QuasiHarmonic Lattice Dynamics of a Prototypical Metal–Organic Framework
Abstract
Quasiharmonic latticedynamical calculations are performed to investigate the combined effect of temperature and pressure on the structural and mechanical properties of a prototypical metal–organic framework material: MOF5. The softening upon compression of an ${A}_{2g}$ phonon mode at the Γ point in the highsymmetry F $m\overline{3}m$ structure is identified, which leads to a symmetry reduction and a group–subgroup phase transition to a lowsymmetry F $m\overline{3}$ phase for compressions larger than 0.8%. The effect of the symmetry reduction on the equationofstate of MOF5 is investigated, which provides a static bulk modulus K reducing from 17 to 14 GPa and a corresponding change of ${K}^{\text{'}}$ (pressure derivative of K) from positive to negative. The effect of pressure on the negative thermal expansion of the framework and on its mechanical response is analyzed. The evolution of the mechanical anisotropy of MOF5 as a function of pressure is also determined, which allows identifying the occurrence of a shearinduced mechanical instability at 0.45 GPa.
 Authors:

 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Univ. of Torino (Italy)
 Publication Date:
 Research Org.:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1607147
 Grant/Contract Number:
 AC0500OR22725
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Advanced Theory and Simulations
 Additional Journal Information:
 Journal Volume: 2; Journal Issue: 11; Journal ID: ISSN 25130390
 Publisher:
 Wiley
 Country of Publication:
 United States
 Language:
 English
 Subject:
 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Citation Formats
Ryder, Matthew R., Maul, Jefferson, Civalleri, Bartolomeo, and Erba, Alessandro. QuasiHarmonic Lattice Dynamics of a Prototypical Metal–Organic Framework. United States: N. p., 2019.
Web. https://doi.org/10.1002/adts.201900093.
Ryder, Matthew R., Maul, Jefferson, Civalleri, Bartolomeo, & Erba, Alessandro. QuasiHarmonic Lattice Dynamics of a Prototypical Metal–Organic Framework. United States. https://doi.org/10.1002/adts.201900093
Ryder, Matthew R., Maul, Jefferson, Civalleri, Bartolomeo, and Erba, Alessandro. Fri .
"QuasiHarmonic Lattice Dynamics of a Prototypical Metal–Organic Framework". United States. https://doi.org/10.1002/adts.201900093. https://www.osti.gov/servlets/purl/1607147.
@article{osti_1607147,
title = {QuasiHarmonic Lattice Dynamics of a Prototypical Metal–Organic Framework},
author = {Ryder, Matthew R. and Maul, Jefferson and Civalleri, Bartolomeo and Erba, Alessandro},
abstractNote = {Quasiharmonic latticedynamical calculations are performed to investigate the combined effect of temperature and pressure on the structural and mechanical properties of a prototypical metal–organic framework material: MOF5. The softening upon compression of an A 2 g phonon mode at the Γ point in the highsymmetry F m 3 ¯ m structure is identified, which leads to a symmetry reduction and a group–subgroup phase transition to a lowsymmetry F m 3 ¯ phase for compressions larger than 0.8%. The effect of the symmetry reduction on the equationofstate of MOF5 is investigated, which provides a static bulk modulus K reducing from 17 to 14 GPa and a corresponding change of K ' (pressure derivative of K) from positive to negative. The effect of pressure on the negative thermal expansion of the framework and on its mechanical response is analyzed. The evolution of the mechanical anisotropy of MOF5 as a function of pressure is also determined, which allows identifying the occurrence of a shearinduced mechanical instability at 0.45 GPa.},
doi = {10.1002/adts.201900093},
journal = {Advanced Theory and Simulations},
number = 11,
volume = 2,
place = {United States},
year = {2019},
month = {7}
}
Web of Science
Works referenced in this record:
Explaining the mechanical mechanisms of zeolitic metal–organic frameworks: revealing auxeticity and anomalous elasticity
journal, January 2016
 Ryder, Matthew. R.; Tan, JinChong
 Dalton Trans., Vol. 45, Issue 10
DensityFunctional Perturbation Theory for QuasiHarmonic Calculations
journal, January 2010
 Baroni, S.; Giannozzi, P.; Isaev, E.
 Reviews in Mineralogy and Geochemistry, Vol. 71, Issue 1
The role of density functional theory methods in the prediction of nanostructured gasadsorbent materials
journal, September 2015
 Cazorla, Claudio
 Coordination Chemistry Reviews, Vol. 300
Identifying the Role of Terahertz Vibrations in MetalOrganic Frameworks: From GateOpening Phenomenon to ShearDriven Structural Destabilization
journal, November 2014
 Ryder, Matthew R.; Civalleri, Bartolomeo; Bennett, Thomas D.
 Physical Review Letters, Vol. 113, Issue 21
Pressurevolumetemperature relations in MgO: An ultrahigh pressuretemperature scale for planetary sciences applications
journal, January 2008
 Wu, Zhongqing; Wentzcovitch, Renata M.; Umemoto, Koichiro
 Journal of Geophysical Research, Vol. 113, Issue B6
Elastic properties of six silicate garnet end members from accurate ab initio simulations
journal, October 2013
 Erba, Alessandro; Mahmoud, Agnes; Orlando, Roberto
 Physics and Chemistry of Minerals, Vol. 41, Issue 2
Energy Ranking of Molecular Crystals Using Density Functional Theory Calculations and an Empirical van der Waals Correction
journal, August 2005
 Neumann, Marcus A.; Perrin, MarcAntoine
 The Journal of Physical Chemistry B, Vol. 109, Issue 32
Pressuredriven mechanical anisotropy and destabilization in zeolitic imidazolate frameworks
journal, January 2019
 Maul, Jefferson; Ryder, Matthew R.; Ruggiero, Michael T.
 Physical Review B, Vol. 99, Issue 1
Effect of gas pressure on negative thermal expansion in MOF5
journal, January 2013
 Lock, Nina; Christensen, Mogens; Kepert, Cameron J.
 Chem. Commun., Vol. 49, Issue 8
Predicting finitetemperature properties of crystalline carbon dioxide from first principles with quantitative accuracy
journal, January 2016
 Heit, Yonaton N.; Nanda, Kaushik D.; Beran, Gregory J. O.
 Chemical Science, Vol. 7, Issue 1
Nuclearrelaxed elastic and piezoelectric constants of materials: Computational aspects of two quantummechanical approaches
journal, December 2016
 Erba, Alessandro; Caglioti, Dominique; ZicovichWilson, Claudio Marcelo
 Journal of Computational Chemistry, Vol. 38, Issue 5
Acoustic phonons and negative thermal expansion in MOF5
journal, January 2014
 Rimmer, Leila H. N.; Dove, Martin T.; Goodwin, Andrew L.
 Phys. Chem. Chem. Phys., Vol. 16, Issue 39
Enhancement of DFTcalculations at petascale: Nuclear Magnetic Resonance, Hybrid Density Functional Theory and Car–Parrinello calculations
journal, August 2013
 Varini, Nicola; Ceresoli, Davide; MartinSamos, Layla
 Computer Physics Communications, Vol. 184, Issue 8
Thermodynamic properties of CaCO3 calcite and aragonite: A quasiharmonic calculation
journal, February 1993
 Catti, M.; Pavese, A.; Price, G. D.
 Physics and Chemistry of Minerals, Vol. 19, Issue 7
Scrutinizing negative thermal expansion in MOF5 by scattering techniques and ab initio calculations
journal, January 2013
 Lock, Nina; Christensen, Mogens; Wu, Yue
 Dalton Trans., Vol. 42, Issue 6
Intermolecular anharmonicity in molecular crystals: interplay between experimental lowfrequency dynamics and quantum quasiharmonic simulations of solid purine
journal, January 2017
 Ruggiero, Michael T.; Zeitler, J. Axel; Erba, Alessandro
 Chemical Communications, Vol. 53, Issue 26
Assessing thermochemical properties of materials through ab initio quantummechanical methods: the case of αAl _{2} O _{3}
journal, January 2015
 Erba, Alessandro; Maul, Jefferson; Demichelis, Raffaella
 Physical Chemistry Chemical Physics, Vol. 17, Issue 17
DFTD3 Study of Some Molecular Crystals
journal, March 2014
 Moellmann, Jonas; Grimme, Stefan
 The Journal of Physical Chemistry C, Vol. 118, Issue 14
Energetic materials: variabletemperature crystal structures of γ and ∊HNIW polymorphs
journal, September 2004
 Bolotina, Nadezhda B.; Hardie, Michaele J.; Speer Jr, Richard L.
 Journal of Applied Crystallography, Vol. 37, Issue 5
On combining temperature and pressure effects on structural properties of crystals with standard ab initio techniques
journal, September 2014
 Erba, A.
 The Journal of Chemical Physics, Vol. 141, Issue 12
Origin of the exceptional negative thermal expansion in metalorganic framework5 ${\text{Zn}}_{4}\text{O}{(1,4\text{benzenedicarboxylate})}_{3}$
journal, August 2008
 Zhou, W.; Wu, H.; Yildirim, T.
 Physical Review B, Vol. 78, Issue 5
Thermodynamics of the Flexible Metal–Organic Framework Material MIL53(Cr) From FirstPrinciples
journal, February 2017
 Cockayne, Eric
 The Journal of Physical Chemistry C, Vol. 121, Issue 8
Elucidating Negative Thermal Expansion in MOF5
journal, September 2010
 Lock, Nina; Wu, Yue; Christensen, Mogens
 The Journal of Physical Chemistry C, Vol. 114, Issue 39
Performance Analysis of Electronic Structure Codes on HPC Systems: A Case Study of SIESTA
journal, April 2014
 Corsetti, Fabiano
 PLoS ONE, Vol. 9, Issue 4
Understanding and Controlling the Dielectric Response of MetalOrganic Frameworks
journal, March 2018
 Ryder, Matthew R.; Donà, Lorenzo; Vitillo, Jenny G.
 ChemPlusChem, Vol. 83, Issue 4
Thermal Expansion of Carbamazepine: Systematic Crystallographic Measurements Challenge Quantum Chemical Calculations
journal, August 2017
 Brandenburg, Jan Gerit; Potticary, Jason; Sparkes, Hazel A.
 The Journal of Physical Chemistry Letters, Vol. 8, Issue 17
Exceptional Negative Thermal Expansion in Isoreticular Metal–Organic Frameworks
journal, June 2007
 Dubbeldam, David; Walton, Krista S.; Ellis, Donald E.
 Angewandte Chemie, Vol. 119, Issue 24
Magnetoelastic coupling in the cobalt adipate metal–organic framework from quasiharmonic lattice dynamics
journal, January 2015
 Svane, Katrine L.; Saines, Paul J.; Walsh, Aron
 Journal of Materials Chemistry C, Vol. 3, Issue 42
Firstprinciples modeling of molecular crystals: structures and stabilities, temperature and pressure: Firstprinciples modeling of molecular crystals
journal, December 2016
 Hoja, Johannes; Reilly, Anthony M.; Tkatchenko, Alexandre
 Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 7, Issue 1
Thermal decomposition of energetic materials. 61. Perfidy in the amino2,4,6trinitrobenzene series of explosives
journal, August 1993
 Brill, T. B.; James, K. J.
 The Journal of Physical Chemistry, Vol. 97, Issue 34
The Effect of High Pressure on MOF5: GuestInduced Modification of Pore Size and Content at High Pressure
journal, October 2011
 Graham, Alexander J.; Allan, David R.; Muszkiewicz, Anna
 Angewandte Chemie International Edition, Vol. 50, Issue 47
Fully optimized contracted Gaussian basis sets for atoms Li to Kr
journal, August 1992
 Schäfer, Ansgar; Horn, Hans; Ahlrichs, Reinhart
 The Journal of Chemical Physics, Vol. 97, Issue 4
Calculation of Dynamical Surface Properties of NobleGas Crystals. I. The Quasiharmonic Approximation
journal, March 1969
 Allen, R. E.; De Wette, F. W.
 Physical Review, Vol. 179, Issue 3
How important is thermal expansion for predicting molecular crystal structures and thermochemistry at finite temperatures?
journal, July 2016
 Heit, Yonaton N.; Beran, Gregory J. O.
 Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials, Vol. 72, Issue 4
The internalstrain tensor of crystals for nuclearrelaxed elastic and piezoelectric constants: on the full exploitation of its symmetry features
journal, January 2016
 Erba, Alessandro
 Physical Chemistry Chemical Physics, Vol. 18, Issue 20
Tracking thermalinduced amorphization of a zeolitic imidazolate framework via synchrotron in situ farinfrared spectroscopy
journal, January 2017
 Ryder, Matthew R.; Bennett, Thomas D.; Kelley, Chris S.
 Chemical Communications, Vol. 53, Issue 52
A consistent and accurate ab initio parametrization of density functional dispersion correction (DFTD) for the 94 elements HPu
journal, April 2010
 Grimme, Stefan; Antony, Jens; Ehrlich, Stephan
 The Journal of Chemical Physics, Vol. 132, Issue 15
LargeScale Condensed Matter DFT Simulations: Performance and Capabilities of the CRYSTAL Code
journal, September 2017
 Erba, A.; Baima, J.; Bush, I.
 Journal of Chemical Theory and Computation, Vol. 13, Issue 10
Microscopic Mechanism of Chiral Induction in a Metal–Organic Framework
journal, May 2016
 Evans, Jack D.; Coudert, FrançoisXavier
 Journal of the American Chemical Society, Vol. 138, Issue 19
Probing the dynamics of instability in zeolitic materials
journal, August 2004
 Greaves, Neville; Meneau, Florian
 Journal of Physics: Condensed Matter, Vol. 16, Issue 33
Investigating the PressureInduced Amorphization of Zeolitic Imidazolate Framework ZIF8: Mechanical Instability Due to Shear Mode Softening
journal, May 2013
 Ortiz, Aurélie U.; Boutin, Anne; Fuchs, Alain H.
 The Journal of Physical Chemistry Letters, Vol. 4, Issue 11
Thermal properties of molecular crystals through dispersioncorrected quasiharmonic ab initio calculations: the case of urea
journal, January 2016
 Erba, Alessandro; Maul, Jefferson; Civalleri, Bartolomeo
 Chemical Communications, Vol. 52, Issue 9
Quantummechanical condensed matter simulations with CRYSTAL
journal, March 2018
 Dovesi, Roberto; Erba, Alessandro; Orlando, Roberto
 Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 8, Issue 4
Exceptional Negative Thermal Expansion in Isoreticular Metal–Organic Frameworks
journal, June 2007
 Dubbeldam, David; Walton, Krista S.; Ellis, Donald E.
 Angewandte Chemie International Edition, Vol. 46, Issue 24
Ab initio study of metalorganic framework5 ${\mathrm{Zn}}_{4}\mathrm{O}(1,4\text{\u2212}\mathrm{benzenedicarboxylate}{)}_{3}$ : An assessment of mechanical and spectroscopic properties
journal, March 2006
 Mattesini, M.; Soler, J. M.; Ynduráin, F.
 Physical Review B, Vol. 73, Issue 9
Intermolecular anharmonicity in molecular crystals: interplay between experimental lowfrequency dynamics and quantum quasiharmonic simulations of solid purine
text, January 2017
 Ruggiero, Michael; Zeitler, Axel; Erba, A.
 Apollo  University of Cambridge Repository
Anisotropic displacement parameters for molecular crystals from periodic Hartree–Fock and density functional theory calculations
journal, April 2013
 Madsen, Anders Østergaard; Civalleri, Bartolomeo; Ferrabone, Matteo
 Acta Crystallographica Section A Foundations of Crystallography, Vol. 69, Issue 3
Anharmonic Vibrational States of Solids from DFT Calculations. Part II: Implementation of the VSCF and VCI Methods
journal, April 2019
 Erba, Alessandro; Maul, Jefferson; Ferrabone, Matteo
 Journal of Chemical Theory and Computation, Vol. 15, Issue 6
Identifying Vibrations That Destabilize Crystals and Characterize the Glassy State
journal, May 2005
 Greaves, G. N.
 Science, Vol. 308, Issue 5726
Ab initio calculation of structural and latticedynamical properties of silicon carbide
journal, December 1994
 Karch, K.; Pavone, P.; Windl, W.
 Physical Review B, Vol. 50, Issue 23
Large negative thermal expansion provided by metalorganic framework MOF5: A firstprinciples study
journal, June 2016
 Wang, Lei; Wang, Cong; Sun, Ying
 Materials Chemistry and Physics, Vol. 175
Anharmonic Vibrational States of Solids from DFT Calculations. Part I: Description of the Potential Energy Surface
journal, April 2019
 Erba, Alessandro; Maul, Jefferson; Ferrabone, Matteo
 Journal of Chemical Theory and Computation, Vol. 15, Issue 6
Influence of the exchangecorrelation functional on the quasiharmonic lattice dynamics of IIVI semiconductors
journal, August 2015
 Skelton, Jonathan M.; Tiana, Davide; Parker, Stephen C.
 The Journal of Chemical Physics, Vol. 143, Issue 6
Toward Computational Materials Design: The Impact of Density Functional Theory on Materials Research
journal, September 2006
 Hafner, Jürgen; Wolverton, Christopher; Ceder, Gerbrand
 MRS Bulletin, Vol. 31, Issue 9
Metal−Organic Frameworks Provide Large Negative Thermal Expansion Behavior
journal, October 2007
 Han, Sang Soo; Goddard, William A.
 The Journal of Physical Chemistry C, Vol. 111, Issue 42
Detecting Molecular Rotational Dynamics Complementing the LowFrequency Terahertz Vibrations in a ZirconiumBased MetalOrganic Framework
journal, June 2017
 Ryder, Matthew R.; Van de Voorde, Ben; Civalleri, Bartolomeo
 Physical Review Letters, Vol. 118, Issue 25
On how differently the quasiharmonic approximation works for two isostructural crystals: Thermal properties of periclase and lime
journal, January 2015
 Erba, A.; Shahrokhi, M.; Moradian, R.
 The Journal of Chemical Physics, Vol. 142, Issue 4
Accurate and Efficient Method for ManyBody van der Waals Interactions
journal, June 2012
 Tkatchenko, Alexandre; DiStasio, Robert A.; Car, Roberto
 Physical Review Letters, Vol. 108, Issue 23
Calculation of Thermal Expansion, Compressiblity, an Melting in Alkali Halides: NaCl and KCl
journal, February 1979
 Boyer, L. L.
 Physical Review Letters, Vol. 42, Issue 9
Structural and elastic anisotropy of crystals at high pressures and temperatures from quantum mechanical methods: The case of Mg _{2} SiO _{4} forsterite
journal, May 2015
 Erba, A.; Maul, J.; De La Pierre, M.
 The Journal of Chemical Physics, Vol. 142, Issue 20
Static and lattice vibrational energy differences between polymorphs
journal, January 2015
 Nyman, Jonas; Day, Graeme M.
 CrystEngComm, Vol. 17, Issue 28
Discovering connections between terahertz vibrations and elasticity underpinning the collective dynamics of the HKUST1 metal–organic framework
journal, January 2016
 Ryder, Matthew R.; Civalleri, Bartolomeo; Cinque, Gianfelice
 CrystEngComm, Vol. 18, Issue 23
Isoreticular zirconiumbased metal–organic frameworks: discovering mechanical trends and elastic anomalies controlling chemical structure stability
journal, January 2016
 Ryder, Matthew R.; Civalleri, Bartolomeo; Tan, JinChong
 Physical Chemistry Chemical Physics, Vol. 18, Issue 13
Introducing kpoint parallelism into VASP
journal, August 2012
 Maniopoulou, Asimina; Davidson, Erlend R. M.; GrauCrespo, Ricardo
 Computer Physics Communications, Vol. 183, Issue 8
ThermoElasticity of Materials from QuasiHarmonic Calculations
journal, December 2018
 Destefanis, Maurizio; Ravoux, Corentin; Cossard, Alessandro
 Minerals, Vol. 9, Issue 1
Thermodynamic Properties of Molecular Crystals Calculated within the QuasiHarmonic Approximation
journal, March 2016
 Červinka, Ctirad; Fulem, Michal; Stoffel, Ralf Peter
 The Journal of Physical Chemistry A, Vol. 120, Issue 12
In silico design and screening of hypothetical MOF74 analogs and their experimental synthesis
journal, January 2016
 Witman, Matthew; Ling, Sanliang; Anderson, Samantha
 Chemical Science, Vol. 7, Issue 9
Thermal properties of the orthorhombic CaSnO3 perovskite under pressure from ab initio quasiharmonic calculations
journal, January 2016
 Maul, J.; Santos, I. M. G.; Sambrano, J. R.
 Theoretical Chemistry Accounts, Vol. 135, Issue 2
C RYSTAL14 : A program for the ab initio investigation of crystalline solids
journal, March 2014
 Dovesi, Roberto; Orlando, Roberto; Erba, Alessandro
 International Journal of Quantum Chemistry, Vol. 114, Issue 19
Understanding the role of vibrations, exact exchange, and manybody van der Waals interactions in the cohesive properties of molecular crystals
journal, July 2013
 Reilly, Anthony M.; Tkatchenko, Alexandre
 The Journal of Chemical Physics, Vol. 139, Issue 2
The rheology of collapsing zeolites amorphized by temperature and pressure
journal, August 2003
 Greaves, G. N.; Meneau, F.; Sapelkin, A.
 Nature Materials, Vol. 2, Issue 9
Fully optimized contracted Gaussian basis sets of triple zeta valence quality for atoms Li to Kr
journal, April 1994
 Schäfer, Ansgar; Huber, Christian; Ahlrichs, Reinhart
 The Journal of Chemical Physics, Vol. 100, Issue 8
Vibrational and quasiharmonic thermal properties of CaO under pressure
journal, December 2003
 Karki, Bijaya B.; Wentzcovitch, Renata M.
 Physical Review B, Vol. 68, Issue 22
High pressure elastic properties of minerals from ab initio simulations: The case of pyrope, grossular and andradite silicate garnets
journal, March 2014
 Erba, A.; Mahmoud, A.; Belmonte, D.
 The Journal of Chemical Physics, Vol. 140, Issue 12
B3LYP augmented with an empirical dispersion term (B3LYPD*) as applied to molecular crystals
journal, January 2008
 Civalleri, Bartolomeo; ZicovichWilson, Claudio M.; Valenzano, Loredana
 CrystEngComm, Vol. 10, Issue 4
Computational characterization and prediction of metal–organic framework properties
journal, January 2016
 Coudert, FrançoisXavier; Fuchs, Alain H.
 Coordination Chemistry Reviews, Vol. 307
cp2k: atomistic simulations of condensed matter systems
journal, June 2013
 Hutter, Jürg; Iannuzzi, Marcella; Schiffmann, Florian
 Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 4, Issue 1
ExchangeHole Dipole Dispersion Model for Accurate Energy Ranking in Molecular Crystal Structure Prediction
journal, January 2017
 Whittleton, Sarah R.; OterodelaRoza, A.; Johnson, Erin R.
 Journal of Chemical Theory and Computation, Vol. 13, Issue 2
Probing the Mechanochemistry of Metal–Organic Frameworks with LowFrequency Vibrational Spectroscopy
journal, November 2018
 Zhang, Wei; Maul, Jefferson; Vulpe, Diana
 The Journal of Physical Chemistry C, Vol. 122, Issue 48