Automatic Prediction of Surface Phase Diagrams Using Ab Initio Grand Canonical Monte Carlo

Wexler, Robert B.; Qiu, Tian; Rappe, Andrew M.

doi:10.1021/acs.jpcc.8b11093

Title: Automatic Prediction of Surface Phase Diagrams Using Ab Initio Grand Canonical Monte Carlo

Journal Article · 02 January 2019 · Journal of Physical Chemistry. C

DOI: https://doi.org/10.1021/acs.jpcc.8b11093 · OSTI ID:1543662

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Univ. of Pennsylvania, Philadelphia, PA (United States)

The properties of a material are often strongly influenced by its surfaces. Depending on the nature of the chemical bonding in a material, its surface can undergo a variety of stabilizing reconstructions that dramatically alter the chemical reactivity, light absorption, and electronic band offsets. For decades, ab initio thermodynamics has been the method of choice for computationally determining the surface phase diagram of a material under different conditions. The surfaces considered for these studies, however, are often human-selected and too few in number, leading both to insufficient exploration of all possible surfaces and to biases toward portions of the composition–structure phase space that often do not encompass the most stable surfaces. To overcome these limitations and automate the discovery of realistic surfaces, we combine density functional theory and grand canonical Monte Carlo (GCMC) into “ab initio GCMC.” This paper presents the successful application of ab initio GCMC to the study of oxide overlayers on Ag(111), which, for many years, mystified experts in surface science and catalysis. Specifically, we report that ab initio GCMC is able to reproduce the surface phase diagram of Ag(111) with no preconceived notions about the system. Using nonlinear, random forest regression, we discover that the Ag coordination number with O and the surface O–Ag–O bond angles are good descriptors of the surface energy. Additionally, using the composition–structure evolution histories produced by ab initio GCMC, we deduce a mechanism for the formation of oxide overlayers based on the Ag₃O₄ pyramid motif that is common to many reconstructions of Ag(111). Lastly, ab initio GCMC is a promising tool for the discovery of realistic surfaces that can then be used to study phenomena on complex surfaces such as heterogeneous catalysis and material growth, enabling reliable and insightful interpretations of experiments.

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Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States); Univ. of Pennsylvania, Philadelphia, PA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0019281

OSTI ID:: 1543662

Journal Information:: Journal of Physical Chemistry. C, Journal Name: Journal of Physical Chemistry. C Journal Issue: 4 Vol. 123; ISSN 1932-7447

Publisher:: American Chemical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (73)

Vapor–liquid equilibria of mixtures containing alkanes, carbon dioxide, and nitrogen Potoff, Jeffrey J.; Siepmann, J. Ilja AIChE Journal, Vol. 47, Issue 7, p. 1676-1682 https://doi.org/10.1002/aic.690470719	journal	July 2001
Understanding the Reactive Adsorption of H ₂ S and CO ₂ in Sodium-Exchanged Zeolites Fetisov, Evgenii O.; Shah, Mansi S.; Knight, Christopher ChemPhysChem, Vol. 19, Issue 4 https://doi.org/10.1002/cphc.201700993	journal	January 2018
Atomic and molecular oxygen adsorption on Ag(111) Campbell, Charles T. Surface Science, Vol. 157, Issue 1 https://doi.org/10.1016/0039-6028(85)90634-x	journal	July 1985
Determining in situ phases of a nanoparticle catalyst via grand canonical Monte Carlo simulations with the ReaxFF potential Senftle, Thomas P.; van Duin, Adri C. T.; Janik, Michael J. Catalysis Communications, Vol. 52 https://doi.org/10.1016/j.catcom.2013.12.001	journal	July 2014
An implementation of artificial neural-network potentials for atomistic materials simulations: Performance for TiO2 Artrith, Nongnuch; Urban, Alexander Computational Materials Science, Vol. 114 https://doi.org/10.1016/j.commatsci.2015.11.047	journal	March 2016
Stranski–Krastanov like oxide growth on Ag(111) at atmospheric oxygen pressures Reicho, A.; Stierle, A.; Costina, I. Surface Science, Vol. 601, Issue 4 https://doi.org/10.1016/j.susc.2006.12.008	journal	February 2007
Nanosilver: A nanoproduct in medical application Chen, X.; Schluesener, H. J. Toxicology Letters, Vol. 176, Issue 1 https://doi.org/10.1016/j.toxlet.2007.10.004	journal	January 2008
Study of molecular shape and non-ideality effects on mixture adsorption isotherms of small molecules in carbon nanotubes: A grand canonical Monte Carlo simulation study Heyden, Andreas; Düren, Tina; J. Keil, Frerich Chemical Engineering Science, Vol. 57, Issue 13 https://doi.org/10.1016/s0009-2509(02)00131-8	journal	July 2002
Structures and thermodynamic phase transitions for oxygen and silver oxide phases on Ag{1 1 1} Michaelides, A.; Bocquet, M. -L; Sautet, P. Chemical Physics Letters, Vol. 367, Issue 3-4 https://doi.org/10.1016/s0009-2614(02)01699-8	journal	January 2003
Atomic imaging of the transition between oxygen chemisorption and oxide film growth on Ag{111} Carlisle, C. I.; Fujimoto, T.; Sim, W. S. Surface Science, Vol. 470, Issue 1-2 https://doi.org/10.1016/s0039-6028(00)00831-1	journal	December 2000
The alloy theoretic automated toolkit: A user guide van de Walle, A.; Asta, M.; Ceder, G. Calphad, Vol. 26, Issue 4 https://doi.org/10.1016/s0364-5916(02)80006-2	journal	December 2002
Oxidation of Ethylene on Oxygen Reconstructed Silver Surfaces Jones, Travis E.; Wyrwich, Regina; Böcklein, Sebastian The Journal of Physical Chemistry C, Vol. 120, Issue 50 https://doi.org/10.1021/acs.jpcc.6b10074	journal	December 2016
Automated Discovery and Construction of Surface Phase Diagrams Using Machine Learning Ulissi, Zachary W.; Singh, Aayush R.; Tsai, Charlie The Journal of Physical Chemistry Letters, Vol. 7, Issue 19 https://doi.org/10.1021/acs.jpclett.6b01254	journal	September 2016
Reaction Ensemble Monte Carlo Simulations of CO ₂ Absorption in the Reactive Ionic Liquid Triethyl(octyl)phosphonium 2-Cyanopyrrolide Mullen, Ryan Gotchy; Corcelli, Steven A.; Maginn, Edward J. The Journal of Physical Chemistry Letters, Vol. 9, Issue 18 https://doi.org/10.1021/acs.jpclett.8b02304	journal	August 2018
Insights into the Electronic Structure of the Oxygen Species Active in Alkene Epoxidation on Silver Jones, Travis E.; Rocha, Tulio C. R.; Knop-Gericke, Axel ACS Catalysis, Vol. 5, Issue 10 https://doi.org/10.1021/acscatal.5b01543	journal	September 2015
Noble Metals on the Nanoscale: Optical and Photothermal Properties and Some Applications in Imaging, Sensing, Biology, and Medicine Jain, Prashant K.; Huang, Xiaohua; El-Sayed, Ivan H. Accounts of Chemical Research, Vol. 41, Issue 12, p. 1578-1586 https://doi.org/10.1021/ar7002804	journal	December 2008
Prediction of adsorption of aromatic hydrocarbons in silicalite from grand canonical Monte Carlo simulations with biased insertions Snurr, Randall Q.; Bell, Alexis T.; Theodorou, Doros N. The Journal of Physical Chemistry, Vol. 97, Issue 51 https://doi.org/10.1021/j100153a051	journal	December 1993
Solvent effects on the barrier to isomerization for a tertiary amide from ab initio and Monte Carlo calculations Duffy, Erin M.; Severance, Daniel L.; Jorgensen, William L. Journal of the American Chemical Society, Vol. 114, Issue 19 https://doi.org/10.1021/ja00045a029	journal	September 1992
Formation of a Stable Surface Oxametallacycle that Produces Ethylene Oxide Linic, Suljo; Barteau, Mark A. Journal of the American Chemical Society, Vol. 124, Issue 2 https://doi.org/10.1021/ja0118136	journal	December 2001
Specific Ethene Surface Activation on Silver Oxide Covered Ag{111} from the Interplay of STM Experiment and Theory Bocquet, Marie-Laure; Sautet, Philippe; Cerda, Jorge Journal of the American Chemical Society, Vol. 125, Issue 10 https://doi.org/10.1021/ja027634l	journal	March 2003
Control of Ethylene Epoxidation Selectivity by Surface Oxametallacycles Linic, Suljo; Barteau, Mark A. Journal of the American Chemical Society, Vol. 125, Issue 14 https://doi.org/10.1021/ja029076g	journal	April 2003
Applicability of the BET Method for Determining Surface Areas of Microporous Metal−Organic Frameworks Walton, Krista S.; Snurr, Randall Q. Journal of the American Chemical Society, Vol. 129, Issue 27 https://doi.org/10.1021/ja071174k	journal	July 2007
Covalent Organic Frameworks as Exceptional Hydrogen Storage Materials Han, Sang Soo; Furukawa, Hiroyasu; Yaghi, Omar M. Journal of the American Chemical Society, Vol. 130, Issue 35, p. 11580-11581 https://doi.org/10.1021/ja803247y	journal	September 2008
Chemical Pressure-Driven Enhancement of the Hydrogen Evolving Activity of Ni ₂ P from Nonmetal Surface Doping Interpreted via Machine Learning Wexler, Robert B.; Martirez, John Mark P.; Rappe, Andrew M. Journal of the American Chemical Society, Vol. 140, Issue 13 https://doi.org/10.1021/jacs.8b00947	journal	March 2018
Monte Carlo Calculations for Alcohols and Their Mixtures with Alkanes. Transferable Potentials for Phase Equilibria. 5. United-Atom Description of Primary, Secondary, and Tertiary Alcohols Chen, Bin; Potoff, Jeffrey J.; Siepmann, J. Ilja The Journal of Physical Chemistry B, Vol. 105, Issue 15 https://doi.org/10.1021/jp003882x	journal	April 2001
ReaxFF: A Reactive Force Field for Hydrocarbons van Duin, Adri C. T.; Dasgupta, Siddharth; Lorant, Francois The Journal of Physical Chemistry A, Vol. 105, Issue 41 https://doi.org/10.1021/jp004368u	journal	October 2001
The Optical Properties of Metal Nanoparticles: The Influence of Size, Shape, and Dielectric Environment Kelly, K. Lance; Coronado, Eduardo; Zhao, Lin Lin The Journal of Physical Chemistry B, Vol. 107, Issue 3 https://doi.org/10.1021/jp026731y	journal	January 2003
High-Coverage Oxygen-Induced Surface Structures on Ag(111) Martin, N. M.; Klacar, S.; Grönbeck, H. The Journal of Physical Chemistry C, Vol. 118, Issue 28 https://doi.org/10.1021/jp504387p	journal	July 2014
Adsorption of Water on Activated Carbons: A Molecular Simulation Study Müller, Erich A.; Rull, Luis F.; Vega, Lourdes F. The Journal of Physical Chemistry, Vol. 100, Issue 4 https://doi.org/10.1021/jp952233w	journal	January 1996
Monte Carlo Simulations of Zn(II) in Water Including Three-Body Effects Marini, Gerhard W.; Texler, Norbert R.; Rode, Bernd M. The Journal of Physical Chemistry, Vol. 100, Issue 16 https://doi.org/10.1021/jp953375t	journal	January 1996
Pillared Graphene A New 3-D Network Nanostructure for Enhanced Hydrogen Storage Dimitrakakis, Georgios K.; Tylianakis, Emmanuel; Froudakis, George E. Nano Letters, Vol. 8, Issue 10, p. 3166-3170 https://doi.org/10.1021/nl801417w	journal	October 2008
Coexisting Surface Phases and Coherent One-Dimensional Interfaces on BaTiO ₃ (001) Morales, Erie H.; Martirez, John Mark P.; Saidi, Wissam A. ACS Nano, Vol. 8, Issue 5 https://doi.org/10.1021/nn501759g	journal	April 2014
Tunable gold catalysts for selective hydrocarbon oxidation under mild conditions Hughes, Mathew D.; Xu, Yi-Jun; Jenkins, Patrick Nature, Vol. 437, Issue 7062 https://doi.org/10.1038/nature04190	journal	October 2005
Visible-light-enhanced catalytic oxidation reactions on plasmonic silver nanostructures Christopher, Phillip; Xin, Hongliang; Linic, Suljo Nature Chemistry, Vol. 3, Issue 6 https://doi.org/10.1038/nchem.1032	journal	May 2011
Grand canonical Monte Carlo simulations of adsorption of mixtures of xylene molecules in faujasite zeolites Lachet, Ve′ronique; Boutin, Anne; Tavitian, Bernard Faraday Discussions, Vol. 106 https://doi.org/10.1039/a701490b	journal	January 1997
The silver–oxygen system in catalysis: new insights by near ambient pressure X-ray photoelectron spectroscopy Rocha, Tulio C. R.; Oestereich, Andreas; Demidov, Demid V. Physical Chemistry Chemical Physics, Vol. 14, Issue 13 https://doi.org/10.1039/c2cp22472k	journal	January 2012
Thermodynamic and spectroscopic properties of oxygen on silver under an oxygen atmosphere Jones, Travis E.; Rocha, Tulio C. R.; Knop-Gericke, Axel Physical Chemistry Chemical Physics, Vol. 17, Issue 14 https://doi.org/10.1039/c5cp00342c	journal	January 2015
Are multiple oxygen species selective in ethylene epoxidation on silver? Carbonio, Emilia A.; Rocha, Tulio C. R.; Klyushin, Alexander Yu. Chemical Science, Vol. 9, Issue 4 https://doi.org/10.1039/c7sc04728b	journal	January 2018
First principles Monte Carlo simulations of unary and binary adsorption: CO ₂ , N ₂ , and H ₂ O in Mg-MOF-74 Fetisov, Evgenii O.; Shah, Mansi S.; Long, Jeffrey R. Chemical Communications, Vol. 54, Issue 77 https://doi.org/10.1039/c8cc06178e	journal	January 2018
Development of a ReaxFF potential for Pd/O and application to palladium oxide formation Senftle, Thomas P.; Meyer, Randall J.; Janik, Michael J. The Journal of Chemical Physics, Vol. 139, Issue 4 https://doi.org/10.1063/1.4815820	journal	July 2013
Advanced capabilities for materials modelling with Quantum ESPRESSO Giannozzi, P.; Andreussi, O.; Brumme, T. Journal of Physics: Condensed Matter, Vol. 29, Issue 46 https://doi.org/10.1088/1361-648x/aa8f79	journal	October 2017
Inhomogeneous Electron Gas Hohenberg, P.; Kohn, W. Physical Review, Vol. 136, Issue 3B, p. B864-B871 https://doi.org/10.1103/physrev.136.b864	journal	November 1964
Self-Consistent Equations Including Exchange and Correlation Effects Kohn, W.; Sham, L. J. Physical Review, Vol. 140, Issue 4A, p. A1133-A1138 https://doi.org/10.1103/physrev.140.a1133	journal	November 1965
New empirical approach for the structure and energy of covalent systems Tersoff, J. Physical Review B, Vol. 37, Issue 12 https://doi.org/10.1103/physrevb.37.6991	journal	April 1988
Optimized pseudopotentials Rappe, Andrew M.; Rabe, Karin M.; Kaxiras, Efthimios Physical Review B, Vol. 41, Issue 2 https://doi.org/10.1103/physrevb.41.1227	journal	January 1990
Dipole correction for surface supercell calculations Bengtsson, Lennart Physical Review B, Vol. 59, Issue 19 https://doi.org/10.1103/physrevb.59.12301	journal	May 1999
Designed nonlocal pseudopotentials for enhanced transferability Ramer, Nicholas J.; Rappe, Andrew M. Physical Review B, Vol. 59, Issue 19 https://doi.org/10.1103/physrevb.59.12471	journal	May 1999
Subsurface oxygen and surface oxide formation at Ag(111): A density-functional theory investigation Li, Wei-Xue; Stampfl, Catherine; Scheffler, Matthias Physical Review B, Vol. 67, Issue 4 https://doi.org/10.1103/physrevb.67.045408	journal	January 2003
Atomic oxygen species on silver: Photoelectron spectroscopy and x-ray absorption studies Bukhtiyarov, V. I.; Hävecker, M.; Kaichev, V. V. Physical Review B, Vol. 67, Issue 23 https://doi.org/10.1103/physrevb.67.235422	journal	June 2003
Charge optimized many-body potential for the Si ∕ SiO 2 system Yu, Jianguo; Sinnott, Susan B.; Phillpot, Simon R. Physical Review B, Vol. 75, Issue 8 https://doi.org/10.1103/physrevb.75.085311	journal	February 2007
Experimental and theoretical study of oxygen adsorption structures on Ag(111) Schnadt, Joachim; Knudsen, Jan; Hu, Xiao Liang Physical Review B, Vol. 80, Issue 7 https://doi.org/10.1103/physrevb.80.075424	journal	August 2009
Evolutionary method for predicting surface reconstructions with variable stoichiometry Zhu, Qiang; Li, Li; Oganov, Artem R. Physical Review B, Vol. 87, Issue 19 https://doi.org/10.1103/physrevb.87.195317	journal	May 2013
Improved atomistic Monte Carlo models based on ab-initio -trained neural networks: Application to FeCu and FeCr alloys Castin, N.; Messina, L.; Domain, C. Physical Review B, Vol. 95, Issue 21 https://doi.org/10.1103/physrevb.95.214117	journal	June 2017
Efficient and accurate machine-learning interpolation of atomic energies in compositions with many species Artrith, Nongnuch; Urban, Alexander; Ceder, Gerbrand Physical Review B, Vol. 96, Issue 1 https://doi.org/10.1103/physrevb.96.014112	journal	July 2017
Critical-point and coexistence-curve properties of the Lennard-Jones fluid: A finite-size scaling study Wilding, Nigel B. Physical Review E, Vol. 52, Issue 1 https://doi.org/10.1103/physreve.52.602	journal	July 1995
Evolution of the Structure and Thermodynamic Stability of the BaTiO 3 ( 001 ) Surface Kolpak, Alexie M.; Li, Dongbo; Shao, Rui Physical Review Letters, Vol. 101, Issue 3 https://doi.org/10.1103/physrevlett.101.036102	journal	July 2008
Atomic and Electronic Structure of the BaTiO 3 (001) ( 5 × 5 ) R 26.6 ° Surface Reconstruction Martirez, John Mark P.; Morales, Erie H.; Saidi, Wissam A. Physical Review Letters, Vol. 109, Issue 25 https://doi.org/10.1103/physrevlett.109.256802	journal	December 2012
Conducting Boron Sheets Formed by the Reconstruction of the α -Boron (111) Surface Amsler, Maximilian; Botti, Silvana; Marques, Miguel A. L. Physical Review Letters, Vol. 111, Issue 13 https://doi.org/10.1103/physrevlett.111.136101	journal	September 2013
New Reconstructions of the (110) Surface of Rutile TiO 2 Predicted by an Evolutionary Method Wang, Qinggao; Oganov, Artem R.; Zhu, Qiang Physical Review Letters, Vol. 113, Issue 26 https://doi.org/10.1103/physrevlett.113.266101	journal	December 2014
Norm-Conserving Pseudopotentials Hamann, D. R.; Schlüter, M.; Chiang, C. Physical Review Letters, Vol. 43, Issue 20 https://doi.org/10.1103/physrevlett.43.1494	journal	November 1979
7 × 7 Reconstruction on Si(111) Resolved in Real Space Binnig, G.; Rohrer, H.; Gerber, Ch. Physical Review Letters, Vol. 50, Issue 2 https://doi.org/10.1103/physrevlett.50.120	journal	January 1983
Empirical Interatomic Potential for Carbon, with Applications to Amorphous Carbon Tersoff, J. Physical Review Letters, Vol. 61, Issue 25 https://doi.org/10.1103/physrevlett.61.2879	journal	December 1988
Phases of the Au(100) surface reconstruction Wang, Xiao-Qian Physical Review Letters, Vol. 67, Issue 25 https://doi.org/10.1103/physrevlett.67.3547	journal	December 1991
Ab initio theory of the Si(111)-(7×7) surface reconstruction: A challenge for massively parallel computation Brommer, Karl D.; Needels, M.; Larson, B. Physical Review Letters, Vol. 68, Issue 9 https://doi.org/10.1103/physrevlett.68.1355	journal	March 1992
Generalized Gradient Approximation Made Simple Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868 https://doi.org/10.1103/physrevlett.77.3865	journal	October 1996
Imaging the Surface and the Interface Atoms of an Oxide Film on Ag { 111 } by Scanning Tunneling Microscopy: Experiment and Theory Carlisle, C. I.; King, D. A.; Bocquet, M. -L. Physical Review Letters, Vol. 84, Issue 17 https://doi.org/10.1103/physrevlett.84.3899	journal	April 2000
Negative Refraction Makes a Perfect Lens Pendry, J. B. Physical Review Letters, Vol. 85, Issue 18, p. 3966-3969 https://doi.org/10.1103/physrevlett.85.3966	journal	October 2000
Revisiting the Structure of the p ( 4 × 4 ) Surface Oxide on Ag(111) Schnadt, J.; Michaelides, A.; Knudsen, J. Physical Review Letters, Vol. 96, Issue 14 https://doi.org/10.1103/physrevlett.96.146101	journal	April 2006
Structure of Ag ( 111 ) − p ( 4 × 4 ) − O : No Silver Oxide Schmid, M.; Reicho, A.; Stierle, A. Physical Review Letters, Vol. 96, Issue 14 https://doi.org/10.1103/physrevlett.96.146102	journal	April 2006
Chemical and steric constraints in inorganic solids Brown, I. D. Acta Crystallographica Section B Structural Science, Vol. 48, Issue 5 https://doi.org/10.1107/s0108768192002453	journal	October 1992
Effects of Oxygen on Silver Surface Structure Rovida, G.; Pratesi, F.; Maglietta, M. Journal of Vacuum Science and Technology, Vol. 9, Issue 2 https://doi.org/10.1116/1.1317785	journal	March 1972
When seeing is not believing: Oxygen on Ag(111), a simple adsorption system? Michaelides, Angelos; Reuter, Karsten; Scheffler, Matthias Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films, Vol. 23, Issue 6 https://doi.org/10.1116/1.2049302	journal	November 2005
Application of the Monte Carlo method to the problem of surface segregation simulation Poyurovskii, L. V.; Ruban, A. V.; Abrikosov, I. A. Journal of Experimental and Theoretical Physics Letters, Vol. 73, Issue 8 https://doi.org/10.1134/1.1381640	journal	April 2001

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Title: Automatic Prediction of Surface Phase Diagrams Using Ab Initio Grand Canonical Monte Carlo

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