280 results found
Papadopoulos AI, Perdomo FA, Tzirakis F, et al., 2021, Molecular engineering of sustainable phase-change solvents: From digital design to scaling-up for CO2 capture, CHEMICAL ENGINEERING JOURNAL, Vol: 420, ISSN: 1385-8947
Febra SA, Bernet T, Mack C, et al., 2021, Extending the SAFT-gamma Mie approach to model benzoic acid, diphenylamine, and mefenamic acid: Solubility prediction and experimental measurement, Fluid Phase Equilibria, Vol: 540, Pages: 1-20, ISSN: 0378-3812
The prediction of the solubility of active pharmaceutical ingredients (APIs) is a significant challenge whichis of importance in pharmaceutical applications and solvent selection. Here, we extend the table of groupinteractions (3 like interactions, 47 unlike interactions) of the SAFT-γ Mie group-contribution equation ofstate to model the phase behaviour and solubility of mefenamic acid, a nonsteroidal anti-inflammatorydrug, in a range of solvents. In addition to mefenamic acid, we also consider its molecular synthons:benzoic acid and diphenylamine. New experimental solubility data are presented for the three moleculesin a range of solvents, and three new SAFT-γ Mie functional groups are defined (aCCOOH, aCNHaC andCH3CO) and characterised, together with their interactions with solvent groups. Literature data for thevapour pressure, single-phase density, saturation density, vapourisation enthalpy, bubble temperature,dew temperature, and bubble pressure are used to characterise the new group interactions. Solubilitydata are used to characterise the new group-group interactions only if there are no other experimentaldata available. The transferability and predictive accuracy of the new models are assessed by comparing the theoretical predictions with the experimental solubility data. Our comparison includes alcohols,ketones, and esters as families of solvents and mixed-solvent solubility predictions.
Diamanti A, Ganase Z, Grant E, et al., 2021, Mechanism, kinetics and selectivity of a Williamson ether synthesis: elucidation under different reaction conditions, REACTION CHEMISTRY & ENGINEERING, Vol: 6, Pages: 1195-+, ISSN: 2058-9883
Watson OL, Jonuzaj S, McGinty J, et al., 2021, Computer Aided Design of Solvent Blends for Hybrid Cooling and Antisolvent Crystallization of Active Pharmaceutical Ingredients, ORGANIC PROCESS RESEARCH & DEVELOPMENT, Vol: 25, Pages: 1123-1142, ISSN: 1083-6160
Gu B, Adjiman C, Xu X, 2021, Correlations for concentration polarisation and pressure drop in spacer-filled RO membrane modules based on CFD simulations, Membranes, Vol: 11, ISSN: 2077-0375
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 r
Adjiman CS, Sahinidis N, Vlachos DG, et al., 2021, Process Systems Engineering Perspective on the Design of Materials and Molecules, INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH, Vol: 60, Pages: 5194-5206, ISSN: 0888-5885
Bowskill DH, Sugden IJ, Konstantinopoulos S, et al., 2021, Crystal structure prediction methods for organic molecules: state of the art., Annual Review of Chemical and Biomolecular Engineering, Vol: 14, ISSN: 1947-5438
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. Expected final online publication date for the Annual Review of Chemical and Biomolecular Engineering, Volume 12 is June 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
Jackson G, Perdomo Hurtado FA, Khalit SH, et al., 2021, Description of the thermodynamics and fluid-phase behaviour of aqueous solutions of linear, branched, and cyclic amines, AIChE Journal, Vol: 67, Pages: 1-19, ISSN: 0001-1541
The SAFT‐ɣ Mie group‐contribution equation of state is used to represent the fluid‐phase behaviour of aqueous solutions of a variety of linear, branched, and cyclic amines. New group interactions are developed in order to model the mixtures of interest, including the like and unlike interactions between alkyl primary, secondary, and tertiary amine groups (NH2, NH, N), cyclic secondary and tertiary amine groups (cNH, cN), and cyclohexylamine groups (cCHNH, cCHN) with water (H2O). The group‐interaction parameters are estimated from appropriate experimental thermodynamic data for pure amines and selected mixtures. By taking advantage of the group‐contribution nature of the method, one can describe the fluid‐phase behaviour of mixtures of molecules comprising those groups over broad ranges of temperature, pressure, and composition. A number of aqueous solutions of amines are studied including linear, branched aliphatic, and cyclic amines. Liquid‐liquid equilibria (LLE) bounded by lower critical solution temperatures (LCSTs) have been reported experimentally and are reproduced here with SAFT‐ɣ Mie approach. The main feature of the approach is the ability not only to represent accurately the experimental data employed in the parameter estimation, but also to predict the vapour‐liquid, liquid‐liquid, and vapor‐liquid‐liquid equilibria, and LCSTs with the same set of parameters. Pure compound and binary phase diagrams of diverse types of amines and their aqueous solutions are assessed in order to demonstrate the main features of the thermodynamic and fluid‐phase behaviour.
Lee YS, Galindo A, Jackson G, et al., 2021, An approach for simultaneous computer-aided solvent design and process design for CO<inf>2</inf> chemical absorption processes, Computer Aided Chemical Engineering, Pages: 167-172
In the field of Computer-Aided Molecular and Process Design (CAMPD), a variety of solution methods have been developed to handle the complexities associated with the non-convexity and non-linearity of molecular structure-property and process models. However, mostalgorithms are prone to failing to generate feasible solutions when the integrated solvent-process model renders a significant portion of the search space infeasible. In this work, we propose a solution approach for the integrated design of an optimal chemical absorption process in which tailored feasibility tests are incorporated into a process optimisation problem. The solution approach allows the exploration of a design space without unnecessary difficulties by recognising infeasibilities. The effectiveness of the approach is demonstrated on an aqueous amine solvent-based CO2 capture process.
Karia T, Adjiman CS, Chachuat B, 2021, Global Optimization of Mixed-Integer Polynomial Programs via Quadratic Reformulation, Computer Aided Chemical Engineering, Pages: 655-661
Mixed-integer polynomial programs (MIPOPs) frequently arise in chemical engineering applications such as pooling, blending and operations planning. Many global optimization solvers rely on mixed-integer linear (MIP) relaxations of MIPOPs and solve them repeatedly as part of a branch-and-bound algorithm using commercial MIP solvers. GUROBI, one of the prominent MIP solvers, recently added the capability to solve mixed-integer quadratically-constrained quadratic programs (MIQCQPs). This paper investigates global optimization of MIPOPs via their reformulation as MIQCQPs followed by their solution to global optimality using GUROBI. The effectiveness of this approach is tested on 60 instances of MIPOPs selected from the library MINLPLib. The performance of the MIQCQP reformulation approach is compared to the state-of-the-art global solvers BARON, ANTIGONE and SCIP in GAMS. For the case of single threading, a reduction of 28% and 42% compared to SCIP and ANTIGONE respectively is observed. This approach, therefore, holds promise for integration into existing global solvers to handle MIPOPs.
Haslam AJ, Gonzalez-Perez A, Di Lecce S, et al., 2020, Expanding the Applications of the SAFT-gamma Mie Group-Contribution Equation of State: Prediction of Thermodynamic Properties and Phase Behavior of Mixtures, JOURNAL OF CHEMICAL AND ENGINEERING DATA, Vol: 65, Pages: 5862-5890, ISSN: 0021-9568
Kohns M, Lazarou G, Forte E, et al., 2020, Predictive models for the phase behaviour and solution properties of weak electrolytes: nitric, sulfuric and carbonic acid, Physical Chemistry Chemical Physics, Vol: 22, Pages: 15248-15269, ISSN: 1463-9076
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 the 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 acid, 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. Here 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.
Di Lecce S, Lazarou G, Khalit SH, et al., 2020, Modelling and prediction of the thermophysical properties of aqueous mixtures of choline geranate and geranic acid (CAGE) using SAFT-gamma Mie (vol 9, pg 38017, 2019), RSC ADVANCES, Vol: 10, Pages: 19463-19465
Lee L, Graham E, Galindo A, et al., 2020, A comparative study of multi-objective optimization methodologies for molecular and process design, Computers and Chemical Engineering, Vol: 136, ISSN: 0098-1354
The need to consider multiple objectives in molecular design, whether based on techno-economic, environmental or health and safety metrics is increasingly recognized. There is, however, limited understanding of the suitability of different multi-objective optimization algorithm for the solution of such design problems. In this work, we present a systematic comparison of the performance of five mixed-integer non-linear programming (MINLP) multi-objective optimization algorithms on the selection of computer-aided molecular design (CAMD) and computer-aided molecular and process design (CAMPD) problems. The five methods are designed to address the discrete and nonlinear nature of the problem, with the aim of generating an accurate approximation of the Pareto front. They include: a weighted sum approach without global search phases (SWS), a weighted sum approach with simulated annealing (SA), a weighted sum approach with multi level single linkage (MLSL), the sandwich algorithm with MLSL and the non dominated sorting genetic algorithm-II (NSGA-II). The algorithms are compared systematically in two steps. The effectiveness of the global search methods is evaluated with SWS, WSSA and WSML. WSML is found to be most effective and a comparative analysis of WSML, SDML and NSGA-II is then undertaken. As a test set of these optimization techniques, two of CAMD and one CAMPD problems of varying dimensionality are formulated as case studies. The results show that the sandwich algorithm with MLSL provides the most efficient generation of a diverse set of Pareto points, leading to the construction of an approximate Pareto front close to exact Pareto front.
Papadopoulos A, Shavalieva G, Papadokonstantakis S, et al., 2020, An approach for simultaneous computer-aided molecular design with holistic sustainability assessment: Application to phase-change CO2 capture solvents, COMPUTERS & CHEMICAL ENGINEERING, Vol: 135, ISSN: 0098-1354
Bowskill DHH, Tropp UE, Gopinath S, et al., 2020, Beyond a heuristic analysis: integration of process and working-fluid design for organic Rankine cycles, MOLECULAR SYSTEMS DESIGN & ENGINEERING, Vol: 5, Pages: 493-510, ISSN: 2058-9689
Paulavicius R, Adjiman CS, 2020, New bounding schemes and algorithmic options for the Branch-and-Sandwich algorithm, JOURNAL OF GLOBAL OPTIMIZATION, Vol: 77, Pages: 197-225, ISSN: 0925-5001
Paulavičius R, Gao J, Kleniati P-M, et al., 2020, BASBL: Branch-And-Sandwich BiLevel solver. Implementation and computational study with the BASBLib test set, Computers & Chemical Engineering, Vol: 132, Pages: 1-23, ISSN: 0098-1354
We describe BASBL, our implementation of the deterministic global optimization algorithm Branch-and-Sandwich for a general class of nonconvex/nonlinear bilevel problems, within the open-source MINOTAUR framework. The solver incorporates the original Branch-and-Sandwich algorithm and modifications proposed in (Paulavičius and Adjiman, J. Glob. Opt., 2019, Submitted). We also introduce BASBLib, an extensive online library of bilevel benchmark problems collected from the literature and designed to enable contributions from the bilevel optimization community. We use the problems in the current release of BASBLib to analyze the performance of BASBL using different algorithmic options and we identify a set of default options that provide good overall performance. Finally, we demonstrate the application of BASBL to a set of flexibility index problems including linear and nonlinear constraints.
Zhang Y, Sugden IJ, Reutzel-Edens SM, et al., 2020, A systematic study of state-of-the-art methods in crystal structure prediction for organic hydrates
Hydrates are co-crystalline materials containing water as one of the molecules in the crystal lattice. The incorporationof water into the crystal lattice produces a unit cell different from that of the anhydrate and, consequently, the physicalproperties of the hydrate can differ significantly from those of the anhydrate. The existence and stability of hydrates isan important consideration in the development of pharmaceutical products: the prevalence of water duringmanufacturing and storage can mean that neat forms of an active pharmaceutical ingredient can undergo a phasetransition to hydrate form, impacting the effectiveness of the drug. Crystal structure prediction (CSP) methods can inprinciple be useful in identifying likely hydrates, by undertaking searches for all polymorphs of water and one or moregiven compounds for a given co-crystal stoichiometry. Minimal information is needed, typically just the chemicalconnectivity diagram , to search for the low lattice energy arrangements of the constituent atoms in space. Applications of CSP to hydrates have resulted in mixed success so far. In the fifth blind test organised by CambridgeCrystallographic Data Centre, one of the targets was a hydrate but none of the 10 groups that attempted to predict itsstructure put forward the correct structure within their shortlist. In the sixth blind test , only 8 groups submittedpredicted structures for the hydrate target, and only one group generated the experimental structure within theirshortlist. In order to gain a better understanding of the challenges that make CSP for hydrates difficult, we present a systematicevaluation of a CSP state-of-the-art method for organic hydrates, in which the lattice energy is partitioned intointramolecular and intermolecular contributions. Intramolecular interactions are modelled via quantum mechanicalcalculations , and intermolecular interactions are divided into electrostatics, modelled using ab initio derived distributedmultipoles , and repu
Wehbe M, Haslam A, Adjiman CS, et al., 2020, Predicting optimal salt forms for active pharmaceutical ingredients using the SAFT-y mie equation of state
Jonuzaj S, Watson OL, Ottoboni S, et al., 2020, Computer-aided Solvent Mixture Design for the Crystallisation and Isolation of Mefenamic Acid, Editors: Pierucci, Manenti, Bozzano, Manca, Publisher: ELSEVIER SCIENCE BV, Pages: 649-654
Konstantinopoulos S, Sugden IJ, Reutzel-Edens SM, et al., 2020, An atomistic lattice dynamics approach for free energy calculations within crystal structure prediction studies
A plethora of organic molecules exhibit polymorphism, which refers to the ability of chemical compounds to pack intodifferent crystalline motifs. This phenomenon is of special importance both to industry and academia since physicaland chemical properties, such as solubility, bioavailability and mechanical strength may vary tremendously betweenpolymorphs. From a thermodynamic standpoint, polymorphs can be identified as minima on the free energy (FE)landscape, with the most stable form corresponding to the global minimum and other forms corresponding to localminima (metastable structures). This thermodynamic understanding has motivated the development of crystalstructure prediction (CSP) tools that are designed to determine all polymorphs for a given compound with the correctorder of stability based on minimal information, such as the chemical connectivity diagram . Recent advances in CSP were highlighted in the last blind test organised by Cambridge Crystallographic Data Centre .It is worth noting that only 7 out of the 25 groups participating in the last test have incorporated FE calculations withintheir workflow, while the remaining groups used only lattice energy in their predictions, thus neglecting temperatureand vibrational effects. Lattice dynamics (LD) theory was deployed successfully for the evaluation of vibrational freeenergies, utilizing either dispersion-corrected periodic density functional theory (DFT-d) or force field methods basedon distributed multipoles expansion (DMA). DFT-d can provide very accurate results at a high computational cost,whereas the DMA-based approach provides a good trade-off between accuracy and efficiency but cannot account forinternal modes arising from intramolecular vibrations. A limitation of both methods is that they rely on the constructionof supercells, which increases computational demands and results in some ambiguity in the generation of dispersioncurves. In this work, we present a recently-developed methodology for pe
Bowskill DH, Sugden IJ, George N, et al., 2020, Efficient Parameterization of a Surrogate Model of Molecular Interactions in Crystals, Editors: Pierucci, Manenti, Bozzano, Manca, Publisher: ELSEVIER SCIENCE BV, Pages: 493-498
Golbert J, Adjiman CS, Brandon NP, 2019, Micro-structural Modelling of SOFC Anodes, ECS Transactions, Vol: 7, Pages: 2041-2047
Di Lecce S, Galindo A, Khalit SH, et al., 2019, Modelling and prediction of the thermophysical properties of aqueous mixtures of Choline Geranate and Geranic acid (CAGE) using SAFT-g Mie, RSC Advances: an international journal to further the chemical sciences, Vol: 9, Pages: 38017-38031, ISSN: 2046-2069
Deep eutectic solvents and room temperature ionic liquids are increasingly recognised as appro-priate materials for use as active pharmaceutical ingredients and formulation additives. Aque-ous mixtures of choline and geranate (CAGE), in particular, have been shown to offer promisingbiomedical properties but the understanding of the thermophysical behaviour of these mixturesremains limited. Here, we develop interaction potentials for use in the SAFT–γgroup–contributionapproach, to study the thermodynamic properties and phase behaviour of aqueous mixtures ofcholine geranate and geranic acid. The determination of the interaction parameters betweenchemical functional groups is carried out in a successive fashion, characterising each group basedon those previously developed. The parameters of the groups relevant to geranic acid are esti-mated using experimental phase–equilibrium data such as vapour pressure and saturated–liquiddensity of simple pure components (n–alkenes, branched alkenes and carboxylic acids) and thephase equilibrium data of mixtures (aqueous solutions of branched alkenes and of carboxylicacids). Geranate is represented by further incorporating the anionic carboxylate group, COO−,which is characterised using aqueous solution data of sodium carboxylate salts, assuming fulldissociation of the salt in water. Choline is described by incorporating the cationic quaternaryammonium group, N+, using data on choline choride solutions. The osmotic pressure of aque-ous mixtures of CAGE at several concentrations is predicted and compared to experimental dataobtained as part of our work to assess the accuracy of the modelling platform. The SAFT–γMieapproach is shown to be predictive, providing a good description of the measured data for a widerange of mixtures and properties. Furthermore, the new group interaction parameters neededto represent CAGE extend the set of functional group
Jonuzaj S, Cui J, Adjiman CS, 2019, Computer-aided design of optimal environmentally benign solvent-based adhesive products, Computers and Chemical Engineering, Vol: 130, ISSN: 0098-1354
The manufacture of improved adhesive products that meet specified target properties has attracted increasing interest over the last decades. In this work, a general systematic methodology for the design of optimal adhesive products with low environmental impact is presented. The proposed approach integrates computer-aided design tools and Generalised Disjunctive Programming (GDP), a logic-based framework, to formulate and solve the product design problem. Key design decisions in product design (i.e., how many components should be included in the final product, which active ingredients and solvent compounds should be used and in what proportions) are optimised simultaneously. This methodology is applied to the design of solvent-based acrylic adhesives, which are commonly used in construction. First, optimal product formulations are determined with the aim to minimize toxicity. This reveals that number of components in the product formulation does not correlate with performance and that high performance can be achieved by investigating different number of components as well as by optimising all ingredients simultaneously rather than sequentially. The relation between two competing objectives (product toxicity and concentration of the active ingredient) is then explored by obtaining a set of Pareto optimal solutions. This leads to significant trade-offs and large areas of discontinuity driven by discrete changes in the list of optimal ingredients in the product.
Febra SA, Aasen A, Adjiman CS, et al., 2019, Intramolecular bonding in a statistical associating fluid theory of ring aggregates, MOLECULAR PHYSICS, ISSN: 0026-8976
Borhani T, Garcia-Munoz S, Luciani C, et al., 2019, Hybrid QSPR models for the prediction of the free energy of solvation of organic solute/solvent pairs, Physical Chemistry Chemical Physics, Vol: 21, Pages: 13706-13720, ISSN: 1463-9076
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 s 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 for the training set. The best PLS model includes six latent variables, and has a R2 value of 0.91 and a RMSE of 0.52 kcal/mol. 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.
Sugden IJ, Adjiman C, Pantelides C, 2019, Accurate and efficient representation of intramolecular energy in ab initio generation of crystal structures. II. Smoothed intramolecular potentials, Acta Crystallographica Section B: Structural Science, Vol: 75, Pages: 423-433, ISSN: 0108-7681
The application of Crystal Structure Prediction (CSP) to industrially-relevant molecules requires the handling of increasingly large and flexible compounds. We present a revised model for the effect of molecular flexibility on the lattice energy that removes the discontinuities and non-differentiabilities present in earlier models (Sugden et al., 2016), with a view to improving the performance of CSP. The approach is based on the concept of computing a weighted average of local models, and has been implemented within the CrystalPredictor code. Through the comparative investigation of several compounds studied in earlier literature, we show that this new model results in large reductions in computational effort (of up to 65%) and in significant increases in reliability. The approach is further applied to investigate, for the first time, the computational polymorphic landscape of flufenamic acid for Z’=1 structures, resulting in the successful identification of all three experimentally resolved polymorphs within reasonable computational time.
Nerantzis D, Adjiman C, 2019, Tighter αBB relaxations through a refi nement scheme for the scaled Gerschgorin theorem, Journal of Global Optimization, Vol: 73, Pages: 467-483, ISSN: 0925-5001
Of central importance to the αBB algorithm is the calculation of the α values that guarantee the convexity of the underestimator. Improvement (reduction) of these values can result in tighter underestimators and thus increase the performance of the algorithm. For instance, it was shown by Wechsung et al. (J Glob Optim 58(3):429-438, 2014) that the emergence of the cluster effect can depend on the magnitude of the α values. Motivated by this, we present a refinement method that can improve (reduce) the magnitude of α values given by the scaled Gerschgorin method and thus create tighter convex underestimators for the αBB algorithm. We apply the new method and compare it with the scaled Gerschgorin on randomly generated interval symmetric matrices as well as interval Hessians taken from test functions. As a measure of comparison, we use the maximal separation distance between the original function and the underestimator. Based on the results obtained, we conclude that the proposed refinement method can significantly reduce the maximal separation distance when compared to the scaled Gerschgorin method. This approach therefore has the potential to improve the performance of the αBB algorithm.
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