Predictive Computing for Solids and Liquids
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1 Predictive Computing for Solids and Liquids So Hirata Department of Chemistry May 214 Blue Waters Symposium 1
2 Schrödinger equation for a water molecule 1-particle, 3-dimensional partial differential equation Ĥ i Z I I e e Z + + I Z J e 2 2m e i=1 2m I I=1 I=1 i=1 4πε r ii i=1 j=i+1 4πε r ij I=1 J=I+1 4πε r Ψ = EΨ IJ sin θ i 2 ri ri ri ri sin θi φi sinθi θi θi Conditions arising from the indistinguishability of electrons ( re 1, re2, re3, re4, re5, re6, re7, re8, re9, re 1, rh1, rh2, ro) ( re2, re 1, re3, re4, re5, re6, re7, re8, re9, re 1, rh1, rh2, ro) ( re3, re 1, re2, re4, re5, re6, re7, re8, re9, re 1, rh1, rh2, ro) ( r, r, r, r, r, r, r, r, r, r r r r ) Ψ = Ψ = Ψ = Ψ,,,... e3 e2 e1 e4 e5 e6 e7 e8 e9 e1 H1 H2 O = 3,628,8 terms! Many-body
3 Systematic many-body methods
4 Automated symbolic algebra Definition of a many-electron theory [ ] [ ] [ ] ; ; Φ Φ = Φ Φ = Φ Φ = C T T T T ab ij C T T T T a i C T T T T He e He e He e E Mathematical expressions A parallel computer program
5 Electron Attachment Theory EA-EOM-CCSD EA-EOM-CCSDT EA-EOM-CCSDTQ Kamiya & Hirata JCP (27) Ionization Theory IP-EOM-CCSD IP-EOM-CCSDT IP-EOM-CCSDTQ Kamiya & Hirata JCP (26) Excited State Theories EOM-CCSD EOM-CCSDT EOM-CCSDTQ Hirata JCP (24) Cluster Expansion CCD, CCSD, CCSDT, CCSDTQ, LCCD, LCCSD, QCISD Hirata JPCA (23) Implemented methods CC CI Linear Expansion CIS, CISD, CISDT, CISDTQ Hirata JPCA (23) PT EOM-CC+perturbation EOM-CCSD(2) T, EOM-CCSD(2) TQ EOM-CCSD(3) T Shiozaki et al. JCP (27) CIS+perturbation CIS(D), CIS(3), CIS(4) Hirata JCP (25) Perturbation MP2, MP3, MP4 Hirata JPCA (23) Combined CC+PT CCSD(T) CCSD(2) T, CCSD(3) T CCSD(2) TQ, CCSD(3) TQ CCSDT(2) Q, CR-CCSD(T) Hirata et al. JCP (24) Shiozaki et al. JCP (27)
6 Structures, thermochemistry, and spectra Hirata et al., J. Chem. Phys. (24); Hirata et al., J. Chem. Phys. (27)
7 Frontiers of predictive computing Applicability Molecules Clusters Polymers Solids Condensed matter Solid-state chemistry Condensed matter physics Materials science Geochemistry High-pressure chemistry Planetary science High-T c superconductivity A DOE report on Computational Materials Science (21): We are at the threshold of a new era where the integrated synthesis, characterization, and modeling of complex materials New theories and chemical and processes will transform our ability to understand algorithms and design new materials and chemistries with predictive power Materials Genome DFT Initiative for MP2 Global Competitiveness CCSD FCI (211): the development of advanced materials can be accelerated through Accuracy advances in computational techniques 7
8 8
9 Embedded-fragment approach Hirata et al., Mol. Phys. (25); Kamiya, Hirata, and Valiev, J. Chem. Phys. (28); Hirata et al., Acc. Chem. Res. (214) N-body (N > 2) Coulomb in point-charge or dipole approximation 1 and 2-body Coulomb Exchange Correlation Pair energy in the presence of selfconsistent atomic charges or dipoles n E = E i + E ij E E i j i=1 n i< j ( ) + Cf. Li, Paulus, Schutz, Manby, Beran, Truhlar, Raghavachari, Herbert, Collins, Gordon, Gao, Fedorov, Kitaura, Zhang, et al.
10 Ice Ih He, Sode, Xantheas, and Hirata, J. Chem. Phys. (212) Xiao He MP2/aug-cc-pVDZ 1
11 Ice Ih He, Sode, Xantheas, and Hirata, J. Chem. Phys. (212) IR, Raman, and Inelastic neutron scattering spectra Xiao He 11
12 Ice Ih He, Sode, Xantheas, and Hirata, J. Chem. Phys. (212) Inelastic neutron scattering spectra Xiao He Heat capacities 12
13 Ice VIII Gilliard, Sode, and Hirata, J. Chem. Phys. (214) Kandis Gilliard MP2/aug-cc-pVDZ CCSD/aug-cc-pVDZ 13
14 Ice VIII Gilliard, Sode, and Hirata, J. Chem. Phys. (214) Pressure dependence of volume and lattice constants Kandis Gilliard Diamond synthesis (18 GPa) Center of the Moon (5 GPa) Bottom of the Mariana Trench (.1 GPa) 14
15 Ice VIII Gilliard, Sode, and Hirata, J. Chem. Phys. (214) Kandis Gilliard Pressure dependence of IR, Raman, and INS spectra 15
16 Solid CO 2 Sode, Keçeli, Yagi, and Hirata, J. Chem. Phys. (212) Olaseni Sode MP2/aug-cc-pVDZ 16
17 Solid CO 2 Sode, Keçeli, Yagi, and Hirata, J. Chem. Phys. (212) Pressure dependence of Raman spectra Olaseni Sode Frequency / cm Experiment (2K) Experiment (4K) Experiment (8K) Experiment (3K) Theory Pressure / GPa ν ν + CO 2 encapsulation in minerals 17
18 Phase transition in solid CO2 Li, Sode, Voth and Hirata, Nature Communications (213) Jinjin Li Pressure dependence of volume Experiment Pa3 (MP2/aug-cc-pVDZ) Volume / cm3 mol -1 Volume / cm3 mol -1 Experiment Theory 2 18 Cmca (MP2/aug-cc-pVDZ) (2) Orthor (1) Cubic Pa3 φ 2 18 Pressure (2) Orthorhombic Cmca (1) Cubic Pa3 Temperature φ K Pressure / GPa 15 2 Pressure 14 Temperature a c 5 b Pressure / GPa 18
19 Phase transition in solid CO2 Li, Sode, Voth and Hirata, Nature Communications (213) Jinjin Li 2 Experiment 1 Experiment 2 Experiment 3 MP2/aug-cc-pVDZ V Fluid Raman spectra Phase III IV 1 VII Raman intensity Raman intensity Raman spectra Phase I Temperature (K) 15 II Experiment (2)(1) Orthorhombic Cubic Pa3 Cmca (1) Cubic Pa3 5 φ I (Pa3) Pressure Temperature (2) Orthorhombic Cmca φ a b Pressure c a III (Cmca) c b Temperature MP2/aug-cc-pVDZ MP2/aug-cc-pVDZ Frequency / cm -1 Experiment 1 2 Pressure (GPa) Frequency / cm -1 19
20 What can be done with Blue Waters? First-principles phase diagram of ice First-principles prediction of thermal expansion of ice First-principles simulation of liquid water First-principles simulation of chemical reactions in aqueous media 2 BIM-MP2 exp Soohaeng Willow goo (R) R(Å) 2
21 Monte Carlo MP2 Willow, Kim and Hirata, J. Chem. Phys. (212) Very long O(n 4 ) summation of products of two 6-dimensional integrals occ. vir. ab ij ij ab E (2) = i, j a, b ε i + ε j ε a ε b Explicit two-electron integrals E (2) = occ. occ. vir. i, j vir. a, b ϕ i ( r 1 )ϕ j r 2 ϕ r a ( r 1 )ϕ b ( r 2 )dr 1 dr 2 ϕ i ( r 3 )ϕ j 12 r 4 ϕ r a ( r 3 )ϕ b ( r 4 )dr 3 dr 4 34 ε i + ε j ε a ε b Laplace transformation of the denominator ( ) 1 E (2) = ϕ i ( r 1 )ϕ j ( r 2 ) 1 ϕ a ( r 1 )ϕ b ( r 2 )dr 1 dr 2 ϕ i ( r 3 )ϕ j r 4 r 12 i, j a, b E (2) = occ. occ. ( ) 1 ( ) 1 ϕ a ( r 3 )ϕ b ( r 4 )dr 3 dr 4 r 34 Change of orders of summations and integrations Single 13-dimensional integral evaluated by Monte Carlo E (2) ( = G r 1, r 3,τ )G ( r 2, r 4,τ )G + ( r 1, r 3,τ )G + ( r 2, r 4,τ ) dr 1 dr 4 dτ r 12 r 34 vir. vir. Soohaeng Willow e ( ε i +ε j ε a ε )τ b dτ ϕ i ( r 1 )ϕ i ( r 3 )e ε iτ ϕ j ( r 2 )ϕ j ( r 4 )e ε jτ ϕ a ( r 1 )ϕ a ( r 3 )e ε aτ ϕ b ( r 2 )ϕ b ( r 4 )e ε bτ i j a b dr 1 dr 4 dτ r 12 r 34
22 Monte Carlo MP2 Willow, Kim and Hirata, J. Chem. Phys. (212) E = f ( x ) dx = f ( x) f ( x) g x dx = ( ) g(x) weight x g g ( x ) function Requirement 1: analytically integrable E = g ( r1, r2, r3, r4 ) = 1 2 4ECoulomb 2 3 f ( x) / g( x) G ( r1, r3, τ ) G ( r2, r4, τ ) G + ( r1, r3, τ ) G + ( r2, r4, τ ) dr1 dr4 dτ r12 r34 Singularities ρ ( r1 ) ρ ( r2 ) ρ ( r3 ) ρ ( r4 ) r12 r34 g (r, r, r, r ) dr dr dr dr 1 Metropolis g ( x ) dx = 1 Requirement 2: cancellation of singularities (2) Soohaeng Willow =1
23 MC-MP2 for Ecorr, IP, and EA Willow, Kim and Hirata, J. Chem. Phys. (212) Willow, Kim and Hirata, J. Chem. Phys. (213) Nitrogen 6-31G**.35 Water HOMO and HOMO 1 Correlated IP and EA Soohaeng Willow.4 Correlation energy ϵ (2) p /Eh.45 p =4 p = MC step / 1 7 Statistical errors CPU time / sec Cost scaling H 2O N 2 CH 4 C 2H m Size (number of orbitals)
24 Parallel MC-MP2, MP3, MP2-R12 Willow, Hermes, Kim and Hirata, J. Chem. Theo. Comput. (213); Willow and Hirata, J. Chem. Phys. (213); Willow, Zhang, Valeev, and Hirata, J. Chem. Phys. (Comm.) (214) C 6 cc-pvdz on 32 processors of Blue Waters Correlated EA Soohaeng Willow Speedup Parallel scaling Number of processors T tot T MC r 5 τ 1 + τ 2 r 6 G + G + G r 3 r 4 G τ 1 G + G + r 1 τ = r 2 Diagrammatics E/Eh C 6 H 6 D T Q cc-pvxz E MP2 E MP2 F12 R12: basis convergence
25 What can be done with Blue Waters? Accurate calculations of opto-electronic properties of conjugated polymers used in organic solar cells, LED, FET, capacitors, etc. Accurate calculations of van der Waals interactions between conjugated polymers, PAHs, graphene, graphite, C 6, etc Val. band edge PPP (1) PT (2) 7 Experiment ev ev DFT 5. ev 4.5 ev 8 Matthew Hermes HF 6.6 ev 6.2 ev MP2 6.4 ev 5.5 ev 9 25
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