evolutionary algorithms for structure discovery theory ... structural diversity is essential to...
TRANSCRIPT
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Evolutionary Algorithms for
Structure Discovery
Qiang Zhu
Q. Zhu, USPEX intro, IUCr meeting,
Montreal August, 2014
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1. (Crystal) Structure Prediction
2.1:
Variable composition Prediction
2.2
Constrained global optimization
2.3
Low dimensional systems
OUTLINE
3. OUTLOOK: Materials Discovery & Design
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(from http://nobelprize.org)
Crystal Structure is the basis for understanding
materials properties and behavior
Structure Diffraction
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J. Maddox
(Nature, 1988)
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To predict crystal structures?
Q. Zhu, USPEX
intro, IUCr meeting,
Montreal Energy Ranking
Ab-initio (DFT / DFT-D)
Generation database/experiment
“I have not failed (ten thousand times). I've just found 10000 ways that won't work” ----- Thomas. Edison
Search is missing!
Phys. Rev. B26, 5668 (1982)
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Computing time
Modern Crystal Structure Prediction (CSP)
Ranking
Searching
Reliable
Transferable
Universal
Economical
Automatic
User friendly
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Q. Zhu, Computational Materials
Design, Cambridge, MA
CSP Breakthroughs (2000s)...
Overview of USPEX
(Oganov JCP. 2006)
Organic crystals
Inorganic crystals (Breakthroughs since 2003) Metadynamics (Martonak, 2003) Data mining (Curtarolo & Ceder, 2003) Minima hopping (Goedecker, 2004) Evolutionary algorithms(EA) /PSO (Oganov, 2006; Ma, 2010;) Random sampling (Pickard, 2006) Genetic algorithms (Ho, 1997, Ho & Wang, 2010)
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Q. Zhu, USPEX intro, IUCr meeting,
Montreal
Ab initio determination
Few INPUTs (Chemical formula + P/T condition)
Evolutionary Algorithm
Self-improved searching process
Oganov A.R., Lyakhov A.O., Valle M. (2011). How evolutionary crystal structure prediction works - and why. Acc. Chem. Res. 44, 227-237.
Website: http://uspex.stonybrook.edu
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USPEX 1) (Random) initial population: from INPUTs : chemical formula 2) Relaxation at P/T conidtion : (free) energy (done by VASP, .etc) 3) Selection: lowest-energy structures as parents 4) New population: Standard variation operations
(1) Heredity (2) Lattice mutation
(4) Permutation (3) Softmutation
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Modern CSP theory
CSP Problem:
Find global energy minimum NP hard Problem ~ exp(βd) Dimensionality d = 3N + 3. Very sensitive to small changes HUGE and ‘noisy’ landscape
ARO et al., Acc. Chem. Res. 2011
CSP Solution:
Global optimization of local minima Reduced dimensionality (d* = 3N + 3 – κ) Simplified curvature of energy landscape
d d*
Au8Pd4 39
Mg4N4H4 39
Mg16O16 99
CSP complexity
d d*
Au8Pd4 39 10.9
Mg4N4H4 39 32.5
Mg16O16 99 11.6
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Fingerprint Theory
Fingerprint function : a 1D-descriptor of the structure
Similar to diffraction spectrum, PCF, ...
Difference between 2 structures is given by “distance“, e.g.:
Cosine distance
ARO & Valle, J. Chem. Phys., 2009
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Simple systems
1 D representation of funnel
Sampling in discrete space, while optimization makes it continuous Heredity
Mutation (small degree)
GaAs
Energy v.s. distance plot
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Complex systems
ARO & Valle, J. Chem. Phys. , 2009
Structural Diversity is essential to explore the complex landscape! Random generation (new blood)
Mutation (large degree)
Energy v.s. distance plot 2D projection
Energy landscape
MgO
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40-atom cell of MgSiO3 post-perovskite
Random USPEX
When searching efficiency matters!
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I. Variable compositional prediction
II. Constrained global optimization
III. Low dimensional systems
Part II: Structure Prediction
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Missing Xenon Paradox
" our atmosphere contains far less xenon, relative to the lighter noble gases, than meteorites similar to the rocky material that formed the Earth,”
----- Anderson, E, .Science, 1977
Hypothesis: Xenon is stored in the Earth’s mantle ? (most likely with perovskite, oxides or silicates) Sanloup et al, Science, 2005
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Xenon Chemistry
Ambient condition Earth’s mantle condition
Xenon does exhibit multiple valence state
Pressures(GPa): 5, 50, 100, 120, 150,
180, 200 , 220
Stoichiometry: XeO, XeO2, XeO3, XeO4
Prediction on
Xe-O system
Grochala, Chem. Soc. Rev, 2007
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AB
A decomposition line B
[EAB - (EA + EB)]>0 AB decompose
[EAB - (EA + EB )]<0 AB is stable
Thermodynamical Stability
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AB
A decomposition line B
Stable structure must be below all the possible decomposition lines !!
AB4
Thermodynamical Stability
[EAB - (EA + EB)]>0 AB decompose
[EAB - (EA + EB )]<0 AB is stable
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AB
Stable structure must be below all the possible decomposition lines !!
AB4
A B
Convex Hull
Thermodynamical Stability
[EAB - (EA + EB)]>0 AB decompose
[EAB - (EA + EB )]<0 AB is stable
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Xenon oxides at high pressure
XeO3
Xe XeO XeO2 XeO4 O
Zhu, et al, Nature Chemistry, 2013
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Rule:
New stoichiometric compounds might exist under
high pressures ! -- can we predict them automatically?
Toroidal Dumbbell Spherical
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Compositional space
Ene
rgy
spac
e
Q2: Allow the compositional variation?
A3: Smart variation operators
Q1: How to evaluate the quality of each
structure with different compositions?
A1: Optimization target: convex hull
fitness
A14B
AB
August, 2014
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Algorithm
Zhu, et al, Springer Series, 2013 October, 2014
Q. Zhu, Computational Materials
Design, Cambridge, MA
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Algorithm
Zhu, et al, Springer Series, 2013 October, 2014
Q. Zhu, Computational Materials
Design, Cambridge, MA
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Algorithm
Zhu, et al, Springer Series, 2013 October, 2014
Q. Zhu, Computational Materials
Design, Cambridge, MA
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arXiv:1408.5551
Cs-F
CsF5
[CsF2] F
Can Cs+ be oxidized further?
Applications
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Can Cs be oxidized further? Yes. Cs+, Cs3+, Cs5+ But, polyfluoride anions also contributes! [F]
- [F3] - [F5]
-
Our results
Cs-F Applications
[CsF5]
[CsF2]+ [F3]-
[Cs]+ [F5]-
arXiv:1408.5551
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Applications
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Zhang, et al, Science, 2013
NaCl3, stable from ~20 GPa
Applications
Diffraction of NaCl by Brag, 1913 Na-Cl
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I. Variable compositional prediction
II. Constrained global optimization
III. Low dimensional systems
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Predicting crystals from motifs
Crystal structures are based on the packing of
well-defined motifs Molecular crystals
Polymers
Inorganic crystals
Q. Zhu, USPEX intro, IUCr meeting,
Montreal
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Applying Constraints
Internal coordinates
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Applications: Molecular Crystals
H2O glycine benzene
Zhu, et al, Acta Cryst B, 2012
Butane-1,4-diammonium dibromide
(111) view 2*2*2 (100) view
Long term challenge
high pressure phase of Methane
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Exp Model USPEX
Exp model USPEX
August, 2014
Applications: Inorganic Crystals
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Variable composition + Molecular crystal structure prediction
October, 2014
Applications: Hydrates/Co-crystals
block 1: Ca + 2Cl block 2 : H2O
Zhu, unpublished
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Motif-based search Bond connectivity
Poly-ethylene
Applications: Polymers
Zhu, J Chem. Phys., 2014
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Motif-based search
Bond connectivity
Orientation PVDF
Applications: Polymers
Zhu, J Chem. Phys., 2014
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Motif-based search
Bond connectivity
Orientation
Cellulose
Nylon-6
Applications: Polymers
Zhu, J Chem. Phys., 2014
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Applications: Polymers
2, Structure (Property) Prediction: 1, Chemical Exploration
3, Synthesis
&Characterization
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I. Variable compositional prediction
II. Constrained global optimization
III. Low dimensional systems
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Diamond (100) -2x1
Frauenheim, PRB, 1993 Zhu, Phys. Rev. B, 2013
Low dimensional Systems: Surfaces
Si(111)-7x7 reconstruction
Wang, PRB, 2004
Catalysis Morphology
Experiment: High resolution STM Prediction by Evolutionary algorithm
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1. Heredity
2. Mutation
3. Permutation
EA in Predicting Surfaces
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Main features
Simple input information
• surface atom
• substrate
More intelligent ?
• Variable number of surface atoms
• Variable reconstruction cell (from 1*1 to N*N)
Diamond (100) 2*1 Diamond (111) 2*1
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Main features
Simple input information
• surface atom
• substrate
More intelligent ?
• Variable number of surface atoms
• Variable reconstruction cell (from 1*1 to N*N)
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A typical phase diagram of GaN (1011) surfaces.
Surface stability is function of chemical potential
Akiyama, Phys. Rev. B, 2010
Predicting Reconstructions with Variable Stoichiometry
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Zhu et al, Phys. Rev. B, 2013
Surfaces with variable stoichiometry
Surface energy
Convex hull
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Cleaved surface S2:Ga-monolayer
S1:Ga-bilayer S3: 1N-Vacancy
S5: N3-trimer S4: 0.5 N-Vacancy
Automated Search Zhu et al, Phys. Rev. B, 2013
Surfaces with variable stoichiometry
GaN: (1011̄)
Variable cell
Variable stoichiometry
Chemical Intuition Akiyama, Phys. Rev. B, 2010
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Zhu, Phys. Rev. B, 2013
Surfaces with variable stoichiometry
Variable cell
Variable stoichiometry
GaN-O: (1011̄)
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System Dimension
•0: Nano-particle; •1: polymers; •2: surfaces/2D crystals; •3: Bulk
Structure Prediction
USPEX: Computational Materials Design
Stoichiometry 0: fixed; 1: variable
Building block 0: atom; 1: molecule
August, 2014
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August, 2014 Q. Zhu, USPEX intro, IUCr meeting,
Montreal
What can USPEX do?
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Charge separation between B12-icosahedra and B2-pairs is clear from DOS
(B12)(B2)
B: Crystal
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August, 2014 Q. Zhu, USPEX intro, IUCr meeting,
Montreal
B: Compounds
Boron compounds are well know for Superconductivity, Thermal ellectrics Mechanical properties
B-H
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B: 2D Crystal
2007: Tang et al. (PRL) construct alpha-sheet.
2011: Luo et al. (JACS) confirm alpha-sheet.
2013: using USPEX, we find two MUCH more stable 2D-structures.
alpha-sheet
Structure 1,
60 meV/atom better
Structure 2,
80 meV/atom better
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Q. Zhu, USPEX intro, IUCr meeting,
Montreal August, 2014
B: 2D Crystal
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USPEX Minima Hopping
B: Surface
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Q. Zhu, USPEX intro, IUCr meeting,
Montreal August, 2014
B: Nano clusters
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OUTLOOK Computational Materials Design
Q. Zhu, USPEX intro, IUCr meeting,
Montreal August, 2014
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Searching for materials with target properties
Global Properties: (hardness, bandgap, thermal electricity, high/low K)
Local Energy
Property landscape
instead of energy landscape
Q. Zhu, USPEX intro, IUCr meeting, Montreal
Hybrid optimization:
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Superdense carbon allotropes
(1) Denser than diamond
(2) sp3 hybridization
(3) superhard
(4) huge refractive indices (up to 2.8!)
(5) strong dispersion of light
(6) tP12 is the widest-gap form of
carbon (7.3 eV)
Q. Zhu, USPEX intro, IUCr meeting, Montreal
Zhu, et al., PRB, 2011
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Simulation for carbon, 16 atoms/cell
Structure
Knoop
hardness,
GPa
Enthalpy,
eV/atom
Diamond 89.7 0.000
Lonsdaleite 89.1 0.026
C2/m 84.3 0.163
I4/mmm 84.0 0.198
Cmcm 83.5 0.282
P2/m 83.4 0.166
I212121 82.9 0.784
Fmmm 82.2 0.322
Cmcm 82.0 0.224
P6522 81.3 0.111
All of the hardest structures are sp3-hybridized
Q. Zhu, USPEX intro, IUCr meeting, Montreal
Superhard carbon allotropes
Lyakhov, et al., PRB, 2011
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Q. Zhu, Computational Materials Design, Cambridge, MA
High Energy Density Materials
Dielectric Const Band gap
Zeng, et al., Acta Cryst, C, 2014
Enthalpy Properties
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USPEX: Computational Materials Design
System Dimension
•0: Nano-particle; •1: polymers; •2: surfaces/2D crystals; •3: Bulk
Q. Zhu, USPEX intro, IUCr meeting,
Montreal
Density Hardness Dielectric constants
Band gap Magnetic moment Super capacitor
Target
Stoichiometry 0: fixed; 1: variable
Building block 0: atom; 1: molecule
Structure Prediction
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Chemical Space
Target Property
Structural Search Big data Machine Learning
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Generalized Evolutionary Metadynamics
Energy landscape
Variable Cell-NEB &
Transition Path Sampling
Synthesis Route
USPEX: Computational Materials Design
System Dimension
•0: Nano-particle; •1: polymers; •2: surfaces/2D crystals; •3: Bulk
Q. Zhu, USPEX intro, IUCr meeting,
Montreal
Density Hardness Dielectric constants
Band gap Magnetic moment Super capacitor
Target
Stoichiometry 0: fixed; 1: variable
Building block 0: atom; 1: molecule
Structure Prediction
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> 2000
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August, 2014 Q. Zhu, USPEX intro, IUCr meeting,
Montreal
Past workshops
2011 August, Xi’an, China
3.5 days (Lectures + tutorials)
1 day social program
2011 June, Poitiers, France
7 days
2.5 Days DFT
3.5 Days in USPEX
Lectures + tutorials
1 Day excursion
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August, 2014 Q. Zhu, USPEX intro, IUCr meeting,
Montreal
Past workshops
2012 December, Stony Brook, US
4.5 days (Lectures + tutorials)
2012 October, Lausanne, Switzerland
4.5 days (Lectures + tutorials)
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August, 2014 Q. Zhu, USPEX intro, IUCr meeting,
Montreal
Past workshops
2013, Guilin, China, 4.5 days
2014, Xi’an, China, 2.5 days
(for experienced users)
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August, 2014 Q. Zhu, USPEX intro, IUCr meeting,
Montreal
7th workshop in IUCr congress
Half-day workshop, 2 hours lecture 2 hours tutorials
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August, 2014 Q. Zhu, USPEX intro, IUCr meeting, Montreal
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F
August, 2014 Q. Zhu, USPEX intro, IUCr meeting,
Montreal
Acknowledgement
M. Rakitin Rapidly growing
user community….
Developers Funds
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Thanks for your attentions!