine which acts against metastatic breast cancer cells. Among various techniques to improve the solubility of this medicine, applying supercritical technologies to produce micro- and nano-sized particles is a possible option. For this purpose, extraction of solubility data is required. In this research, the solubility of palbociclib in supercritical carbon dioxide (ScCO₂) at different equilibrium conditions was measured at temperatures between 308 and 338 K and pressures within 12-27 MPa, for the first time. The minimum and maximum solubility data were found to be 8.1 × 10^-7 (at 338 K and 12 MPa) and 2.03 × 10^-5 (at 338 K and 27 MPa), respectively. Thereafter, two sets of models, including ten semi-empirical equations and three Peng-Robinson (PR) based integrated models were used to correlate the experimental solubility data. Bian's model and PR equation of state using van der Waals mixing rules (PR + vdW) showed better accuracy among the examined semi-empirical and integrated models, respectively. Furthermore, the self-consistency of the obtained data was confirmed using two distinct semi-empirical models. At last, the total and vaporization enthalpies of palbociclib solubility in ScCO₂ were calculated from correlation results of semi-empirical equations and estimated to be 40.41 and 52.67 kJ/mol, respectively.

Physical and numerical aspects of sodium ion solvation free energies via the cluster-continuum model

Sodium cation solvation Gibbs free energies (ΔG_solv(Na⁺)) have been obtained in water, dimethylformamide, dimethyl sulfoxide, ethanol, acetone, acetonitrile, and methanol through the "monomer cycle" cluster-continuum approach where a solvent reference state is described by infinitely separated molecules. The following steps are vital for obtaining reliable ΔG_solv(Na⁺) values: (a) a meticulous conformational search involving dispersion corrected density functional theory (DFT-D) and the continuum solvation model (CSM); (b) gas-phase DFT-D geometry optimization followed by single-point (SP) domain-based local pair natural orbital coupled clusters including single, double, and partly triple excitation (DLPNO-CCSD(T)) calculations in conjunction with the complete basis set extrapolation; (c) advanced statistical thermodynamic treatment of the low harmonic frequencies (<100 cm^-1) to obtain the robust gas-phase Gibbs free energy correction; (d) gas-phase and dielectric continuum SP with non-electrostatic contributions included in the CSM; (e) an evaluation of the relative thermodynamic stability of the Na⁺(S)_n clusters to identify the number of explicit solvent molecules n to be considered. Our refined computational protocol is promising with a Pearson correlation coefficient between the predicted and experimental data, ρ, of 0.82, and the mean signed and mean unsigned errors of 0.3 and 1.4 kcal mol^-1, respectively.

Osmotic Attraction: A New Mechanism of Nanoparticle Aggregation

Solvent-induced interactions of nanoparticles in colloidal solutions can substantially affect their physicochemical and transport properties. Predicting these interactions is challenging because the natural causes of the interactions are unclear. Here, we present a comprehensive experimental and theoretical study of the coagulation stability of the surfacted magnetic colloids. The magnetite nanoparticles stabilized by erucic acid were dispersed in 19 different good solvents. The colloidal stability was reduced by the gradual addition of a precipitant. As a precipitant, 19 other liquids were used. We show that coagulation is not associated with either dispersion or magnetic interactions. The coagulation mechanism is due to the osmotic attraction of nanoparticles induced by a specific local distribution of precipitant molecules. The precipitant molecules are repelled from the hydrophobic tails of the surfactant and form a depleted zone inside the surfactant layer leading to the appearance of the osmotic attraction between the nanoparticles and their subsequent coagulation when the critical concentration of the precipitant is reached. The quantitative description of the phenomenon is carried out within the framework of the generalized Asakura-Oosawa model of the attractive depletion forces between two adjacent particles and the Langmuir adsorption model for the equilibrium concentration of precipitant molecules in the surfactant layer of nanoparticles. The calculated precipitant critical concentrations, the coagulation curves of the polydisperse systems, and the variation of the coagulation criterion occurring upon changing the surfactant are in good agreement with the experimental data. The osmotic attraction mechanism is equally suitable for nanoparticles of any nature─plasmonic, semiconductor, or magnetic. This is determined by the surfactant-solvent interactions and is generic for many solvent-mediated systems taken at arbitrary concentrations of precipitant.

Purely Predicting the Pharmaceutical Solubility: What to Expect from PC-SAFT and COSMO-RS?

A pair of popular thermodynamic models for pharmaceutical applications, namely, the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state and the conductor-like screening model for real solvents (COSMO-RS) are thoroughly benchmarked for their performance in predicting the solubility of active pharmaceutical ingredients (APIs) in pure solvents. The ultimate goal is to provide an illustration of what to expect from these progressive frameworks when applied to the thermodynamic solubility of APIs based on activity coefficients in a purely predictive regime without specific experimental solubility data (the fusion properties of pure APIs were taken from experiments). While this kind of prediction represents the typical modus operandi of the first-principles-aided COSMO-RS, PC-SAFT is a relatively highly parametrized model that relies on experimental data, against which its pure-substance and binary interaction parameters (k_ij) are fitted. Therefore, to make this benchmark as fair as possible, we omitted any binary parameters of PC-SAFT (i.e., k_ij = 0 in all cases) and preferred pure-substance parameter sets for APIs not trained to experimental solubility data. This computational approach, together with a detailed assessment of the obtained solubility predictions against a large experimental data set, revealed that COSMO-RS convincingly outperformed PC-SAFT both qualitatively (i.e., COSMO-RS was better in solvent ranking) and quantitatively, even though the former is independent of both substance- and mixture-specific experimental data. Regarding quantitative comparison, COSMO-RS outperformed PC-SAFT for 9 of the 10 APIs and for 63% of the API-solvent systems, with root-mean-square deviations of the predicted data from the entire experimental data set being 0.82 and 1.44 log units, respectively. The results were further analyzed to expand the picture of the performance of both models with respect to the individual APIs and solvents. Interestingly, in many cases, both models were found to qualitatively incorrectly predict the direction of deviations from ideality. Furthermore, we examined how the solubility predictions from both models are sensitive to different API parametrizations.

Atom surface fragment contribution method for predicting the toxicity of ionic liquids

In this study, a novel method-atom surface fragment contribution (ASFC)-was proposed for assessing the properties of compounds. We developed a predictive model using the ASFC method based on the sigma surface areas (S_σ-surface) of fragments/groups for estimating the toxicity of ILs. A toxicity dataset of 140 ILs towards leukemia rat cell line (ICP-81) was gathered and employed to train and validate models. The S_σ-surface values of atoms in each group were firstly calculated from the COSMO profiles of cations and anions for ILs. Then the S_σ-surface values of 26 groups were obtained and used as input descriptors for modelling. The R² and MSE of the built ASFC model were 0.924 and 0.071, respectively. Results indicate that the ASFC model developed by the new approach possesses great accuracy and reliability. In total, the ASFC method has extensive potential for the application of estimating diverse properties of ILs and other compounds due to its remarkable advantages.

Making thermodynamic models of mixtures predictive by machine learning: matrix completion of pair interactions

Predictive models of thermodynamic properties of mixtures are paramount in chemical engineering and chemistry. Classical thermodynamic models are successful in generalizing over (continuous) conditions like temperature and concentration. On the other hand, matrix completion methods (MCMs) from machine learning successfully generalize over (discrete) binary systems; these MCMs can make predictions without any data for a given binary system by implicitly learning commonalities across systems. In the present work, we combine the strengths from both worlds in a hybrid approach. The underlying idea is to predict the pair-interaction energies, as they are used in basically all physical models of liquid mixtures, by an MCM. As an example, we embed an MCM into UNIQUAC, a widely-used physical model for the Gibbs excess energy. We train the resulting hybrid model in a Bayesian machine-learning framework on experimental data for activity coefficients in binary systems of 1146 components from the Dortmund Data Bank. We thereby obtain, for the first time, a complete set of UNIQUAC parameters for all binary systems of these components, which allows us to predict, in principle, activity coefficients at arbitrary temperature and composition for any combination of these components, not only for binary but also for multicomponent systems. The hybrid model even outperforms the best available physical model for predicting activity coefficients, the modified UNIFAC (Dortmund) model.

Embedding matrix completion methods from machine learning in classical thermodynamic models creates powerful hybrid models for predicting properties of mixtures.

Alkane/Water Partition Coefficient Calculation Based on the Modified AM1 Method and Internal Hydrogen Bonding Sampling Using COSMO-RS

We introduce a physics-based model for calculating partition coefficients of solutes between water and alkanes, using a combination of a semi-empirical method for COSMO charge density calculation and statistical sampling of internal hydrogen bonds (IHBs). We validate the model on the experimental partition data (∼3500 molecules) of small organics, drug-like molecules, and statistical assessment of modeling of proteins and ligand drugs. The model combines two novel algorithms: a bond-correction method for improving the calculation of COSMO charge density from AM1 calculations and a sampling method to deal with IHBs. From a comparison of simulated and experimental partition coefficients, we find a root-mean-square deviation of roughly one log 10 unit. From IHB analysis, we know that IHBs can be present in two states: open (in water) and closed (in apolar solvent). The difference can lead to a shift of as much as two log 10 units per IHB; not taking this effect into account can lead to substantial errors. The method takes a few minutes of calculation time on a single core, per molecule. Although this is still much slower than quantitative structure–activity relationship, it is much faster than molecular simulations and can be readily incorporated into any screening method.

A predictive PC-SAFT EOS based on COSMO for pharmaceutical compounds

The present study was conducted to develop a predictive type of PC-SAFT EOS by incorporating the COSMO computations. With the proposed model, the physical adjustable inputs to PC-SAFT EOS were determined from the suggested correlations with dependency to COSMO computation results. Afterwards, we tested the reliability of the proposed predictive PC-SAFT EOS by modeling the solubility data of certain pharmaceutical compounds in pure and mixed solvents and their octanol/water partition coefficients. The obtained RMSE based on logarithmic scale for the predictive PC-SAFT EOS was 1.435 for all of the solubility calculations. The reported values (1.435) had a lower value than RMSE for COSMO-SAC model (4.385), which is the same as that for RMSE for COSMO-RS model (1.412). The standard RMSE for octanol/water partition coefficient of the investigated pharmaceutical compounds was estimated to be 1.515.

Investigation of COSMO-SAC model for solubility and cocrystal formation of pharmaceutical compounds

In this study, a predictive model named COSMO-SAC was investigated in solid/liquid equilibria for pharmaceutical compounds. The examined properties were the solubility of drug in the pure and mixed solvents, octanol/water partition coefficient, and cocrystal formation. The results of the original COSMO-SAC model (COSMO-SAC (2002)) was compared with a semi-predictive model named Flory–Huggins model and a revised version of the COSMO-SAC (COSMO-SAC (2010)). The results indicated the acceptable accuracy of the COSMO-SAC (2002) in the considered scope. The results emphasized on the suitability of the COSMO-SAC model for simple molecules containing C, H, and O by covalent and hydrogen bonding interactions. Applicability of the COSMO-SAC for more complicated molecules made of various functional groups such as COO and COOH doubly requires more modification in the COSMO-SAC.

Assessment of the SM12, SM8, and SMD Solvation Models for Predicting Limiting Activity Coefficients at 298.15 K

The SMx (x = 12, 8, or D) universal solvent models are implicit solvent models which using electronic structure calculations can compute solvation free energies at 298.15 K. While solvation free energy is an important thermophysical property, within the thermodynamic modeling of phase equilibrium, limiting (or infinite dilution) activity coefficients are preferred since they may be used to parameterize excess Gibbs free energy models to model phase equilibrium. Conveniently, the two quantities are related. Therefore the present study was performed to assess the ability to use the SMx universal solvent models to predict limiting activity coefficients. Two methods of calculating the limiting activity coefficient where compared: (1) the solvation free energy and self-solvation free energy were both predicted and (2) the self-solvation free energy was computed using readily available vapor pressure data. Overall the first method is preferred as it results in a cancellation of errors, specifically for the case in which water is a solute. The SM12 model was compared to both the Universal Quasichemical Functional-group Activity Coefficients (UNIFAC) and modified separation of cohesive energy density (MOSCED) models. MOSCED was the highest performer, yet had the smallest available compound inventory. UNIFAC and SM12 exhibited comparable performance. Therefore further exploration and research should be conducted into the viability of using the SMx models for phase equilibrium calculations.

Molecular Mean-Field Theory of Ionic Solutions: A Poisson-Nernst-Planck-Bikerman Model

We have developed a molecular mean-field theory—fourth-order Poisson–Nernst–Planck–Bikerman theory—for modeling ionic and water flows in biological ion channels by treating ions and water molecules of any volume and shape with interstitial voids, polarization of water, and ion-ion and ion-water correlations. The theory can also be used to study thermodynamic and electrokinetic properties of electrolyte solutions in batteries, fuel cells, nanopores, porous media including cement, geothermal brines, the oceanic system, etc. The theory can compute electric and steric energies from all atoms in a protein and all ions and water molecules in a channel pore while keeping electrolyte solutions in the extra- and intracellular baths as a continuum dielectric medium with complex properties that mimic experimental data. The theory has been verified with experiments and molecular dynamics data from the gramicidin A channel, L-type calcium channel, potassium channel, and sodium/calcium exchanger with real structures from the Protein Data Bank. It was also verified with the experimental or Monte Carlo data of electric double-layer differential capacitance and ion activities in aqueous electrolyte solutions. We give an in-depth review of the literature about the most novel properties of the theory, namely Fermi distributions of water and ions as classical particles with excluded volumes and dynamic correlations that depend on salt concentration, composition, temperature, pressure, far-field boundary conditions etc. in a complex and complicated way as reported in a wide range of experiments. The dynamic correlations are self-consistent output functions from a fourth-order differential operator that describes ion-ion and ion-water correlations, the dielectric response (permittivity) of ionic solutions, and the polarization of water molecules with a single correlation length parameter.