Modeling the Thermodynamic Properties of Saturated Lactones in Nonideal Mixtures with the SAFT-γ Mie Approach.

The prediction of the thermodynamic properties of lactones is an important challenge in the flavor, fragrance, and pharmaceutical industries. Here, we develop a predictive model of the phase behavior of binary mixtures of lactones with hydrocarbons, alcohols, ketones, esters, aromatic compounds, water, and carbon dioxide. We extend the group-parameter matrix of the statistical associating fluid theory SAFT-γ Mie group-contribution method by defining a new cyclic ester group, denoted cCOO. The group is composed of two spherical Mie segments and two association electron-donating sites of type e1 that can interact with association electron-accepting sites of type H in other molecules. The model parameters of the new cCOO group interactions (1 like interaction and 17 unlike interactions) are characterized to represent target experimental data of physical properties of pure fluids (vapor pressure, single-phase density, and vaporization enthalpy) and mixtures (vapor-liquid equilibria, liquid-liquid equilibria, solid-liquid equilibria, density, and excess enthalpy). The robustness of the model is assessed by comparing theoretical predictions with experimental data, mainly for oxolan-2-one, 5-methyloxolan-2-one, and oxepan-2-one (also referred to as γ-butyrolactone, γ-valerolactone, and ε-caprolactone, respectively). The calculations are found to be in very good quantitative agreement with experiments. The proposed model allows for accurate predictions of the thermodynamic properties and highly nonideal phase behavior of the systems of interest, such as azeotrope compositions. It can be used to support the development of novel molecules and manufacturing processes.

Predictive models for the phase behaviour and solution properties of weak electrolytes: nitric, sulphuric, and carbonic acids.

The distribution of ionic species in electrolyte systems is important in many fields of science and engineering, ranging from the study of degradation mechanisms to the design of systems for electrochemical energy storage. Often, other phenomena closely related to ionic speciation, such as ion pairing, clustering and hydrogen bonding, which are difficult to investigate experimentally, are also of interest. Here, we develop an accurate molecular approach, accounting for reactions as well as association and ion pairing, to deliver a predictive framework that helps validate experiment and guides future modelling of speciation phenomena of weak electrolytes. We extend the SAFT-VRE Mie equation of state [D. K. Eriksen et al., Mol. Phys., 2016, 114, 2724-2749] to study aqueous solutions of nitric, sulphuric, and carbonic acids, considering complete and partially dissociated models. In order to incorporate the dissociation equilibria, correlations to experimental data for the relevant thermodynamic equilibrium constants of the dissociation reactions are taken from the literature and are imposed as a boundary condition in the calculations. The models for water, the hydronium ion, and carbon dioxide are treated as transferable and are taken from our previous work. We present new molecular models for nitric acid, and the nitrate, bisulfate, sulfate, and bicarbonate anions. The resulting framework is used to predict a range of phase behaviour and solution properties of the aqueous acids over wide ranges of concentration and temperature, including the degree of dissociation, as well as the activity coefficients of the ionic species, and the activity of water and osmotic coefficient, density, and vapour pressure of the solutions. The SAFT-VRE Mie models obtained in this manner provide a means of elucidating the mechanisms of association and ion pairing in the systems studied, complementing the experimental observations reported in the literature.

Hybrid QSPR models for the prediction of the free energy of solvation of organic solute/solvent pairs.

Due to the importance of the Gibbs free energy of solvation in understanding many physicochemical phenomena, including lipophilicity, phase equilibria and liquid-phase reaction equilibrium and kinetics, there is a need for predictive models that can be applied across large sets of solvents and solutes. In this paper, we propose two quantitative structure property relationships (QSPRs) to predict the Gibbs free energy of solvation, developed using partial least squares (PLS) and multivariate linear regression (MLR) methods for 295 solutes in 210 solvents with total number of data points of 1777. Unlike other QSPR models, the proposed models are not restricted to a specific solvent or solute. Furthermore, while most QSPR models include either experimental or quantum mechanical descriptors, the proposed models combine both, using experimental descriptors to represent the solvent and quantum mechanical descriptors to represent the solute. Up to twelve experimental descriptors and nine quantum mechanical descriptors are considered in the proposed models. Extensive internal and external validation is undertaken to assess model accuracy in predicting the Gibbs free energy of solvation for a large number of solute/solvent pairs. The best MLR model, which includes three solute descriptors and two solvent properties, yields a coefficient of determination (R2) of 0.88 and a root mean squared error (RMSE) of 0.59 kcal mol-1 for the training set. The best PLS model includes six latent variables, and has an R2 value of 0.91 and a RMSE of 0.52 kcal mol-1. The proposed models are compared to selected results based on continuum solvation quantum chemistry calculations. They enable the fast prediction of the Gibbs free energy of solvation of a wide range of solutes in different solvents.

Repulsion-dispersion parameters for the modelling of organic molecular crystals containing N, O, S and Cl.

In lattice energy models that combine ab initio and empirical components, it is important to ensure consistency between these components so that meaningful quantitative results are obtained. A method for deriving parameters of atom-atom repulsion dispersion potentials for crystals, tailored to different ab initio models, is presented. It is based on minimization of the sum of squared deviations between experimental and calculated structures and energies. The solution algorithm is designed to avoid convergence to local minima in the parameter space by combining a deterministic low-discrepancy sequence for the generation of multiple initial parameter guesses with an efficient local minimization algorithm. The proposed approach is applied to derive transferable exp-6 potential parameters suitable for use in conjunction with a distributed multipole electrostatics model derived from isolated molecule charge densities calculated at the M06/6-31G(d,p) level of theory. Data for hydrocarbons, azahydrocarbons, oxohydrocarbons, organosulphur compounds and chlorohydrocarbons are used for the estimation. A good fit is achieved for the new set of parameters with a mean absolute error in sublimation enthalpies of 4.1 kJ mol-1 and an average rmsd15 of 0.31 Å. The parameters are found to perform well on a separate cross-validation set of 39 compounds.

On the use of molecular-based thermodynamic models to assess the performance of solvents for CO2 capture processes: monoethanolamine solutions.

Predictive models play an important role in the design of post-combustion processes for the capture of carbon dioxide (CO2) emitted from power plants. A rate-based absorber model is presented to investigate the reactive capture of CO2 using aqueous monoethanolamine (MEA) as a solvent, integrating a predictive molecular-based equation of state: SAFT-VR SW (Statistical Associating Fluid Theory-Variable Range, Square Well). A distinctive physical approach is adopted to model the chemical equilibria inherent in the process. This eliminates the need to consider reaction products explicitly and greatly reduces the amount of experimental data required to model the absorber compared to the more commonly employed chemical approaches. The predictive capabilities of the absorber model are analyzed for profiles from 10 pilot plant runs by considering two scenarios: (i) no pilot-plant data are used in the model development; (ii) only a limited set of pilot-plant data are used. Within the first scenario, the mass fraction of CO2 in the clean gas is underestimated in all but one of the cases, indicating that a best-case performance of the solvent can be obtained with this predictive approach. Within the second scenario a single parameter is estimated based on data from a single pilot plant run to correct for the dramatic changes in the diffusivity of CO2 in the reactive solvent. This parameter is found to be transferable for a broad range of operating conditions. A sensitivity analysis is then conducted, and the liquid viscosity and diffusivity are found to be key properties for the prediction of the composition profiles. The temperature and composition profiles are sensitive to thermodynamic properties that correspond to major sources of heat generation or dissipation. The proposed modelling framework can be used as an early assessment of solvents to aid in narrowing the search space, and can help in determining target solvents for experiments and more detailed modelling.

General computational algorithms for ab initio crystal structure prediction for organic molecules.

The prediction of the possible crystal structure(s) of organic molecules is an important activity for the pharmaceutical and agrochemical industries, among others, due to the prevalence of crystalline products. This chapter considers the general requirements that crystal structure prediction (CSP) methodologies need to fulfil in order to be able to achieve reliable predictions over a wide range of organic systems. It also reviews the current status of a multistage CSP methodology that has recently proved successful for a number of systems of practical interest. Emphasis is placed on recent developments that allow a reconciliation of conflicting needs for, on the one hand, accurate evaluation of the energy of a proposed crystal structure and on the other hand, comprehensive search of the energy landscape for the reliable identification of all low-energy minima. Finally, based on the experience gained from this work, current limitations and opportunities for further research in this area are identified. We also consider issues relating to the use of empirical models derived from experimental data in conjunction with ab initio CSP.

Group contribution methodology based on the statistical associating fluid theory for heteronuclear molecules formed from Mie segments.

A generalization of the recent version of the statistical associating fluid theory for variable range Mie potentials [Lafitte et al., J. Chem. Phys. 139, 154504 (2013)] is formulated within the framework of a group contribution approach (SAFT-γ Mie). Molecules are represented as comprising distinct functional (chemical) groups based on a fused heteronuclear molecular model, where the interactions between segments are described with the Mie (generalized Lennard-Jonesium) potential of variable attractive and repulsive range. A key feature of the new theory is the accurate description of the monomeric group-group interactions by application of a high-temperature perturbation expansion up to third order. The capabilities of the SAFT-γ Mie approach are exemplified by studying the thermodynamic properties of two chemical families, the n-alkanes and the n-alkyl esters, by developing parameters for the methyl, methylene, and carboxylate functional groups (CH3, CH2, and COO). The approach is shown to describe accurately the fluid-phase behavior of the compounds considered with absolute average deviations of 1.20% and 0.42% for the vapor pressure and saturated liquid density, respectively, which represents a clear improvement over other existing SAFT-based group contribution approaches. The use of Mie potentials to describe the group-group interaction is shown to allow accurate simultaneous descriptions of the fluid-phase behavior and second-order thermodynamic derivative properties of the pure fluids based on a single set of group parameters. Furthermore, the application of the perturbation expansion to third order for the description of the reference monomeric fluid improves the predictions of the theory for the fluid-phase behavior of pure components in the near-critical region. The predictive capabilities of the approach stem from its formulation within a group-contribution formalism: predictions of the fluid-phase behavior and thermodynamic derivative properties of compounds not included in the development of group parameters are demonstrated. The performance of the theory is also critically assessed with predictions of the fluid-phase behavior (vapor-liquid and liquid-liquid equilibria) and excess thermodynamic properties of a variety of binary mixtures, including polymer solutions, where very good agreement with the experimental data is seen, without the need for adjustable mixture parameters.

Accurate statistical associating fluid theory for chain molecules formed from Mie segments.

A highly accurate equation of state (EOS) for chain molecules formed from spherical segments interacting through Mie potentials (i.e., a generalized Lennard-Jones form with variable repulsive and attractive exponents) is presented. The quality of the theoretical description of the vapour-liquid equilibria (coexistence densities and vapour pressures) and the second-derivative thermophysical properties (heat capacities, isobaric thermal expansivities, and speed of sound) are critically assessed by comparison with molecular simulation and with experimental data of representative real substances. Our new EOS represents a notable improvement with respect to previous versions of the statistical associating fluid theory for variable range interactions (SAFT-VR) of the generic Mie form. The approach makes rigorous use of the Barker and Henderson high-temperature perturbation expansion up to third order in the free energy of the monomer Mie system. The radial distribution function of the reference monomer fluid, which is a prerequisite for the representation of the properties of the fluid of Mie chains within a Wertheim first-order thermodynamic perturbation theory (TPT1), is calculated from a second-order expansion. The resulting SAFT-VR Mie EOS can now be applied to molecular fluids characterized by a broad range of interactions spanning from soft to very repulsive and short-ranged Mie potentials. A good representation of the corresponding molecular-simulation data is achieved for model monomer and chain fluids. When applied to the particular case of the ubiquitous Lennard-Jones potential, our rigorous description of the thermodynamic properties is of equivalent quality to that obtained with the empirical EOSs for LJ monomer (EOS of Johnson et al.) and LJ chain (soft-SAFT) fluids. A key feature of our reformulated SAFT-VR approach is the greatly enhanced accuracy in the near-critical region for chain molecules. This attribute, combined with the accurate modeling of second-derivative properties, allows for a much improved global representation of the thermodynamic properties and fluid-phase equilibria of pure fluids and their mixtures.

Uncovering the Most Kinetically Influential Reaction Pathway Driving the Generation of HCN from Oxyma/DIC Adduct: A Theoretical Study.

The combination of ethyl (hydroxyimino)cyanoacetate (Oxyma) and diisopropylcarbodiimide (DIC) has demonstrated superior performance in amino acid activation for peptide synthesis. However, it was recently reported that Oxyma and DIC could react to generate undesired hydrogen cyanide (HCN) at 20 °C, raising safety concerns for the practical use of this activation strategy. To help minimize the risks, there is a need for a comprehensive investigation of the mechanism and kinetics of the generation of HCN. Here we show the results of the first systematic computational study of the underpinning mechanism, including comparisons with experimental data. Two pathways for the decomposition of the Oxyma/DIC adduct are derived to account for the generation of HCN and its accompanying cyclic product. These two mechanisms differ in the electrophilic carbon atom attacked by the nucleophilic sp2-nitrogen in the cyclization step and in the cyclic product generated. On the basis of computed "observed" activation energies, ΔG obs ⧧, the mechanism that proceeds via the attack of the sp2-nitrogen at the oxime carbon is identified as the most kinetically favorable one, a conclusion that is supported by closer agreement between predicted and experimental 13C NMR data. These results can provide a theoretical basis to develop a design strategy for suppressing HCN generation when using Oxyma/DIC for amino acid activation.

The polymorphs of ROY: application of a systematic crystal structure prediction technique.

We investigate the ability of current ab initio crystal structure prediction techniques to identify the polymorphs of 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile, also known as ROY because of the red, orange and yellow colours of its polymorphs. We use a methodology combining the generation of a large number of structures based on a computationally inexpensive model using the CrystalPredictor global search algorithm, and the further minimization of the most promising of these structures using the CrystalOptimizer local minimization algorithm which employs an accurate, yet efficiently constructed, model based on isolated-molecule quantum-mechanical calculations. We demonstrate that this approach successfully predicts the seven experimentally resolved structures of ROY as lattice-energy minima, with five of these structures being within the 12 lowest energy structures predicted. Some of the other low-energy structures identified are likely candidates for the still unresolved polymorphs of this molecule. The relative stability of the predicted structures only partially matches that of the experimentally resolved polymorphs. The worst case is that of polymorph ON, whose relative energy with respect to Y is overestimated by 6.65 kJ mol(-1). This highlights the need for further developments in the accuracy of the energy calculations.

Efficient Screening of Coformers for Active Pharmaceutical Ingredient Cocrystallization.

Controlling the physical properties of solid forms for active pharmaceutical ingredients (APIs) through cocrystallization is an important part of drug product development. However, it is difficult to know a priori which coformers will form cocrystals with a given API, and the current state-of-the-art for cocrystal discovery involves an expensive, time-consuming, and, at the early stages of pharmaceutical development, API material-limited experimental screen. We propose a systematic, high-throughput computational approach primarily aimed at identifying API/coformer pairs that are unlikely to lead to experimentally observable cocrystals and can therefore be eliminated with only a brief experimental check, from any experimental investigation. On the basis of a well-established crystal structure prediction (CSP) methodology, the proposed approach derives its efficiency by not requiring any expensive quantum mechanical calculations beyond those already performed for the CSP investigation of the neat API itself. The approach and assumptions are tested through a computational investigation on 30 potential 1:1 multicomponent systems (cocrystals and solvate) involving 3 active pharmaceutical ingredients and 9 coformers and one solvent. This is complemented with a detailed experimental investigation of all 30 pairs, which led to the discovery of five new cocrystals (three API-coformer combinations, a polymorphic cocrystal example, and one with different stoichiometries) and a cis-aconitic acid polymorph. The computational approach indicates that, for some APIs, a significant proportion of all potential API/coformer pairs could be investigated with only a brief experimental check, thereby saving considerable experimental effort.

How many more polymorphs of ROY remain undiscovered.

With 12 crystal forms, 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecabonitrile (a.k.a. ROY) holds the current record for the largest number of fully characterized organic crystal polymorphs. Four of these polymorph structures have been reported since 2019, raising the question of how many more ROY polymorphs await future discovery. Employing crystal structure prediction and accurate energy rankings derived from conformational energy-corrected density functional theory, this study presents the first crystal energy landscape for ROY that agrees well with experiment. The lattice energies suggest that the seven most stable ROY polymorphs (and nine of the twelve lowest-energy forms) on the Z' = 1 landscape have already been discovered experimentally. Discovering any new polymorphs at ambient pressure will likely require specialized crystallization techniques capable of trapping metastable forms. At pressures above 10 GPa, however, a new crystal form is predicted to become enthalpically more stable than all known polymorphs, suggesting that further high-pressure experiments on ROY may be warranted. This work highlights the value of high-accuracy crystal structure prediction for solid-form screening and demonstrates how pragmatic conformational energy corrections can overcome the limitations of conventional density functionals for conformational polymorphs.

Towards crystal structure prediction of complex organic compounds--a report on the fifth blind test.

Following on from the success of the previous crystal structure prediction blind tests (CSP1999, CSP2001, CSP2004 and CSP2007), a fifth such collaborative project (CSP2010) was organized at the Cambridge Crystallographic Data Centre. A range of methodologies was used by the participating groups in order to evaluate the ability of the current computational methods to predict the crystal structures of the six organic molecules chosen as targets for this blind test. The first four targets, two rigid molecules, one semi-flexible molecule and a 1:1 salt, matched the criteria for the targets from CSP2007, while the last two targets belonged to two new challenging categories - a larger, much more flexible molecule and a hydrate with more than one polymorph. Each group submitted three predictions for each target it attempted. There was at least one successful prediction for each target, and two groups were able to successfully predict the structure of the large flexible molecule as their first place submission. The results show that while not as many groups successfully predicted the structures of the three smallest molecules as in CSP2007, there is now evidence that methodologies such as dispersion-corrected density functional theory (DFT-D) are able to reliably do so. The results also highlight the many challenges posed by more complex systems and show that there are still issues to be overcome.

Correlations for Concentration Polarization and Pressure Drop in Spacer-Filled RO Membrane Modules Based on CFD Simulations.

Empirical correlations for mass transfer coefficient and friction factor are often used in process models for reverse osmosis (RO) membrane systems. These usually involve four dimensionless groups, namely Reynolds number (Re), Sherwood number (Sh), friction factor (f), and Schmidt number (Sc), with the associated coefficients and exponents being obtained by fitting to experimental data. However, the range of geometric and operating conditions covered by the experiments is often limited. In this study, new dimensionless correlations for concentration polarization (CP) modulus and friction factor are presented, which are obtained by dimensional analysis and using simulation data from computational fluid dynamics (CFD). Two-dimensional CFD simulations are performed on three configurations of spacer-filled channels with 76 combinations of operating and geometric conditions for each configuration, covering a broad range of conditions encountered in RO membrane systems. Results obtained with the new correlations are compared with those from existing correlations in the literature. There is good consistency in the predicted CP with mean discrepancies less than 6%, but larger discrepancies for pressure gradient are found among the various friction factor correlations. Furthermore, the new correlations are implemented in a process model with six spiral wound modules in series and the predicted recovery, pressure drop, and specific energy consumption are compared with a reference case obtained by ROSA (Reverse Osmosis System Analysis, The Dow Chemical Company). Differences in predicted recovery and pressure drop are up to 5% and 83%, respectively, highlighting the need for careful selection of correlations when using predictive models in process design. Compared to existing mass transfer correlations, a distinct advantage of our correlations for CP modulus is that they can be directly used to estimate the impact of permeate flux on CP at a membrane surface without having to resort to the film theory.

Crystal Structure Prediction Methods for Organic Molecules: State of the Art.

The prediction of the crystal structures that a given organic molecule is likely to form is an important theoretical problem of significant interest for the pharmaceutical and agrochemical industries, among others. As evidenced by a series of six blind tests organized over the past 2 decades, methodologies for crystal structure prediction (CSP) have witnessed substantial progress and have now reached a stage of development where they can begin to be applied to systems of practical significance. This article reviews the state of the art in general-purpose methodologies for CSP, placing them within a common framework that highlights both their similarities and their differences. The review discusses specific areas that constitute the main focus of current research efforts toward improving the reliability and widening applicability of these methodologies, and offers some perspectives for the evolution of this technology over the next decade.

Computer Aided Design of Solvent Blends for Hybrid Cooling and Antisolvent Crystallization of Active Pharmaceutical Ingredients.

Choosing a solvent and an antisolvent for a new crystallization process is challenging due to the sheer number of possible solvent mixtures and the impact of solvent composition and crystallization temperature on process performance. To facilitate this choice, we present a general computer aided mixture/blend design (CAMbD) formulation for the design of optimal solvent mixtures for the crystallization of pharmaceutical products. The proposed methodology enables the simultaneous identification of the optimal process temperature, solvent, antisolvent, and composition of solvent mixture. The SAFT-γ Mie group-contribution approach is used in the design of crystallization solvents; based on an equilibrium model, both the crystal yield and solvent consumption are considered. The design formulation is implemented in gPROMS and applied to the crystallization of lovastatin and ibuprofen, where a hybrid approach combining cooling and antisolvent crystallization is compared to each method alone. For lovastatin, the use of a hybrid approach leads to an increase in crystal yield compared to antisolvent crystallization or cooling crystallization. Furthermore, it is seen that using less volatile but powerful crystallization solvents at lower temperatures can lead to better performance. When considering ibuprofen, the hybrid and antisolvent crystallization techniques provide a similar performance, but the use of solvent mixtures throughout the crystallization is critical in maximizing crystal yields and minimizing solvent consumption. We show that our more general approach to rational design of solvent blends brings significant benefits for the design of crystallization processes in pharmaceutical and chemical manufacturing.

Correction: Modelling and prediction of the thermophysical properties of aqueous mixtures of choline geranate and geranic acid (CAGE) using SAFT-γ Mie.

[This corrects the article DOI: 10.1039/C9RA07057E.].