Applications of 1st-Principles Based Evolution Algorithms in Material Design and Discovery Jer-Lai Kuo (郭哲來) Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei, Taiwan 1st Workshop of HPC on Nano-scale Materials Research Aug/13/2009, NCKU, Tainan, Taiwan Outlines: • What is 1st-Principles Simulations? Why do we need Evolution Algoritm? • Proton Order/Disorder transitions in Ice a 70 year old problem in ice physics. • ZnO based alloy Alloy Synthesis on the Cloud ? • Structure of nano-sized clusters Knowing the structure is the FIRST step toward understanding Material Properties Collaborators and Group Members $$ = Prof. Mike Klein Prof. Ong Yewsoon Prof. Zhu Zexuan Chem@UPenn SCE@NTU ShenZhen U/China Fan XiaoFeng Wu Hongyu Nguyen Quoc Chinh Bing Dan Zhang Jingyun Lee Ching-Tao Basis of 1st-Principles Methods Dirac (1929): “The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known.” Schrödinger equation: Erwin Schrödinger Paul A. M. Dirac Nobel Prize in Physics 1933 HH == EE e1 e2 n1 n2 Walter Kohn John A. Pople “for his development of DFT and comp. Nobel Prize in Chem. 1998 methods in quantum chemistry” Multi-scale simulation from Ab Initio Experimental/Thermodynamic data/Material properties We are developing automatic • Large number of atoms algorithms to bundle these • Many configurations General Ising model & components together Monte Carlo Simulations Genetic/Evolution Algorithm Formation Energy Structure, lattice const. Electronic Properties • Small unit cells • Few configurations VASP/CPMD/Wien2k Quantum Mechanical Calculations Gaussian/Molpro… Material Synthesis on the CLOUD GRID → CLOUD Outlines: • What is 1st-Principles Simulations: Why Multi-scale and go CLOUD? • Proton Order/Disorder transitions in Ice a 70 year old problem in ice physics. • BexZn1-xO? Alloy Synthesis on the Cloud. • Structure of nano-sized clusters Knowing the structure is the FIRST step toward understanding Material Properties WHAT!! Ordinary Ice is NOT crystal. • Snow flakes have beautiful hex-symmetry !! http://www.its.caltech.edu/~atomic/snowcrystals/ •A crystal is a solid in which the components are packed in a regularly ordered, repeating pattern extending in all three spatial dimensions http://www.lsbu.ac.uk/water/phase.html • Ice has a disordered proton distribution. In this 48-water unit cell of ice-Ih, there are 2,404,144,962 H-bond isomers. 3,600,000 H-bond isomers. Residual Entropy of ice-Ih L.Pauling JACS 57, 2680 (1935) 3 2N , S k ln 3.37 J / K W.F. Giauque and J.W.Stout, JACS 58, 1144 (1936) S(T 0) 3.4 0.6 J / K Not just ice-Ih, many phases of ice are proton-disordered. Thermal properties of ice is essential to many important issues in physics, chemistry, and environment. Finding the proton-ordered ice, will help us better understand H-bonding. Nature ,vol 391, p.268 Proton Order/Disorder transition Training graph invariants on small unit cells (Quantum Mech.) Testing the prediction on larger unit cells. (ab initio) – QM MC simulations on very large unit cells to simulate disorder/order transition. –SM XI Ih VIII VII Singer, Kuo, et al, Phys. Rev. Lett. 94, 135702 (2005)] What else about ice: • New Phases? • Effects of Pressure? • X-ray Absorption Spectra Zhang Jingyun Outlines: • What is 1st-Principles Simulations: Why Multi-scale and go CLOUD? • Proton Order/Disorder transitions in Ice a 70 year old problem in ice physics. • ZnO based alloy Alloy Synthesis on the Cloud ? • Structure of nano-sized clusters Knowing the structure is the FIRST step toward understanding Material Properties ZnO Alloys for opto-electronic applications ZnO Band Gaps and light E = h v LED g Solar Cells Tunable Eg MgO ZnO Sun cream EZnO = h v1 EMgO = h v2 Semiconductor Alloys – BexZn1-xO Cluster Expansion Theory BexZn1-xO ZnO (Eg=3.4eV) MgO (Eg=7.7eV) BeO (Eg=10.6eV) APL 88, 052103 ( 2006) 216 = 65,536 2N How many Jij are needed? wurtzite P6 mc How many are needed? N 3 2 ZnO BeO x=0 652 sym-distinc x=1 =(Zn, Zn, …) =(Be, Be, …) Fan, Zhu et al,APL, 91, 121121 (‘07). BexZn1-xO Alloys 0.3 Formation Enthalpy: 0.2 ΔH f [σ,x] E[σ,BexZn1xO] xE[BeO](1 x)E[ZnO] 0.1 Formation enthalpy (eV/cation) Lattice constants 0.0 0.0 0.2 0.4 0.6 0.8 1.0 5.4 Be concentration X (a) 5.0 (b) 5.2 Band Gaps 4.5 5.0 4.0 9.0 (a) (b) 10.5 3.5 4.8 7.5 3.0 9.0 4.6 6.0 2.5 7.5 Lattice parameter c ( Å) parameter c ( Lattice Formation enthalpy (eV/cation) enthalpy Formation 4.4 4.5 2.0 x=0.375 x=0.4375 x=0.5 x=0.5625 x=0.625 6.0 4.2 1.5 3.0 0.0 0.2 0.4 0.6 0.8 1.0 Bandenergy gap (eV) 4.65 4.70 4.75 4.80 4.85 4.90 (eV) energy gap Band 4.5 Be concentration x Lattice constant c (Å) 1.5 3.0 XF Fan, .., and Jer-Lai Kuo, 0.00.20.40.60.81.0 0.0 0.2 0.4 0.6 0.8 1.0 Be concentration x App. Phys. Lett. 91, 121121 (2007) Be concentration x [100] SL [001] SL Exp Effect of Lattice Vibration Phonon DOS . PWSCF: linear response good for crystal. PHONE: calculate DOS Effect of Lattice Vibration Approximations made: • Bragg-Williams app. • Neglect short range order • Harmonic app. • Small super-cell size CK Gan, XF Fan, and Jer-Lai Kuo, Comp. Mat. Sci (in press) Non-isostructural alloys MgxZn1-xO, CdxZn1-xO,…. 66 0.30 0.35 0.25 0.30 0.20 0.25 0.20 0.15 0.15 0.10 0.10 0.05 0.05 Formation enthalpy (eV/cation) Formation enthalpy 0.00 0.00 Formation enthalpy (eV/cation) enthalpy Formation 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 MgO 1-x ZnO CdO 1-x ZnO X. F. Fan, HD Sun, Z.X. Shen, and Jer-Lai Kuo, J. Phys. Cond. Matt. 20, 235221 (2008) Material Discovery on the CLOUD 1st-Principle Calculations to replace wet-lab based methods? Improve efficiency 2 month (2007) with in-house PC clusters 2 days (2008) with in-house PC clusters 2 hrs (2009) with large HPC? Material Design Outlines: • What is 1st-Principles Simulations: Why Multi-scale and go CLOUD? • Proton Order/Disorder transitions in Ice a 70 year old problem in ice physics. • BexZn1-xO? Alloy Synthesis on the Cloud. • Structure of nano-sized clusters Knowing the structure is the FIRST step toward understanding Material Properties Basic scheme of the Multi-scale Method • Use empirical models to quickly 1. GA to search explore the PES of water with empirical models • Ab initio results can be used in return to reparameterized models 2. Refine with ab initio method A1 A A2 3 3. Refine with B1 A4 A5 B B B2 3 B4 5 high level ab initio A replaced by (BA) Nguyen QC.. Jer-Lai Kuo, J. Phys. Chem. A 112, 6257 (2008) Exploring the Energy Landscape of Clusters using Genetic Algorithms Asynchronized GA: by Bernd Hartke the closest atoms Genetic Algorithm Mutation & Crossover : works directly on coordinates of molecular clusters A collector was implemented Collection to gather new isomer of isomers found by GA suitable for GRID comp. Soh, Nguyen ...Ong, Kuo IEEE/ACM trans… Parameterizing empirical models • Levenberg-Marquardt nonlinear least square algorithm + Genetic Algorithm • Objective function M 1 k k 2 F( p) (EOSS 2 (p) E DFT ) M k1 p: parameter, M: # of data points, k k EOss2 , EDFT : OSS2 and DFT binding energy of configuration k ?x i New point pi Local minima m How to distinguish diff. isomers? “Ultra fast shape recognition” Ballester and Richards, J. Comp. Chem. 28, 1711 (2007) • Similarity index ranges from 0 to 1: – 0 : totally different – 1 : exactly the same • Differ by just 1 atom, SI= 0.966 ctd {dk }: to molecular centroid (ctd) To make them independent to the cst {dk }: to the closest atom (cst) of ctd size of cluster, the first, second {dkfct}: to the furthest atom (fct) of ctd and third moments of each set are used. {dkftf}: to the furthest atom (ftf) of fct HSA: from isomers to thermal prop. d) n=8 5 4 3 Harmonic superposition approximation 2 1 0.8 The canonical partition function Z (β) can be 0.6 0.4 approximated as the summation of harmonic 0.2 0 50 100 150 200 250 300 350 400 contributions of all collected local minima. e) n=9 5 4 Z( ) na Z a ( ) 3 2 a 1 0.8 0.6 The finite temperature behavior (heat 0.4 0.2 capacity curves, structural transitions, canonical 0 50 100 150 200 250 300 350 400 probabilities .i.e.) of Wn+ clusters can be f) n=10 derived afterward. 5 4 3 2 1 0.8 0.6 Nguyen, Ong, and Kuo, 0.4 0.2 "A multi-scale approach to study thermal behavior of 0 + 50 100 150 200 250 300 350 400 protonated water clusters H (H2O)n'', Temperature (K) J. Chem. Theory and Comp. ) Cv - HSA Cv - PT T L SR DR MR + Two-stage melting of H (H2O)18 Cage Flower Tree 3-coord 2-coord Kuo and Klein J. Chem. Phys. 112, 24516 (2005). + Melting of H (H2O)21 cage (135~155K) (Temp) cold -------------------------------------------------- warm 3 3 3 2 3600 3650 3700 3750 3800 3600 3650 3700 3750 3800 3600 3650 3700 3750 3800 Frequency (cm-1) * * Mass spectra 17 19 21 23 25 27 17 19 21 23 25 27 17 19 21 23 25 27 Cluster Size (n) 0.6 0.6 0.6 Dissociation 0.4 0.4 0.4 0.2 0.2 0.2 * Dissociation Fraction Dissociation 0.0 * 0.0 0.0 17 19 21 23 25 27 17 19 21 23 25 27 17 19 21 23 25 27 Cluster Size (n) Collaborators and Group Members $$ = Prof.