Development of accurate force fields for a Pareto screening of high-performance metal-organic frameworks

Jelle Wieme
Puzzelen met moleculaire bouwblokken: het ontwerp van nieuwe materialen met de computer“I have not failed. I’ve just found 10 000 ways that won’t work.”                                                                                                                         Thomas EdisonMetaal-organische roosters (MOF’s) vormen sedert enkele jaren een nieuwe klasse van materialen.  Ze vertonen interessante eigenschappen die kunnen gebruikt worden in verscheidene toepassingen zoals katalysatoren in chemische processen.

Development of accurate force fields for a Pareto screening of high-performance metal-organic frameworks

Puzzelen met moleculaire bouwblokken: het ontwerp van nieuwe materialen met de computer“I have not failed. I’ve just found 10 000 ways that won’t work.”

                                                                                                                         Thomas Edison

Metaal-organische roosters (MOF’s) vormen sedert enkele jaren een nieuwe klasse van materialen.  Ze vertonen interessante eigenschappen die kunnen gebruikt worden in verscheidene toepassingen zoals katalysatoren in chemische processen. Deze materialen worden gevormd door verschillende moleculaire bouwstenen met elkaar te combineren. Dit kan echter op bijna een oneindig aantal manieren. Computersimulaties kunnen het onderzoek naar de beste materialen in de goede richting duwen.

Iedere dag zijn wetenschappers op zoek naar nieuwe en betere materialen voor praktische toepassingen. Decennialang werd dit gedaan door het beproefde concept van trial-and-error. Nieuwe materialen werden uitgeprobeerd om te beoordelen of ze voldoen aan alle productvereisten. Deze aanpak gaf aanleiding tot enkele bekende succesverhalen zoals het ontwerp van de gloeilamp. Na ettelijke mislukte pogingen om een geschikte gloeidraad te vinden, vond Thomas Edison het juiste materiaal. Deze manier van werken is echter tijdrovend en duur, en in het huidige economische klimaat niet wenselijk. De oplossing is het selecteren van een materiaal na het uitrekenen van zijn eigenschappen op de computer.

Een klasse van materialen waar deze computationele aanpak zich uitstekend toe leent zijn de metaal-organische roosters (MOF’s). Omstreeks de eeuwwisseling werden deze nanoporeuze kristallijne materialen voor het eerst gesynthetiseerd. Het ontwerpen van MOF’s wordt gezien als één van de grootste successen van de nanotechnologie omwille van hun exceptionele eigenschappen. Neem nu het volgende voorbeeld: het inwendig oppervlak van slechts één gram van sommige MOF's kan tot veertig tennisvelden groot zijn. Bovendien vertonen andere MOF’s een structurele flexibiliteit die aanleiding geeft tot  ‘ademend’ gedrag (zie onderstaande figuur) onder invloed van bijvoorbeeld variërende temperatuur, concentratie van CO2 in de omgeving en druk. Deze eigenschappen zorgen ervoor dat MOF’s uitstekende kandidaten zijn voor een brede waaier aan toepassingen zoals katalysatoren in chemische processen en als detectoren op de nanoschaal. 

MOF’s zijn opgebouwd uit twee types van moleculaire bouwblokken: anorganische metaalclusters en organische moleculen. De atypische opbouw van deze materialen is verantwoordelijk voor hun uitzonderlijke eigenschappen. De metaalclusters worden onderling verbonden door de organische moleculen die ook wel organische linkers worden genoemd. Dit alles gebeurt op de nanoschaal en  geeft aanleiding tot een bijna ontelbaar aantal mogelijke MOF’s. Recentelijk werd dit geïllustreerd door een Amerikaanse onderzoeksgroep die op basis van slechts 102 van deze bouwblokken meer dan 130 000 hypothetische MOF’s hebben voorgesteld. Gedurende de afgelopen jaren zijn er duizenden nieuwe MOF’s geproduceerd. De ganse verzameling van hypothetische structuren maken en testen in het labo is niet mogelijk en zelfs voor een computationele aanpak is deze grote hoeveelheid een hele uitdaging.

In het Centrum voor Moleculaire Modellering werd gedurende dit onderzoek een nieuwe methodologie ontwikkeld die toelaat om de verzameling van hypothetische MOF’s op een efficiënte manier te doorzoeken naar waardevolle kandidaten voor verschillende toepassingen. Op basis van kwantummechanische computerberekeningen op de moleculaire bouwstenen wordt een model - een zogenaamd krachtveld - opgesteld voor iedere MOF. Met zo’n krachtveld kan de invloed van bijvoorbeeld temperatuur en druk op het materiaal worden onderzocht en kunnen eigenschappen zoals de sterkte van het materiaal bepaald worden op een accurate wijze via simulaties. Aangezien er slechts een beperkt aantal bouwblokken beschikbaar zijn, biedt deze aanpak een significant voordeel. Gedurende het onderzoek werd deze methodologie verfijnd en ze is nu klaar om toegepast te worden op de verzameling van hypothetische MOF’s.

Het selecteren en ontwerpen van nieuwe materialen voor praktische toepassingen is in het beste geval tijdrovend, maar vaak ook duur en beide zijn economisch niet wenselijk. Metaal-organische roosters, een nieuwe klasse van nanoporeuze kristallijne materialen, hebben exceptionele eigenschappen die potentieel interessant zijn voor een brede waaier aan toepassingen. Met slechts 102 bouwblokken werden recentelijk meer dan 130 000 hypothetische MOF’s voorgesteld. Met de ontwikkelde werkwijze wordt het mogelijk gemaakt om deze grote verzameling van veelbelovende materialen te karakteriseren vanop de computer. Dit alles brengt ons een stapje dichter bij het efficiënt ontwerpen van materialen.

Bibliografie

Mijn bibliografie is enkel beschikbaar in latex en pdf-formaat. Onderstaande is gekopieerd van mijn thesis(maar kan dus ook onderaan mijn scriptie gevonden worden). [1] F. Salles, A. Ghou, G. Maurin, R. G. Bell, C. Mellot-Draznieks, and G. Ferey, \MolecularDynamics Simulations of Breathing MOFs: Structural Transitions of MIL-53(Cr) upon ThermalActivation and CO2 Adsorption," Angew. Chem. Int. Ed., vol. 47, no. 44, pp. 8487{8491,2008.[2] S. Curtarolo, G. L. W. Hart, M. B. Nardelli, N. Mingo, S. Sanvito, and O. Levy, \TheHigh-Throughput Highway to Computational Materials Design," Nat. Mater., vol. 12, no. 3,pp. 191{201, 2013.[3] V. Pareto, Manuale di Economia Politica. Societa Editrice Libraria, 1906.[4] T. Bligaard, G. H. Johannesson, A. V. Ruban, H. L. Skriver, K. W. Jacobsen, and J. K.Nrskov, \Pareto-Optimal Alloys," Appl. Phys. Lett., vol. 83, no. 22, pp. 4527{4529, 2003.[5] M. P. Andersson, T. Bligaard, A. Kustov, K. E. Larsen, J. Greeley, T. Johannessen, C. H.Christensen, and J. K. J. K. Nrskov, \Toward Computational Screening in HeterogeneousCatalysis: Pareto-Optimal Methanation Catalysts," J. Catal., vol. 239, no. 2, pp. 501{506,2006.[6] C. O'Mahony and N. Wilson, \Sorted Pareto Dominance: An Extension to Pareto Dominanceand Its Application in Soft Constraints," IEEE ICTAI, vol. 1, pp. 798{805, 2012.[7] O. Aguirre and H. Taboada, \A Clustering Method Based on Dynamic Self Organizing Treesfor Post-Pareto Optimality Analysis," Procedia Comput. Sci., vol. 6, pp. 195{200, 2011.[8] I. Das, \A Preference Ordering among Various Pareto Optimal Alternatives," Struct. Optim.,vol. 18, no. 1, pp. 30{35, 1999.[9] K. Lejaeghere, S. Cottenier, and V. V. Speybroeck, \Ranking the Stars: A Rened ParetoApproach to Computational Materials Design," Phys. Rev. Lett., vol. 111, no. 7, p. 075501,2013.[10] H. Li, M. Eddaoudi, M. O'Keee, and O. M. Yaghi, \Design and Synthesis of an ExceptionallyStable and Highly Porous Metal-Organic Framework," Nature, vol. 402, no. 6759, pp. 276{279,1999.[11] M. Eddaoudi, J. Kim, N. Rosi, D. Vodak, J. Wachter, M. O'Keee, and O. M. Yaghi, \SystematicDesign of Pore Size and Functionality in Isoreticular MOFs and Their Application inMethane Storage," Science, vol. 295, no. 5554, pp. 469{472, 2002.[12] C. Serre, F. Millange, C. Thouvenot, M. Nogues, G. Marsolier, D. Louer, and G. Ferey, \VeryLarge Breathing Eect in the First Nanoporous Chromium(III)-Based Solids: MIL-53 orCrIII(OH) fO2C-C6H4-CO2g fHO2C-C6H4-CO2Hgx H2Oy," J. Am. Chem. Soc., vol. 124,no. 45, pp. 13519{13526, 2002.[13] K. S. Park, Z. Ni, A. P. C^ote, J. Y. Choi, R. Huang, F. J. Uribe-Romo, H. K. Chae,M. O'Keee, and O. M. Yaghi, \Exceptional Chemical and Thermal Stability of ZeoliticImidazolate Frameworks," Proc. Natl. Acad. Sci., vol. 103, no. 27, pp. 10186{10191, 2006.[14] L. Vanduyfhuys, T. Verstraelen, M. Vandichel, M. Waroquier, and V. Van Speybroeck, \AbInitio Parametrized Force Field for the Flexible Metal-Organic Framework MIL-53(Al)," J.Chem. Theory Comput., vol. 8, no. 9, pp. 3217{3231, 2012.[15] R. E. Morris and P. S. Wheatley, \Gas Storage in Nanoporous Materials," Angew. Chem. Int.Ed., vol. 47, no. 27, pp. 4966{4981, 2008.[16] S.-L. Li and Q. Xu, \Metal-Organic Frameworks as Platforms for Clean Energy," Energ.Environ. Sci., vol. 6, no. 6, pp. 1656{1683, 2013.[17] C. Rosler and R. A. Fischer, \Metal-Organic Frameworks as Hosts for Nanoparticles," Crys-tEngComm, vol. 17, no. 2, pp. 199{217, 2014.[18] L. E. Kreno, K. Leong, O. K. Farha, M. Allendorf, R. P. V. Duyne, and J. T. Hupp, \Metal-Organic Framework Materials as Chemical Sensors," Chem. Rev., vol. 112, no. 2, pp. 1105{1125, 2012.[19] J. Lee, O. K. Farha, J. Roberts, K. A. Scheidt, S. T. Nguyen, and J. T. Hupp, \Metal-OrganicFramework Materials as Catalysts," Chem. Soc. Rev., vol. 38, no. 5, p. 1450, 2009.[20] P. Horcajada, R. Gref, T. Baati, P. K. Allan, G. Maurin, P. Couvreur, G. Ferey, R. E.Morris, and C. Serre, \Metal-Organic Frameworks in Biomedicine," Chem. Rev., vol. 112,no. 2, pp. 1232{1268, 2012.[21] S. T. Meek, J. A. Greathouse, and M. D. Allendorf, \Metal-Organic Frameworks: A RapidlyGrowing Class of Versatile Nanoporous Materials," Adv. Mater., vol. 23, no. 2, pp. 249{267,2011.[22] M. Kurmoo, \Magnetic Metal-Organic Frameworks," Chem. Soc. Rev., vol. 38, no. 5, p. 1353,2009.[23] C. G. Silva, A. Corma, and H. Garca, \Metal-Organic Frameworks as Semiconductors," J.Mater. Chem., vol. 20, no. 16, pp. 3141{3156, 2010.[24] S. Horike, S. Shimomura, and S. Kitagawa, \Soft Porous Crystals," Nat. Chem., vol. 1, no. 9,pp. 695{704, 2009.[25] A. Schneemann, V. Bon, I. Schwedler, I. Senkovska, S. Kaskel, and R. A. Fischer, \FlexibleMetal-Organic Frameworks," Chem. Soc. Rev., vol. 43, no. 16, pp. 6062{6096, 2014.[26] C. R. Murdock, B. C. Hughes, Z. Lu, and D. M. Jenkins, \Approaches for Synthesizing BreathingMOFs by Exploiting Dimensional Rigidity," Coord. Chem. Rev., vol. 258-259, pp. 119{136,2014.[27] Y. J. Colon and R. Q. Snurr, \High-Throughput Computational Screening of Metal-OrganicFrameworks," Chem. Soc. Rev., vol. 43, no. 16, pp. 5735{5749, 2014.[28] H. Furukawa, K. E. Cordova, M. O'Keee, and O. M. Yaghi, \The chemistry and applicationsof metal-organic frameworks," Science, vol. 341, no. 6149, p. 1230444, 2013.[29] M. O'Keee, M. A. Peskov, S. J. Ramsden, and O. M. Yaghi, \The Reticular ChemistryStructure Resource (RCSR) Database Of, and Symbols For, Crystal Nets," Accts. Chem.Res., vol. 41, no. 12, pp. 1782{1789, 2008.[30] F. H. Allen, \The Cambridge Structural Database: A Quarter of a Million Crystal Structuresand Rising," Acta Crystallogr., Sect. B: Struct. Sci., vol. 58, pp. 380{388, 2002.[31] Y. G. Chung, J. Camp, M. Haranczyk, B. J. Sikora, W. Bury, V. Krungleviciute, T. Yildirim,O. K. Farha, D. S. Sholl, and R. Q. Snurr, \Computation-Ready, Experimental Metal-OrganicFrameworks: A Tool To Enable High-Throughput Screening of Nanoporous Crystals," Chem.Mat., vol. 26, no. 21, pp. 6185{6192, 2014.[32] C. E. Wilmer, M. Leaf, C. Y. Lee, O. K. Farha, B. G. Hauser, J. T. Hupp, and R. Q. Snurr,\Large-Scale Screening of Hypothetical Metal-Organic Frameworks," Nat. Chem., vol. 4, no. 2,pp. 83{89, 2012.[33] T. Watanabe and D. S. Sholl, \Accelerating Applications of Metal-Organic Frameworks forGas Adsorption and Separation by Computational Screening of Materials," Langmuir, vol. 28,no. 40, pp. 14114{14128, 2012.[34] M. Fernandez, P. G. Boyd, T. D. Da, M. Z. Aghaji, and T. K. Woo, \Rapid and AccurateMachine Learning Recognition of High Performing Metal Organic Frameworks for CO2Capture," J. Phys. Chem. Lett., vol. 5, no. 17, pp. 3056{3060, 2014.[35] C. E. Wilmer, O. K. Farha, Y.-S. Bae, J. T. Hupp, and R. Q. Snurr, \Structure-propertyrelationships of porous materials for carbon dioxide separation and capture," Energ. Environ.Sci., vol. 5, no. 12, pp. 9849{9856, 2012.[36] M. Fernandez, T. K. Woo, C. E. Wilmer, and R. Q. Snurr, \Large-Scale QuantitativeStructure-Property Relationship (QSPR) Analysis of Methane Storage in Metal-OrganicFrameworks," J. Phys. Chem. C, vol. 117, no. 15, pp. 7681{7689, 2013.[37] D. A. Gomez, J. Toda, and G. Sastre, \Screening of Hypothetical Metal-Organic Frameworksfor H2 Storage," Phys. Chem. Chem. Phys., vol. 16, no. 35, pp. 19001{19010, 2014.[38] Y. J. Colon, D. Fairen-Jimenez, C. E. Wilmer, and R. Q. Snurr, \High-Throughput Screeningof Porous Crystalline Materials for Hydrogen Storage Capacity Room Temperature," J. Phys.Chem. C, vol. 118, no. 10, pp. 5383{5389, 2014.[39] D. A. Gomez-Gualdron, C. E. Wilmer, O. K. Farha, J. T. Hupp, and R. Q. Snurr, \Exploringthe Limits of Methane Storage and Delivery in Nanoporous Materials," J. Phys. Chem. C,vol. 118, no. 13, pp. 6941{6951, 2014.[40] B. J. Sikora, R. Winnegar, D. M. Proserpio, and R. Q. Snurr, \Textural Properties of a LargeCollection of Computationally Constructed MOFs and Zeolites," Microporous and MesoporousMaterials, vol. 186, pp. 207{213, 2014.[41] B. J. Sikora, C. E. Wilmer, M. L. Greeneld, and R. Q. Snurr, \Thermodynamic Analysisof Xe/Kr Selectivity in over 137000 Hypothetical Metal-organic Frameworks," Chem. Sci.,vol. 3, no. 7, pp. 2217{2223, 2012.[42] A. U. Ortiz, A. Boutin, A. H. Fuchs, and F.-X. Coudert, \Anisotropic Elastic Properties ofFlexible Metal-Organic Frameworks: How Soft Are Soft Porous Crystals?," Phys. Rev. Lett.,vol. 109, no. 19, p. 195502, 2012.[43] A. I. Skoulidas and D. S. Sholl, \Self-Diusion and Transport Diusion of Light Gases inMetal-Organic Framework Materials Assessed Using Molecular Dynamics simulations," J.Phys. Chem. B, vol. 109, no. 33, pp. 15760{15768, 2005.[44] Q. Yang, C. Zhong, and J.-F. Chen, \Computational Study of CO2 Storage in Metal-OrganicFrameworks," J. Phys. Chem. C, vol. 112, no. 5, pp. 1562{1569, 2008.[45] Q. Yang, D. Liu, C. Zhong, and J.-R. Li, \Development of Computational Methodologiesfor Metal-Organic Frameworks and Their Application in Gas Separations," Chem. Soc. Rev.,vol. 113, no. 10, pp. 8261{8323, 2013.[46] S. Amirjalayer, M. Tapolsky, and R. Schmid, \Molecular Dynamics Simulation of BenzeneDiusion in MOF-5: Importance of Lattice Dynamics," Angew. Chem. Int. Ed., vol. 46, no. 3,pp. 463{466, 2007.[47] Y. Sun and H. Sun, \An All-Atom Force Field Developed for Zn4O(RCO2)6 Metal-OrganicFrameworks," J. Mol. Model., vol. 20, no. 3, p. 2146, 2014.[48] A. K. Rappe, C. J. Casewit, K. S. Colwell, W. A. Goddard III, and W. M. Ski, \UFF, a FullPeriodic Table Force Field for Molecular Mechanics and Molecular Dynamics Simulations,"J. Am. Chem. Soc., vol. 114, no. 25, pp. 10024{10035, 1992.[49] S. L. Mayo, B. D. Olafson, and W. A. Goddard III, \DREIDING: A Generic Force Field forMolecular Simulations," J. Phys. Chem., vol. 94, no. 26, pp. 8897{8909, 1990.[50] N. L. Allinger, Y. H. Yuh, and J. H. Lii, \Molecular Mechanics. The MM3 Force Field forHydrocarbons. 1.," J. Am. Chem. Soc., vol. 111, no. 23, pp. 8551{8566, 1989.[51] W. D. Cornell, P. Cieplak, C. I. Bayly, I. R. Gould, K. M. Merz, D. M. Ferguson, D. C.Spellmeyer, T. Fox, J. W. Caldwell, and P. A. Kollman, \A Second Generation Force Fieldfor the Simulation of Proteins, Nucleic Acids, and Organic Molecules," J. Am. Chem. Soc.,vol. 117, no. 19, pp. 5179{5197, 1995.[52] P. Dauber-Osguthorpe, V. A. Roberts, D. J. Osguthorpe, J. Wol, M. Genest, and A. T.Hagler, \Structure and Energetics of Ligand Binding to Proteins: Escherichia Coli DihydrofolateReductase-Trimethoprim, a Drug-Receptor System," Proteins: Struct., Funct., Bioinf.,vol. 4, no. 1, pp. 31{47, 1988.[53] J. M. Wang, R. M. Wolf, J. W. Caldwell, P. A. Kollman, and D. A. Case, \Development andTesting of a General Amber Force Field," J. Comput. Chem., vol. 25, no. 9, pp. 1157{1174,2004.[54] J. A. Greathouse and M. D. Allendorf, \Force Field Validation for Molecular Dynamics Simulationsof IRMOF-1 and Other Isoreticular Zinc Carboxylate Coordination Polymers," J.Phys. Chem. C, vol. 112, no. 15, pp. 5795{5802, 2008.[55] D. Dubbeldam, K. S. Walton, D. E. Ellis, and R. Q. Snurr, \Exceptional Negative ThermalExpansion in Isoreticular Metal-Organic Frameworks," Angew. Chem. Int. Ed., vol. 46, no. 24,pp. 4496{4499, 2007.[56] M. Tapolsky, S. Amirjalayer, and R. Schmid, \Ab Initio Parameterized MM3 Force Fieldfor the Metal-Organic Framework MOF-5," J. Comput. Chem., vol. 28, no. 7, pp. 1169{1176,2007.[57] Z. Hu, L. Zhang, and J. Jiang, \Development of a Force Field for Zeolitic ImidazolateFramework-8 with Structural Flexibility," J. Chem. Phys., vol. 136, no. 24, p. 244703, 2012.[58] M. A. Addicoat, N. Vankova, I. F. F. Akter, and T. Heine, \Extension of the Universal ForceField to Metal-Organic Frameworks," J. Chem. Theory Comput., vol. 10, no. 2, pp. 880{891,2013.[59] J. K. Bristow, D. Tiana, and A.Walsh, \Transferable Forceeld for Metal-Organic Frameworksfrom First-Principles: BTW-FF," J. Chem. Theory Comput., vol. 10, no. 10, pp. 4644{4652,2014.[60] R. F. W. Bader, \Atoms in Molecules," Acc. Chem. Res., vol. 18, no. 1, pp. 9{15, 1985.[61] M. Tapolsky and R. Schmid, \Systematic First Principles Parametrization of Force Fieldsfor Metal-Organic Frameworks Using a Genetic Algorithm Approach," J. Phys. Chem. B,vol. 113, no. 5, pp. 1341{1352, 2009.[62] B. H. Besler, K. M. Merz, and P. A. Kollman, \Atomic Charges Derived from Semi-EmpiricalMethods," J. Comput. Chem., vol. 11, no. 4, pp. 431{439, 1990.[63] M. Tapolsky, S. Amirjalayer, and R. Schmid, \First-Principles-Derived Force Field for CopperPaddle-Wheel-Based Metal-Organic Frameworks," J. Phys. Chem. C, vol. 114, no. 34,pp. 14402{14409, 2010.[64] S. Bureekaew, S. Amirjalayer, M. Tapolsky, C. Spickermann, T. K. Roy, and R. Schmid,\MOF-FF - A Flexible First-Principles Derived Force Field for Metal-Organic Frameworks,"Phys. Status Solidi B, vol. 250, no. 6, pp. 1128{1141, 2013.[65] S. Amirjalayer and R. Schmid, \Adsorption of Hydrocarbons in Metal-Organic Frameworks:A Force Field Benchmark on the Example of Benzene in Metal-Organic Framework 5," J.Phys. Chem. C, vol. 116, no. 29, pp. 15369{15377, 2012.[66] S. Grimme, \A General Quantum Mechanically Derived Force Field (QMDFF) for Moleculesand Condensed Phase Simulations," J. Chem. Theory Comput., vol. 10, no. 10, pp. 4497{4514,2014.[67] L. Vanduyfhuys, S. Vandenbrande, T. Verstraelen, R. Schmid, M. Waroquier, and V. VanSpeybroeck, \QuickFF: A Program for a Quick and Easy Derivation of Force Fields for Metal-Organic Frameworks from Ab Initio Input," J. Comput. Chem., vol. 36, no. 13, pp. 1015{1027,2015.[68] J. S. Grosch and F. Paesani, \Molecular-Level Characterization of the Breathing Behaviorof the Jungle-Gym-Type DMOF-1 Metal-Organic Framework," J. Am. Chem. Soc., vol. 134,no. 9, pp. 4207{4215, 2012.[69] H. Wang, L. Zhao, W. Xu, S. Wang, Q. Ding, X. Lu, and W. Guo, \The Properties of theBonding Between CO and ZIF-8 Structures: a Density Functional Theory Study," Theor.Chem. Acc., vol. 134, no. 3, pp. 1{9, 2015.[70] S. K. Burger, P. W. Ayers, and J. Schoeld, \Ecient Parameterization of Torsional Termsfor Force Fields," J. Comput. Chem., vol. 35, no. 19, pp. 1438{1445, 2014.[71] S. Hamad, S. R. G. Balestra, R. Bueno-Perez, S. Calero, and A. R. Ruiz-Salvador, \AtomicCharges for Modeling Metal-Organic Frameworks: Why and How," J. Solid State Chemistry,vol. 233, pp. 144{151, 2015.[72] H. Hu, Z. Lu, and W. Yang, \Fitting Molecular Electrostatic Potentials from Quantum MechanicalCalculations," J. Chem. Theory Comput., vol. 3, no. 3, pp. 1004{1013, 2007.[73] P. Bultinck, C. V. Alsenoy, P. W. Ayers, and R. Carbo-Dorca, \Critical Analysis and Extensionof the Hirshfeld Atoms in Molecules," J. Chem. Phys., vol. 126, no. 14, p. 144111,2007.[74] F. L. Hirshfeld, \Bonded-Atom Fragments for Describing Molecular Charge Densities," Theor.Chem. Acc., vol. 44, no. 2, pp. 129{138, 1977.[75] T. Verstraelen, S. V. Sukhomlinov, V. Van Speybroeck, M. Waroquier, and K. S. Smirnov,\Computation of Charge Distribution and Electrostatic Potential in Silicates with the Use ofChemical Potential Equalization Models," J. Phys. Chem. C, vol. 116, no. 1, pp. 490{504,2012.[76] T. Verstraelen, P. W. Ayers, V. Van Speybroeck, and M.Waroquier, \Hirshfeld-E Partitioning:AIM Charges with an Improved Trade-o between Robustness and Accurate Electrostatics,"J. Chem. Theory Comput., vol. 9, no. 5, pp. 2221{2225, 2013.[77] J. Chen and T. J. Martinez, \The dissociation catastrophe in uctuating-charge models and itsimplications for the concept of atomic electronegativity," in Advances in the Theory of Atomicand Molecular Systems (P. Piecuch, J. Maruani, G. Delgado-Barrio, and S. Wilson, eds.),vol. 19 of Progress in Theoretical Chemistry and Physics, pp. 397{415, Springer Netherlands,2009.[78] T. A. Halgren, \Merck Molecular Force Field. II. MMF94 van der Waals and ElectrostaticParameters for Intermolecular Interactions," J. Comput. Chem., vol. 17, no. 5-6, pp. 520{552,1996.[79] A. M. Walker, B. Civalleri, B. Slater, C. Mellot-Draznieks, F. Cora, C. M. Zicovich-Wilson,G. Roman-Perez, J. M. Soler, and J. D. Gale, \Flexibility in a Metal-Organic FrameworkMaterial Controlled by Weak Dispersion Forces: The Bistability of MIL-53(Al)," Angew.Chem. Int. Ed., vol. 49, no. 41, pp. 7501{7503, 2010.[80] N. L. Allinger, X. Zhou, and J. Bergsma, \Molecular Mechanics Parameters," THEOCHEM,vol. 312, no. 1, pp. 69{83, 1994.[81] S. Grimme, \Semi-Empirical GGA-Type Density Functional Constructed with a Long-RangeDispersion Correction," J. Comput. Chem., vol. 27, no. 15, pp. 1787{1799, 2006.[82] S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, \A Consistent and Accurate Ab InitioParametrization of Density Functional Dispersion Correction (DFT-D) for the 94 ElementsH-Pu," J. Chem. Phys., vol. 132, no. 15, p. 154104, 2010.[83] M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman,G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li,H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara,K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai,T. Vreven, J. A. M. Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N.Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C.Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox,J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev,A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G.Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels,  O. Farkas,J. B. Foresman, J. V. Ortiz, J. Cioslowski, and D. J. Fox, \Gaussian 09, Revision D.01,"Gaussian, Inc., 2009.[84] T. Verstraelen, V. Van Speybroeck, and M. Waroquier, \ZEOBUILDER: A GUI Toolkit forthe Construction of Complex Molecular Structures on the Nanoscale with Building Blocks,"J. Chem. Inf. Model., vol. 48, no. 7, pp. 1530{1541, 2008.[85] A. Becke, \Density-Functional Thermochemistry .3. the Role of Exact Exchange," J. Chem.Phys., vol. 98, no. 7, pp. 5648{5652, 1993.[86] M. J. Frisch, M. J. Pople, and J. S. Binkley, \Self-Consistent Molecular-Orbital Methods .25.Supplementary Functions for Gaussian-Basis Sets," J. Chem. Phys., vol. 80, no. 7, pp. 3265{3269, 1984.[87] F. Furche and J. P. Perdew, \The Performance of Semilocal and Hybrid Density Functionalsin 3d Transition-Metal Chemistry," J. Chem. Phys., vol. 124, no. 4, p. 044103, 2006.[88] T. Verstraelen, S. Vandenbrande, M. Chan, F. H. Zadeh, C. Gonzalez, and P. A. Limacher.Horton 1.2.1, http://theochem.github.com/horton/.[89] T. Verstraelen, L. Vanduyfhuys, S. Vandenbrande, and S. M. J. Rogge. Ya, yet another forceeld, http://molmod.ugent.be/software/.[90] B. Civalleri, F. Napoli, Y. Noel, C. Roetti, and R. Dovesi, \Ab-initio Prediction of MaterialsProperties with CRYSTAL: MOF-5 as a Case Study," CrystEngComm, vol. 8, no. 5, pp. 364{371, 2006.[91] D. F. Bahr, J. A. Reid, W. M. Mook, C. A. Bauer, R. Stumpf, A. J. Skulan, N. R. Moody,B. A. Simmons, M. M. Shindel, and M. D. Allendorf, \Mechanical Properties of Cubic ZincCarboxylate IRMOF-1 Metal-Organic Framework Crystals," Phys. Rev. B, vol. 76, no. 18,p. 184106, 2007.[92] P. G. Yot, Q. Ma, J. Haines, Q. Yang, A. Ghou, T. Devic, C. Serre, V. Dimitriev, G. Ferey,C. Zhong, and G. Maurin, \Large Breathing of the MOF MIL-47(V(IV)) under MechanicalPressure: A Joint Experimental-Modelling Exploration," Chem. Sci., vol. 3, no. 2, pp. 1100{1104, 2012.[93] Y. Liu, J.-H. Her, A. Dailly, A. J. Ramirez-Cuesta, D. A. Neumann, and C. M. Brown,\Reversible Structural Transition in MIL-53 with Large Temperature Hysteresis," J. Am.Chem. Soc., vol. 130, no. 35, pp. 11813{11818, 2008.[94] J. P. S. Mowat, S. R. Miller, A. M. Z. Slawin, V. R. Seymour, S. E. Ashbrook, and P. A.Wright, \Synthesis, Characterisation and Adsorption Properties of Microporous ScandiumCarboxylates with Rigid and Flexible Frameworks," Microporous Mesoporous Mater., vol. 142,no. 1, pp. 322{333, 2011.[95] C. Volkringer, T. Loiseau, N. Guillou, G. Ferey, E. Elkam, and A. Vimont, \XRD and IRStructural Investigations of a Particular Breathing Eect in the MOF-Type Gallium TerephtalateMIL-53(Ga)," Dalton Trans., no. 12, pp. 2241{2249, 2009.[96] P. Serra-Crespo, E. Stavitski, F. Kapteijn, and J. Gascon, \High Compressibility of a FlexibleMetal-Organic Framework," R. Soc. Chem. Adv., vol. 2, no. 12, pp. 5051{5053, 2012.[97] F. Millange, N. Guillou, R. I. Walton, J.-M. Greneche, I. Margiolaki, and G. Ferey, \Eect ofthe Nature of the Metal on the Breathing Steps in MOFs with Dynamic Frameworks," Chem.Commun., no. 39, pp. 4732{4734, 2008.[98] P. J. Hay and W. R. Wadt, \Abinitio Eective Core Potentials for Molecular Calculations -Potentials for the Transition-Metal Atoms Sc to Hg," J. Chem. Phys., vol. 82, no. 1, pp. 270{283, 1985.[99] I. Beurroies, M. Boulhout, P. L. Llewellyn, B. Kuchta, G. Ferey, C. Serre, and R. Denoyel,\Using Pressure to Provoke the Structural Transition of Metal-Organic Frameworks," Angew.Chem. Int. Ed., vol. 49, no. 41, pp. 7526{7529, 2010.[100] A. V. Neimark, F.-X. Coudert, C. Triguero, A. Boutin, A. H. Fuchs, I. Beurroies, and R. Denoyel,\Structural Transitions in MIL-53(Cr): View from Outside and Inside," Langmuir,vol. 27, no. 8, pp. 4734{4741, 2011.[101] J. P. S. Mowat, V. R. Seymour, J. M. Grin, S. P. Thompson, A. M. Z. Slawin, D. Fairen-Jimenez, T. Duren, S. E. Ashbrook, and P. A. Wright, \A Novel Structural Form of MIL-53Observed for the Scandium Analogue and Its Response to Temperature Variation and CO2Adsorption," Dalton Trans., vol. 41, no. 14, pp. 3938{3941, 2012.[102] H. Leclerc, T. Devic, S. Devautour-Vinot, P. Bazin, N. Audebrand, G. Ferey, M. Daturi,A. Vimont, and G. Clet, \Inuence of the Oxidation State of the Metal Center on the Flexibilityand Adsorption Properties of a Porous Metal Organic Framework," J. Phys. Chem. C,vol. 115, no. 40, pp. 19828{19840, 2011.[103] A. Boutin, D. Bousquet, A. U. Ortiz, F.-X. Coudert, A. H. Fuchs, A. Ballandras, G. Weber,I. Bezverkhyy, J.-P. Bellat, G. Ortiz, G. Chaplais, J.-L. Paillaud, C. Marichal, H. Nouali,and J. Patarin, \Temperature-Induced Structural Transitions in the Gallium-Based MIL-53Metal-Organic Framework," J. Phys. Chem. C, vol. 117, no. 16, pp. 8180{8188, 2013.[104] T. Loiseau, C. Serre, C. Huguenard, G. Fink, F. Taulelle, M. Henry, T. Bataille, and G. Ferey,\A Rationale for the Large Breathing of the Porous Aluminum Terephthalate (MIL-53) UponHydration," Chem. Eur. J., vol. 10, no. 6, pp. 1373{1382, 2004.[105] A. U. Ortiz, Etude par simulation moleculaire de la exibilite des materiaux nanoporeux:proprietes structurales, mecaniques et thermodynamiques. PhD thesis, Universite Pierre etMarie Curie - Paris VI, 2014.[106] X. Wang, J. Eckert, L. Liu, and A. J. Jacobson, \Breathing and Twisting: An Investigationof Framework Deformation and Guest Packing in Single Crystals of a Microporous VanadiumBenzenedicarboxylate," Inorg. Chem., vol. 50, no. 5, pp. 2028{2036, 2011.[107] R. S. Mulliken, \Electronic Population Analysis on LCAO-MO Molecular Wave Functions.I," J. Chem. Phys., vol. 23, no. 10, pp. 1833{1840, 1955.[108] D. E. P. Vanpoucke, J. W. Jaeken, S. De Baerdemacker, K. Lejaeghere, and V. Van Speybroeck,\Quasi-1D Physics in Metal-Organic Frameworks: MIL-47(V) from First Principles,"Beilstein J. Nanotechnol., no. 5, pp. 1738{1748, 2014.[109] S. Biswas, D. E. P. Vanpoucke, T. Verstraelen, M. Vandichel, S. Couck, K. Leus, Y.-Y.Liu, M. Waroquier, V. Van Speybroeck, J. F. M. Denayer, and P. V. D. Voort, \New FunctionalizedMetal-Organic Frameworks MIL-47-X (X = -Cl, -Br, -CH3, -CF3, -OH, -OCH3):Synthesis, Characterization, and CO2 Adsorption Properties," J. Phys. Chem. C, vol. 117,no. 44, pp. 22784{22796, 2013.[110] K. Barthelet, J. Marrot, D. Riou, and G. Ferey, \A Breathing Hybrid Organic-Inorganic Solidwith Very Large Pores and High Magnetic Characteristics," Angew. Chem. Int. Ed., vol. 41,no. 2, pp. 281{284, 2002.[111] S. S. Y. Chui, S. M. F. Lo, J. P. H. Charmant, A. G. Orpen, and I. D. Williams, \A ChemicallyFunctionalizable Nanoporous Material [Cu3(TMA)2(H2O)3]n," Science, vol. 283, no. 5405,pp. 1148{1150, 1999.[112] J. I. Feldblyum, M. Liu, D. W. Gidley, and A. J. Matzger, \Reconciling the Discrepanciesbetween Crystallographic Porosity and Guest Access As Exemplied by Zn-HKUST-1," J.Am. Chem. Soc., vol. 133, no. 45, pp. 18257{18263, 2011.[113] P. Maniam and N. Stock, \Investigation of Porous Ni-Based Metal-Organic Frameworks ContainingPaddle-Wheel Type Inorganic Building Units via High-Throughput Methods," Inorg.Chem., vol. 50, no. 11, pp. 5085{5097, 2011.[114] P. Ryan, I. Konstantinov, R. Q. Snurr, and L. J. Broadbelt, \DFT Investigation of HydroperoxideDecomposition over Copper and Cobalt Sites within Metal-Organic Frameworks," J.Catal., vol. 286, pp. 95{102, 2012.[115] B. Lukose, B. Supronowicz, P. S. Petkov, J. Frenzel, A. B. Kuc, G. Seifert, G. N. Vayssilov, andT. Heine, \Structural properties of Metal-Organic Frameworks within the Density-FunctionalBased Tight-Binding Method," Phys. Status Solidi B, vol. 249, no. 2, pp. 335{342, 2012.[116] V. K. Peterson, Y. Liu, C. M. Brown, and C. J. Kepert, \Neutron Powder Diraction Studyof D2 Sorption in Cu3(1,3,5-benzenetricarboxylate)2," J. Am. Chem. Soc., vol. 128, no. 49,pp. 15578{15579, 2006.[117] S. Amirjalayer, M. Tapolsky, and R. Schmid, \Exploring Network Topologies of CopperPaddle Wheel Based Metal-Organic Frameworks with a First-Principles Derived Force Field,"J. Phys. Chem. C, vol. 115, no. 31, pp. 15133{15139, 2011.[118] D. N. Dybtsev, H. Chun, and K. Kim, \Rigid and Flexible: A Highly Porous Metal-OrganicFramework with Unusual Guest-Dependent Dynamic Behavior," Angew. Chem. Int. Ed.,vol. 43, no. 38, pp. 5033{5036, 2004.[119] J.-C. Tan, B. Civalleri, C.-C. Lin, L. Valenzano, R. Galvelis, P.-F. Chen, T. D. Bennett,C. Mellot-Draznieks, C. M. Zicovich-Wilson, and A. K. Cheetham, \Exceptionally Low ShearModulus in a Prototypical Imidazole-Based Metal-Organic Framework," Phys. Rev. Lett.,vol. 108, no. 9, p. 095502, 2012.[120] L. Sarkisov and J. Kim, \Computational Structure Characterization Tools for the Era ofMaterial Informatics," Chem. Eng. Sci., vol. 121, pp. 322{330, 2015.[121] R. L. Martin, B. Smit, and M. Haranczyk, \Addressing Challenges of Identifying GeometricallyDiverse Sets of Crystalline Porous Materials," J. Chem. Inf. Comput. Sci., vol. 52, no. 2,pp. 308{318, 2011.[122] T. F. Willems, C. H. Rycroft, M. Kazi, J. C. Meza, and M. Haranczyk, \Algorithms and Toolsfor High-Throughput Geometry-Based Analysis of Crystalline Porous Materials," MicroporousMesoporous Mater., vol. 149, pp. 134{141, 2012.[123] M. Pinheiro, R. L. Martin, C. H. Rycroft, A. Jones, E. Iglesia, and M. Haranczyk, \Characterizationand Comparison of Pore Landscapes in Crystalline Porous Materials," J. Mol.Graphics Modell., vol. 44, pp. 208{219, 2013.[124] J.-C. Tan, T. D. Bennett, and A. K. Cheetham, \Chemical Structure, Network Topology,and Porosity Eects on the Mechanical Properties on the Mechanical Properties of ZeoliticImidazolate Frameworks," Proc. Natl. Acad. Sci., vol. 107, no. 22, pp. 9938{9943, 2010.[125] D. R. Gaskell, Introduction to the thermodynamics of materials. Tayler & Francis, 5th ed.,2008.[126] P. Canepa, K. Tan, Y. Du, H. Lu, Y. J. Chabal, and T. Thonhauser, \Structural, Elastic,Thermal, and Electronic Response of Small-Molecule-Loaded Metal Organic FrameworksMaterials," J. Mater. Chem. A, vol. 3, no. 3, pp. 986{995, 2015.[127] A. Ghysels, T. Verstraelen, K. Hemelsoet, M. Waroquier, and V. Van Speybroeck, \TAMkin:A Versatile Package for Vibrational Analysis and Chemical Kinetics," J. Chem. Inf. Model.,vol. 50, no. 9, pp. 1736{1750, 2010.[128] S. Nose, \A molecular dynamics method for simulations in the canonical ensemble," Mol.Phys., vol. 52, no. 2, pp. 255{268, 1984.[129] W. G. Hoover, \Canonical Dynamics: Equilibrium Phase-Space Distributions," Phys. Rev.A, vol. 31, no. 3, pp. 1695{1697, 1985.[130] G. J. Martyna, M. L. Klein, and M. Tuckerman, \Nose-Hoover Chains - the Canonical EnsembleVia Continuous Dynamics," J. Chem. Phys, vol. 97, no. 4, pp. 2635{2643, 1992.[131] P. Langevin, \Sur la theorie du mouvement brownien," C. R. Acad. Sci., vol. 146, pp. 530{533,1908.[132] G. J. Martyna, D. J. Tobias, and M. L. Klein, \Constant-Pressure Molecular-Dynamics Algorithms,"J. Chem. Phys., vol. 101, no. 5, pp. 4177{4189, 1994.[133] H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, A. DiNola, and J. R. Haak,\Molecular Dynamics with Coupling to an External Bath," J. Chem. Phys., vol. 81, pp. 3684{3690, 1984.[134] S. E. Feller, Y. H. Zhang, R. W. Pastor, and B. R. Brooks, \Constant-Pressure Molecular-Dynamics Simulation - the Langevin Piston Method," J. Chem. Phys., vol. 103, no. 11,pp. 4613{4621, 1995.[135] B. Mu and K. S. Walton, \Thermal Analysis and Heat Capacity of Metal-Organic Frameworks,"J. Phys. Chem. C., vol. 115, no. 46, pp. 22748{22754, 2011.[136] J. Cao and G. A. Voth, \The Formulation of Quantum Statistical Mechanics Based on theFeynman Path Centroid Density. I. Equilibrium Properties," J. Chem. Phys., vol. 100, no. 7,pp. 5093{5105, 1994.[137] J. Cao and G. A. Voth, \The Formulation of Quantum Statistical Mechanics Based on theFeynman Path Centroid Density. II. Dynamical Properties," J. Chem. Phys., vol. 100, no. 7,pp. 5106{5117, 1994.[138] M. Ceriotti, D. E. Manolopoulos, and M. Parrinello, \Accelerating the convergence of pathintegral dynamics with a generalized Langevin equation," J. Chem. Phys., vol. 134, p. 084104,2011.[139] M. Ceriotti, J. More, and D. E. Manolopoulos, \i-PI: A Python Interface for Ab Initio Path IntegralMolecular Dynamics Simulations," Comput. Phys. Commun., vol. 185, no. 3, pp. 1019{1026, 2014.[140] G. D. Barrera, J. a. O. Bruno, T. H. K. Barron, and N. L. Allan, \Negative thermal expansion,"J. Phys.: Condens. Matter, vol. 17, no. 4, pp. R217{R252, 2005.[141] C. Lind, \Two Decades of Negative Thermal Expansion Research: Where Do We Stand?,"Materials, vol. 5, pp. 1125{1154, 2012.[142] S. S. Han and W. A. Goddard, \Metal-Organic Frameworks Provide Large Negative ThermalExpansion Behavior," J. Phys. Chem. C, vol. 111, no. 42, pp. 15185{15191, 2007.[143] J. L. C. Rowsell, E. S. Spencer, J. Eckert, J. A. K. Howard, and O. M. Yaghi, \Gas AdsorptionSites in a Large-Pore Metal-Organic Framework," Science, vol. 309, no. 5739, pp. 1350{1354,2005.[144] W. Zhou, H. Wu, T. Yildirim, J. R. Simpson, and A. R. H. Walker, \Origin ofthe Exceptional Negative Thermal Expansion in Metal-Organic Framework-5 Zn4O(1,4-benzenedicarboxylate)3," Phys. Rev. B, vol. 78, no. 5, p. 054114, 2008.[145] N. Lock, Y. Wu, M. Christensen, L. J. Cameron, V. K. Peterson, A. J. Bridgeman, C. J.Kepert, and B. B. Iversen, \Elucidating Negative Thermal Expansion in MOF-5," J. Phys.Chem. C, vol. 114, no. 39, pp. 16181{16186, 2010.[146] L. H. N. Rimmer, M. T. Dove, A. L. Goodwin, and D. C. Palmer, \Acoustic Phonons andNegative Thermal Expansion in MOF-5," Phys. Chem. Chem. Phys., vol. 16, pp. 21144{21152,2014.[147] S. Henke, A. Schneemann, and R. A. Fischer, \Massive Anisotropic Thermal Expansion andThermo-Responsive Breathing in Metal-Organic Frameworks Modulated by Linker Functionalization,"Adv. Funct. Mater., vol. 23, pp. 5990{5996, 2013.[148] P. Lama, R. K. Das, V. J. Smith, and L. J. Barbour, \A Combined Stretching-Tilting MechanismProduces Negative, Zero and Positive Linear Thermal Expansion in a Semi-FlexibleCd(II)-MOF," Chem. Commun., vol. 50, no. 49, pp. 6464{6467, 2014.[149] Y.-S. Wei, K.-J. Chen, P.-Q. Liao, B.-Y. Zhu, R.-B. Lin, H.-L. Zhou, B.-Y. Wang, W. Xue,J.-P. Zhang, and X.-M. Chen, \Turning on the Flexibility of Isoreticular Porous CoordinationFrameworks for Drastically Tunable Framework Breathing and Thermal Expansion," Chem.Sci., vol. 4, pp. 1539{1546, 2013.[150] I. Grobler, V. J. Smith, P. M. Bhatt, S. A. Herbert, and L. J. Barbour, \Tunable AnisotropicThermal Expansion of a Porous Zinc(II) Metal-Organic Framework," J. Am. Chem. Soc.,vol. 135, no. 17, pp. 6411{6414, 2013.[151] V. K. Peterson, G. J. Kearley, Y. Wu, A. J. Ramirez-Cuesta, E. Kemner, and C. J. Kepert,\Local Vibrational Mechanism for Negative Thermal Expansion: A Combined Neutron Scatteringand First-Principles Study," Angew. Chem. Int. Ed., vol. 49, no. 3, pp. 585{588, 2010.[152] K. W. Chapman, G. J. Halder, and P. J. Chupas, \Pressure-Induced Amorphization andPorosity Modication in a Metal-Organic Framework," J. Am. Chem. Soc., vol. 131, no. 48,pp. 17546{17547, 2009.[153] J.-C. Tan and A. K. Cheetham, \Mechanical Properties of Hybrid Inorganic-Organic FrameworkMaterials: Establishing Fundamental Structure-property Relationships," Chem. Soc.Rev., vol. 40, no. 2, pp. 1059{1080, 2011.[154] H. Wu, T. Yildirim, and W. Zhou, \Exceptional Mechanical Stability of Highly Porous ZirconiumMetal-Organic Framework UiO-66 and Its Important Implications," J. Phys. Chem.Lett., vol. 4, no. 6, pp. 925{930, 2013.[155] W. Li, S. Henke, and A. K. Cheetham, \Research Update: Mechanical Properties of Metal-Organic Frameworks - Inuence of Structure and Chemical Bonding," APL Mat., vol. 2,no. 12, p. 123902, 2014.[156] J.-C. Tan, B. Civalleri, A. Erba, and E. Albanese, \Quantum Mechanical Predictions toElucidate the Anisotropic Elastic Properties of Zeolitic Imidazolate Frameworks: ZIF-4 vs.ZIF-Zni," CrystEngComm, vol. 17, no. 2, pp. 375{382, 2014.[157] C. Kittel, Introduction to Solid State Physics. Wiley, 8th ed., 2004.[158] J. J. Gilman, Electronic Basis of the Strength of Materials. Cambridge University Press, 2003.[159] F. Mouhat and F.-X. Coudert, \Necessary and Sucient Elastic Stability Conditions in VariousCrystal Systems," Phys. Rev. B, vol. 90, no. 22, p. 224104, 2014.[160] W. F. Perger, J. Criswell, B. Civalleri, and R. Dovesi, \Ab-Initio Calculation of Elastic Constantsof Crystalline Systems with the CRYSTAL Code," Comput. Phys. Commun., vol. 180,no. 10, pp. 1753{1759, 2009.[161] R. Golesorkhtabar, P. Pavone, J. Spitaler, P. Puschnig, and C. Draxl, \ElaStic: A Tool forCalculating Second-Order Elastic Constants from First Principles," Comput. Phys. Commun.,vol. 184, no. 8, pp. 1861{1873, 2013.[162] W. Zhou and T. Yildirim, \Lattice Dynamics of Metal-Organic Frameworks: Neutron InelasticScattering and First-Principles Calculations," Phys. Rev. B, vol. 74, no. 18, p. 180301, 2006.[163] M. Mattesini, J. M. Soler, and F. Yndurain, \Ab Initio Study of Metal-Organic Framework-5Zn4O(1,4-benzenedicarboxylate): An Assessment of Mechanical and Spectroscopic Properties,"Phys. Rev. B, vol. 73, no. 9, p. 094111, 2006.[164] A. Samanta, T. Furuta, and J. Li, \Theoretical Assessment of the Elastic Constants andHydrogen Storage Capacity of Some Metal-Organic Framework Materials," J. Chem. Phys.,vol. 125, no. 8, p. 084714, 2006.[165] A. Kuc, A. Enyashin, and G. Seifert, \Metal-Organic Frameworks: Structural, Energetic,Electronic, and Mechanical Properties," J. Phys. Chem. B, vol. 111, no. 28, pp. 8179{8186,2007.[166] A. U. Ortiz, A. Boutin, A. H. Fuchs, and F.-X. Coudert, \Metal-Organic Frameworks withWine-Rack Motif: What Determines Their Flexibility and Elastic Properties?," J. Chem.Phys., vol. 138, no. 17, p. 174703, 2013.[167] A. U. Ortiz, A. Boutin, K. J. Gagnon, A. Cleareld, and F.-X. Coudert, \Remarkable PressureResponses of Metal-Organic Frameworks: Proton Transfer and Linker Coiling in Zinc AlkylGates," J. Am. Chem. Soc., vol. 136, no. 32, pp. 11540{11545, 2014.[168] A. U. Ortiz, A. Boutin, and F.-X. Coudert, \Prediction of Flexibility of Metal-Organic FrameworksCAU-13 and NOTT-300 by First Principles Molecular Simulations," Chem. Commun.,vol. 50, no. 44, pp. 5867{5870, 2014.[169] T. D. Bennett, J.-C. Tan, S. A. Moggach, R. Galvelis, C. Mellot-Draznieks, B. A. Reisner,A. Thirumurugan, D. R. Alland, and A. K. Cheetham, \Mechanical Properties of DenseZeolitic Imidazolate Frameworks (ZIFs): A High-Pressure X-Ray Diraction, Nanoindentationand Computational Study of the Zinc Framework Zn(Im)2, and Its Lithium-Boron Analogue,LiB(Im)4," Chem. Eur. J., vol. 16, no. 35, pp. 10684{10690, 2010.[170] T. D. Bennett, J. Sotelo, J.-C. Tan, and S. A. Moggach, \Mechanical Properties of ZeoliticMetal-Organic Frameworks: Mechanically Flexible Topologies and Stabilization against StructuralCollapse," CrystEngComm, vol. 17, no. 2, pp. 286{289, 2014.[171] H. Ledbetter, \Sound Velocities, Elastic Constants: Temperature Dependence," Mater. Sci.Eng. A, vol. 442, no. 1-2, pp. 31{34, 2006.[172] L. B. du Bourg, A. U. Ortiz, A. Boutin, and F.-X. Coudert, \Thermal and Mechanical Stabilityof Zeolitic Imidazolate Frameworks Polymorphs," APL Mat., vol. 2, no. 12, p. 124110, 2014.[173] Y. L. Page and P. Saxe, \Symmetry-General Least-Squares Extraction of Elastic Coecientsfrom Ab Initio Total Energy Calculations," Phys. Rev. B, vol. 63, no. 17, p. 174103, 2001.[174] A. U. Ortiz, A. Boutin, A. H. Fuchs, and F.-X. Coudert, \Investigating the Pressure-InducedAmorphization of Zeolitic Imidazolate Famework ZIF-8: Mechanical Instability Due to ShearMode Softening," J. Phys. Chem. Lett., vol. 4, no. 11, pp. 1861{1865, 2013.[175] S. Henke, W. Li, and A. K. Cheetham, \Guest-Dependent Mechanical Anisotropy in Pillared-Layered Soft Porous Crystals - a Nanoindentation Study," Chem. Sci., vol. 5, no. 6, pp. 2392{2397, 2014.[176] J.-C. Tan, P. Jain, and A. K. Cheetham, \Inuence of Ligand Field Stabilization Energy onthe Elastic Properties of Multiferroic MOFs with the Perovskite Architecture," Dalton Trans.,vol. 41, no. 14, pp. 3949{3952, 2012.[177] S.-L. Shang, H. Zhang, Y. Wang, and Z.-K. Liu, \Temperature-dependent elastic stinessconstants of -and -Al2O3 from rst-principles calculations," J. Phys.: Condens. Matter,vol. 22, no. 37, p. 375403, 2010.[178] M. J. Mehl, J. E. Osburn, D. A. Papaconstantopoulos, and B. M. Klein, \Structural Propertiesof Ordered High-Melting-Temperature Intermetallic Alloys from First-Principles Total-EnergyCalculations," Phys. Rev. B, vol. 41, pp. 10311{10323, 1990.[179] M. J. Mehl, B. M. Klein, and D. A. Papaconstantopoulos, First principles calculations ofelastic properties of metals, ch. 9, pp. 195{210. Intermetallic compounds, Chichester [etc.]Wiley & Sons 1995-2002, 1995.[180] Y. L. Page and P. Saxe, \Symmetry-General Least-Squares Extraction of Elastic Data forStrained Materials from Ab Initio Calculations of Stress," Phys. Rev. B, vol. 65, no. 10,p. 104104, 2002.[181] S. Shang, Y. Wang, and Z.-K. Liu, \First-Principles Elastic Constants of - and -Al2O3,"Appl. Phys. Lett., vol. 90, no. 10, p. 101909, 2007.[182] R. Yu, J. Zhu, and H. Q. Ye, \Calculations of Single-Crystal Elastic Constants Made Simple,"Comput. Phys. Commun., vol. 181, no. 3, pp. 671{675, 2010.[183] M. J. Mehl, \Pressure Dependence of the Elastic Moduli in Aluminum-Rich Al-Li Compounds,"Phys. Rev. B, vol. 47, no. 5, pp. 2493{2500, 1993.[184] P. Ravindran, L. Fast, P. A. Korzhavyi, B. Johansson, J. Wills, and O. Eriksson, \DensityFunctional Theory for Calculation of Elastic Properties of Orthorhombic Crystals: Applicationto TiSi2," J. Appl. Phys., vol. 84, no. 9, pp. 4891{4904, 1998.[185] W. Voigt, Lehrbuch der Kristallphysik, p. 962. Leipzig: Teubner, 2nd ed., 1928.[186] A. Reuss, \Berechnung der Fliegrenze von Mischkristallen auf Grund der Plastizitattsbediengung fur Einkristalle," Z. Angew. Math. Mech., vol. 9, no. 1, pp. 49{58, 1929.[187] R. Hill, \The Elastic Behaviour of a Crystalline Aggregate," Proc. Phys. Soc. A, vol. 65, no. 5,p. 349, 1952.[188] A. Marmier, Z. A. D. Lethbridge, R. I. Walton, C. W. Smith, S. C. Parker, and K. E. Evans,\ElAM: A Computer Program for the Analysis and Representation of Anisotropic ElasticProperties," Comput. Phys. Commun., vol. 181, no. 12, pp. 2012{2015, 2010.[189] F. D. Murnaghan, \The Compressibility of Media Under Extreme Pressures," Proc. Natl.Acad. Sci. U.S.A., vol. 30, no. 9, pp. 244{247, 1947.[190] P. Vinet, J. R. Smith, J. Ferrante, and J. H. Rose, \Temperature Eects on the UniversalEquation of State of Solids," Phys. Rev. B, vol. 35, no. 4, pp. 1945{1953, 1987.[191] G. N. Greaves, A. L. Greer, R. S. Lakes, and T. Rouxel, \Poisson's Ratio and Modern Materials,"Nat. Mater., vol. 10, no. 11, pp. 823{837, 2011.[192] L. Sarkisov, R. L. Martin, M. Haranczyk, and B. Smit, \On the Flexibility of Metal-OrganicFrameworks," J. Am. Chem. Soc., vol. 136, no. 6, pp. 2228{2231, 2014.[193] P. Serra-Crespo, A. Dikhtriarenko, E. Stavitski, J. Juan-Alcaniz, F. Kapteijn, F.-X. Coudert,and J. Gascon, \Experimental Evidence of Negative Linear Compressibility in the MIL-53Metal-Organic Framework Family," CrystEngComm, vol. 17, no. 2, pp. 276{280, 2015.[194] J.-C. Tan, J. D. Furman, and A. K. Cheetham, \Relating Mechanical Properties and ChemicalBonding in an Inorganic-Organic Framework Material: A Single-Crystal NanoindentationStudy," J. Am. Chem. Soc., vol. 131, no. 40, pp. 14252{14254, 2009.[195] K. W. Chapman, G. J. Halder, and P. J. Chupas, \Guest-Dependent High Pressure Phenomenain a Nanoporous Metal-Organic Framework Material," J. Am. Chem. Soc., vol. 130,no. 32, pp. 10524{10526, 2008.

 

Universiteit of Hogeschool
Master of Science in Engineering Physics
Publicatiejaar
2015
Kernwoorden
Deel deze scriptie