Coupled-cluster and perturbation methods for macromolecules

Coupled-cluster and perturbation methods for macromolecules So Hirata Quantum Theory Project and MacroCenter Departments of Chemistry & Physics, University of Florida

Contents Accurate electronic structure methods for small molecules Accurate vibrational structure methods for small molecules Electronic and vibrational methods for polymers Accurate electronic methods for clusters and molecular crystals

Contents Accurate electronic structure methods for small molecules Accurate vibrational structure methods for small molecules Electronic and vibrational methods for polymers Accurate electronic methods for clusters and molecular crystals

Automated symbolic algebra Hirata JPCA (2003); Hirata TCA (2006); Hirata JP Conf. Ser. (2006) Definition of a many-electron theory [ ] [ ] [ ] 0 0 0 0 2 1 2 1 2 1 2 1 2 1 2 1 0 ; 0 ; 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

Implemented methods Hirata JPCA (2003); Hirata TCA (2006); Hirata JP Conf Ser (2006) Electron Attachment Theory EA-EOM-CCSD EA-EOM-CCSDT EA-EOM-CCSDTQ Kamiya & Hirata (2007) Ionization Theory IP-EOM-CCSD IP-EOM-CCSDT IP-EOM-CCSDTQ Kamiya & Hirata JCP (2006) Excited State Theories EOM-CCSD EOM-CCSDT EOM-CCSDTQ Hirata JCP (2004) Cluster Expansion CCD, CCSD, CCSDT, CCSDTQ, LCCD, LCCSD, QCISD Hirata JPCA (2003) CC CI Linear Expansion CIS, CISD, CISDT, CISDTQ Hirata JPCA (2003) PT EOM-CC+perturbation EOM-CCSD(2) T, EOM-CCSD(2) TQ EOM-CCSD(3) T Shiozaki et al. (2007) CIS+perturbation CIS(D), CIS(3), CIS(4) Hirata JCP (2005) Perturbation MP2, MP3, MP4 Hirata JPCA (2003) 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 (2004) Shiozaki et al. (2007)

Implemented methods Hirata JPCA (2003); Hirata TCA (2006); Hirata JP Conf Ser (2006) Scalar Relativistic ECP + Spin-Orbit ECP CC, CI, MBPT EOM-CC, IP-EOM-CC EA-EOM-CC, CIS+PT CC+PT Hirata et al. JCP (2007) 1-Electron Properties Transition Moments CC, CI, MBPT EOM-CC Hirata JCP (2004) CC CI PT Active-Space CCSDt, CCSDTq, CCSDtq, CISDt, CISDTq, CISDtq Fan & Hirata JCP (2006) EOM-CCSDt, EOM- CCSDTq, EOM- CCSDtq, IP-EOM- CCSDt, IP-EOM- CCSDTq, IP-EOM- CCSDtq, EA-EOM- CCSDt, EA-EOM- CCSDTq, EA-EOM- CCSDtq Fan, Kamiya & Hirata (2007)

Geometries and binding energies Hirata, Yanai, de Jong, Nakajima & Hirao JCP (2004)

Photoelectron and relativity Hirata, Yanai, Harrison, Kamiya & Fan JCP (2007)

Explicitly-correlated CC e 1 e 2 1 12 Ψ ϕ k r k ( ) r Ψ f ( ) ϕ ( ) r r r ij i, j k k

Explicitly-correlated CC Shiozaki, Kamiya, Hirata & Valeev PCCP (2008) Tˆ Ψ= e Φ ˆ αβ kl S F t ji kl ij 0 { } Tˆ = t a b ji ab ij { αβ } Tˆ Sˆ e + Ψ= Φ F = αβ exp γ r kl ab F 0 = ( ) kl 12 Orbital basis p, q, r,... αβ ij 0 Sˆ = t αβ ji ij Complete Basis κ, λ, μ,... { αβ } Muneaki Kamiya University of Florida Occupied i, j, k,... Virtual Complementary Complete a, b, c,... Virtual α, β, γ,... Complete Virtual α, β, γ,... Toru Shiozaki University of Florida

Explicitly-correlated CC Shiozaki, Kamiya, Hirata & Valeev PCCP (2008) Ψ = { } Tˆ = t a b ji ab ij e Tˆ Φ { }( Tˆ ) Φ i j ba He ˆ Φ = 0 a t ij 0 0 C 0 ab Orbital basis p, q, r,... Complete Basis κ, λ, μ,... Muneaki Kamiya University of Florida Occupied i, j, k,... Virtual Complementary Complete a, b, c,... Virtual α, β, γ,... Complete Virtual α, β, γ,... Toru Shiozaki University of Florida

Explicitly-correlated CC Shiozaki, Kamiya, Hirata & Valeev PCCP (2008) Ψ = Tˆ Sˆ e + { } kl* ( Tˆ + S αβ ˆ ) αβ Φ i j F He ˆ Φ = 0 a t ij Φ ˆ αβ kl S = F t ji kl 0 0 C ij 0 { αβ } kl Orbital basis p, q, r,... Complete Basis κ, λ, μ,... Muneaki Kamiya University of Florida Occupied i, j, k,... Virtual Complementary Complete a, b, c,... Virtual α, β, γ,... Complete Virtual α, β, γ,... Toru Shiozaki University of Florida

Explicitly-correlated CC Shiozaki, Kamiya, Hirata & Valeev PCCP (2008) { } kl* ( Tˆ + Sˆ αβ He ) αβ Φ i j F ˆ Φ = 0 a t 0 0 C H ˆ f κ 1 4 v κλ = λ + ˆ αβ kl S = F t αβ ji { } { κ λ } μν κλνμ kl ij { } v pq F αβ αβ ij kl ij Orbital basis p, q, r,... Complete Basis κ, λ, μ,... Muneaki Kamiya University of Florida Occupied i, j, k,... Virtual Complementary Complete a, b, c,... Virtual α, β, γ,... Complete Virtual α, β, γ,... Toru Shiozaki University of Florida

Explicitly-correlated CC Shiozaki, Kamiya, Hirata & Valeev PCCP (2008) ab v pq F αβ αβ ij pq κλ pq rs pq kα pq α k κλ ij rs ij kα ij α k ij = v F v F v F v F ( 1 ) 12 12 pq ij pq rs pq ka pq a k rs ij ka ij a k ij = r f v F v F v F Orbital basis p, q, r,... Complete Basis κ, λ, μ,... Edward F. Valeev Virginia Tech Occupied i, j, k,... Virtual Complementary Complete a, b, c,... Virtual α, β, γ,... Complete Virtual α, β, γ,... Toru Shiozaki University of Florida

Explicitly-correlated CC Shiozaki, Kamiya, Hirata & Valeev PCCP (2008); Same team (in preparation) Diagrammatic evaluation of expectation values Edward F. Valeev Virginia Tech The resolution of the identity insertions Identification of special intermediates such as f 12 /r 12 CABS substitutions Special common subexpression eliminations Strength reduction Factorization Common subexpression eliminations Muneaki Kamiya University of Florida Code synthesis Toru Shiozaki University of Florida

Explicitly-correlated CC Shiozaki, Kamiya, Hirata & Valeev (in preparation) Ne H 2 O F 2 The first complete CCSD-R12 results!! Toru Shiozaki University of Florida Muneaki Kamiya University of Florida Edward F. Valeev Virginia Tech

Contents Accurate electronic structure methods for small molecules Accurate vibrational structure methods for small molecules Electronic and vibrational methods for polymers Accurate electronic methods for clusters and molecular crystals

Anharmonicity in polyethylene Keçeli & Hirata (in preparation) HF/6-31G* MP2/6-31G* Murat Keçeli University of Florida

Anharmonicity in polyacetylene Keçeli & Hirata (in preparation) HF/6-31G* MP2/6-31G* Murat Keçeli University of Florida

CCSD for polymers Hirata, Bartlett, et al. CPL (2001); Hirata, Bartlett, et al. JCP (2004)

Fast MP2 for polymers Shimazaki & Hirata (in preparation) E = 1 BZ [ k ] [ k ] [ k ] [ k ] i j a b cell [ k ] [ k ] [ ] [ ] 4 i j ka k K b i, j, a, bk, k, k ei + ej ea eb i j a i j a b 2 ka 1 r 12 kb momentum conservation ki + kj = ka + kb ki k j cost ( 2K ) 3

Fast MP2 for polymers Shimazaki & Hirata (in preparation) k p π 2π ( K 1) π Kπ = 0, ±, ±, K, ±, Ka Ka Ka Ka cost ( 2K ) 3 Normal MP2 k + k = k + k i j a b Accuracy 100% Speed 1

Fast MP2 for polymers Shimazaki & Hirata (in preparation) k p 4 8 K = 0, ± π, ± π, K, < + π Ka Ka Ka cost 3 3 ( 1 ) ( 2K ) 4 (mod 4) MP2 k + k = k + k i j a b Accuracy 100.2% Speed 11

Fast MP2 for polymers Shimazaki & Hirata (in preparation) k p = 0 cost 1 Γ MP2 k = k = k = k = i j a b 0 Accuracy 94% Speed 80

Contents Accurate electronic structure methods for small molecules Accurate vibrational structure methods for small molecules Electronic and vibrational methods for polymers Accurate electronic methods for clusters and molecular crystals

Fast methods for water clusters Hirata et al. MP (2005) N-body (N > 2) Coulomb in dipole-dipole approximation 1 and 2-body Coulomb Exchange Correlation n ( ) E = E E E + E ij i j i i< j i Pair Self-consistent Monomer energy in in the dipoles presence field of dipole field n

Fast methods: ESP+BSSE Kamiya, Hirata & Valiev JCP (2007) N-body (N > 2) Coulomb with more accurate short-range potentials Partial charges that reproduce the electrostatic potential around the molecule n ( ) Counterpoise BSSE correction E = E E E + E ij i j i i< j i n Muneaki Kamiya University of Florida

Fast methods for water clusters Hirata et al. MP (2005); Kamiya, Hirata, Valiev JCP (2008) One-body Two-body Higher Coulomb Exact Exact >dipole Exchange Exact Exact Neglected Correlation Exact Exact Neglected Total energy 99.999 100.001% Binding energy A few kcal/mol Excitation energy A few hundredths ev Accurate Systematic Fast Easy to implement BSSE correction Analytical derivatives

Fast methods for water clusters Hirata et al. MP (2005) 0.0 0.0 Conventional MP2 1.4 1.0 2.2 1.7 Binary interaction MP2 12.2 14.4 kcal/mol

Fast methods for water clusters Hirata et al. MP (2005) A record equation-of-motion coupledcluster singles and doubles (EOM-CCSD) calculation with aug-cc-pvdz of a 247- atom cluster (740 cm 1 )

Molecular crystals Maddox (Nature, 1988): One of the continuing scandals in the physical sciences is that it remains in general impossible to predict the structure of even the simplest crystalline solids from a knowledge of their chemical composition. Solids such as crystalline water (ice) are still thought to lie beyond mortals ken.

Forces and force constants Hirata et al. MP (2005); Hirata (in preparation) n ( ) E = E E E + E ij i j i i< j i n n E Eij E E i j Ei E = + + x i< j x x x i x x 2 n 2 2 2 n 2 E Eij E E i j Ei = + x y i< j x y x y x y i x y n LR

Crystalline hydrogen fluoride Sode, Keçeli & Hirata (in preparation) Olaseni Sode University of Florida

Solid formic acid: energetics Hirata (in preparation) MP2 aug-cc-pvtz BSSE CCSD aug-cc-pvdz +2.9 kcal/mol +2.6 kcal/mol ±0.0 kcal/mol ±0.0 kcal/mol +0.5 kcal/mol +0.7 kcal/mol

Solid formic acid: k = 0 frequencies Hirata (in preparation) β 1

Solid formic acid: phonon dispersion Hirata (in preparation) β 1 β 1

Solid formic acid: inelastic neutron Hirata (in preparation) α β 1 β 2

Acknowledgements US Department of Energy US National Science Foundation University of Florida Division of Sponsored Research Hewlett Packard Company & ACS American Chemical Society PRF Japan Society for the Promotion of Science