Coupled-cluster and perturbation methods for … and perturbation methods for macromolecules So...
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Coupled-cluster and perturbation methods for
macromolecules
So HirataQuantum Theory Project
and MacroCenterDepartments of Chemistry & Physics, University of Florida
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ContentsAccurate electronic structure methods
for small moleculesAccurate vibrational structure methods
for small molecules
Electronic and vibrational methodsfor polymers
Accurate electronic methodsfor clusters
and molecular crystals
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ContentsAccurate electronic structure methods
for small moleculesAccurate vibrational structure methods
for small molecules
Electronic and vibrational methodsfor polymers
Accurate electronic methodsfor clusters
and molecular crystals
![Page 4: Coupled-cluster and perturbation methods for … and perturbation methods for macromolecules So Hirata Quantum Theory Project and MacroCenter Departments of Chemistry & Physics, University](https://reader030.fdocuments.net/reader030/viewer/2022021801/5b2003fb7f8b9ab3188b4eb1/html5/thumbnails/4.jpg)
Automated symbolic algebra Hirata JPCA (2003); Hirata TCA (2006); Hirata JP Conf. Ser. (2006)
Definition of a many-electron theory[ ] [ ] [ ] 0000
212121212121 0 ;0 ; ΦΦ=ΦΦ=ΦΦ= +−−+−−+−−C
TTTTabijC
TTTTaiC
TTTT HeeHeeHeeE
Mathematical expressions
A parallel computer program
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Implemented methods Hirata JPCA (2003); Hirata TCA (2006); Hirata JP Conf Ser (2006)
CI
PTCC Combined CC+PTCCSD(T)
CCSD(2)T
, CCSD(3)TCCSD(2)TQ
, CCSD(3)TQCCSDT(2)Q
, CR-CCSD(T)Hirata et al. JCP (2004)Shiozaki et al.
(2007)
Linear ExpansionCIS, CISD, CISDT, CISDTQ
Hirata JPCA (2003)
CIS+perturbationCIS(D), CIS(3), CIS(4)
Hirata JCP (2005)
PerturbationMP2,
MP3, MP4Hirata JPCA (2003)Excited State Theories
EOM-CCSDEOM-CCSDT
EOM-CCSDTQHirata JCP (2004)
Ionization TheoryIP-EOM-CCSD
IP-EOM-CCSDTIP-EOM-CCSDTQKamiya & Hirata JCP (2006)
Cluster ExpansionCCD, CCSD, CCSDT,
CCSDTQ, LCCD,LCCSD, QCISD
Hirata JPCA (2003)
Electron Attachment TheoryEA-EOM-CCSD
EA-EOM-CCSDTEA-EOM-CCSDTQ
Kamiya & Hirata (2007)
EOM-CC+perturbationEOM-CCSD(2)T
, EOM-CCSD(2)TQEOM-CCSD(3)T
Shiozaki et al.
(2007)
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Implemented methods Hirata JPCA (2003); Hirata TCA (2006); Hirata JP Conf Ser (2006)
CC PT
CI
Active-SpaceCCSDt, 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)
Scalar Relativistic ECP+ Spin-Orbit ECP
CC, CI, MBPTEOM-CC, IP-EOM-CCEA-EOM-CC, CIS+PT
CC+PTHirata et al. JCP (2007)
1-Electron PropertiesTransition Moments
CC, CI, MBPTEOM-CC
Hirata
JCP (2004)
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Geometries and binding energies Hirata, Yanai, de Jong, Nakajima & Hirao JCP (2004)
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Photoelectron and relativity Hirata, Yanai, Harrison, Kamiya & Fan JCP (2007)
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Explicitly-correlated CC
e1e21
12r−
( ) ( ), j kij i kf ϕΨ ≈ ∏∑ r r r
( )k kϕΨ ≈ ∏∑ r
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Explicitly-correlated CC Shiozaki, Kamiya, Hirata & Valeev PCCP (2008)
ˆˆ0
STe +Ψ = Φ
Toru ShiozakiUniversity of Florida
Muneaki KamiyaUniversity of Florida
ˆ0
TeΨ = Φ
{ }† †ˆ klkl ijS F t jiαβ α β= ( )12expklF r klαβ αβ γ= −
{ }† †ˆijS t jiαβ α β={ }† †ˆ ab
ijT t a b ji=
Occupiedi, j, k, ...
Virtuala, b, c, ...
Complementary Complete Virtual α′, β ′, γ ′, ...
Orbital basisp, q, r, ...
Complete Basisκ, λ, μ, ...
Complete Virtual α, β, γ, ...
0abijF ≡
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Explicitly-correlated CC Shiozaki, Kamiya, Hirata & Valeev PCCP (2008)
Toru ShiozakiUniversity of Florida
Muneaki KamiyaUniversity of Florida
{ }† †ˆ abijT t a b ji=
{ }( )ˆ† †0 0
Cˆ 0T ab
iji j ba He tΦ Φ = a
ˆ0
TeΨ = Φ
Occupiedi, j, k, ...
Virtuala, b, c, ...
Complementary Complete Virtual α′, β ′, γ ′, ...
Orbital basisp, q, r, ...
Complete Basisκ, λ, μ, ...
Complete Virtual α, β, γ, ...
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Explicitly-correlated CC Shiozaki, Kamiya, Hirata & Valeev PCCP (2008)
Toru ShiozakiUniversity of Florida
Muneaki KamiyaUniversity of Florida
{ } ( )ˆ† † ˆ*0 0
Cˆ 0k kll T S
iji j F He tαβαβ +Φ Φ = a
ˆˆ0
STe +Ψ = Φ
{ }† †ˆ klkl ijS F t jiαβ α β=
Occupiedi, j, k, ...
Virtuala, b, c, ...
Complementary Complete Virtual α′, β ′, γ ′, ...
Orbital basisp, q, r, ...
Complete Basisκ, λ, μ, ...
Complete Virtual α, β, γ, ...
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Explicitly-correlated CC Shiozaki, Kamiya, Hirata & Valeev PCCP (2008)
Toru ShiozakiUniversity of Florida
Muneaki KamiyaUniversity of Florida
{ } ( )† † *0 0
C
ˆˆˆ 0kl kli
T SjHei j F tαβαβ +Φ Φ = a
{ } { }† † †1ˆ4vH f κλμν
κλ νκ μλ κ λ= +
{ }† †ˆ klkl ijS F t jiαβ α β=
pqijv Fαβ
αβ
Occupiedi, j, k, ...
Virtuala, b, c, ...
Complementary Complete Virtual α′, β ′, γ ′, ...
Orbital basisp, q, r, ...
Complete Basisκ, λ, μ, ...
Complete Virtual α, β, γ, ...
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Explicitly-correlated CC Shiozaki, Kamiya, Hirata & Valeev PCCP (2008)
Toru ShiozakiUniversity of Florida
( )112 12
pq pq rs pq k pq kij rs ij k ij k ij
pq pq rs pq k pq krs ij k ij k ijij
a
pq
a
i
a
j
a
v F v F v F v F
r f v F v F v F
v Fαβαβ
κλ α ακλ α α
′
′′
′
′−′
′ ′= − − −
= − − −
Occupiedi, j, k, ...
Virtuala, b, c, ...
Complementary Complete Virtual α′, β ′, γ ′, ...
Orbital basisp, q, r, ...
Complete Basisκ, λ, μ, ...
Complete Virtual α, β, γ, ...
ab
Edward F. ValeevVirginia Tech
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Explicitly-correlated CC Shiozaki, Kamiya, Hirata & Valeev PCCP (2008); Same team (in preparation)
Toru ShiozakiUniversity of Florida
Muneaki KamiyaUniversity of Florida
Diagrammatic evaluation of expectation values
Identification of special intermediates such as f12 /r12
The resolution of the identity insertions
CABS substitutions
Special common subexpression
eliminations
Factorization
Strength reduction
Common subexpression
eliminations
Code synthesis
Edward F. ValeevVirginia Tech
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Explicitly-correlated CC Shiozaki, Kamiya, Hirata & Valeev (in preparation)
Toru ShiozakiUniversity of Florida
Muneaki KamiyaUniversity of Florida
Edward F. ValeevVirginia Tech
Ne H2
O F2
The first complete CCSD-R12 results!!
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ContentsAccurate electronic structure methods
for small moleculesAccurate vibrational structure methods
for small molecules
Electronic and vibrational methodsfor polymers
Accurate electronic methodsfor clusters
and molecular crystals
![Page 18: Coupled-cluster and perturbation methods for … and perturbation methods for macromolecules So Hirata Quantum Theory Project and MacroCenter Departments of Chemistry & Physics, University](https://reader030.fdocuments.net/reader030/viewer/2022021801/5b2003fb7f8b9ab3188b4eb1/html5/thumbnails/18.jpg)
Anharmonicity in polyethylene Keçeli & Hirata (in preparation)
HF/6-31G* MP2/6-31G*
Murat KeçeliUniversity of Florida
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Anharmonicity in polyacetylene Keçeli & Hirata (in preparation)
HF/6-31G* MP2/6-31G*
Murat KeçeliUniversity of Florida
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CCSD for polymers Hirata, Bartlett, et al. CPL (2001); Hirata, Bartlett, et al. JCP (2004)
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Fast MP2 for polymers Shimazaki & Hirata (in preparation)
2[ ][ ] [ ] [ ]
cell [ ][ ] [ ] [ ], , ,
BZ
, ,
14
ji a b
i ji b
aj a
kk k k
kk k ki j a b i jk bk k a
i j a bE
K e e e e=
+ − −∑∑
i j a bk k k k+ = +112r−
ik jk
ak bk
( )3cost 2K∝
momentum conservation
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Fast MP2 for polymers Shimazaki & Hirata (in preparation)
i j a bk k k k+ = +Normal MP2 Accuracy
100%Speed
1
( )120, , , , ,pK Kk
Ka Ka Ka Kaππ π π−
= ± ± ±K
( )3cost 2K∝
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Fast MP2 for polymers Shimazaki & Hirata (in preparation)
( ) ( )3 314cost 2K∝
i j a bk k k k+ = +(mod 4) MP2 Accuracy
100.2%Speed
11
4 80, , , ,pKk
Ka Ka Kaπ π π
= ± ± < +K
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Fast MP2 for polymers Shimazaki & Hirata (in preparation)
cost 1∝
0pk =
0i j a bk k k k= = = =Γ
MP2 Accuracy
94%Speed
80
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ContentsAccurate electronic structure methods
for small moleculesAccurate vibrational structure methods
for small molecules
Electronic and vibrational methodsfor polymers
Accurate electronic methodsfor clusters
and molecular crystals
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Fast methods for water clusters Hirata et al. MP (2005)
( )n n
ij i j ii j i
E E E E E<
′ ′ ′ ′= − − +∑ ∑
Pair energy in the presence of dipole field
Self-consistent dipolesMonomer in dipole field
N-body (N > 2) Coulomb in dipole-dipole approximation
1 and 2-bodyCoulombExchangeCorrelation
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Fast methods: ESP+BSSE Kamiya, Hirata & Valiev JCP (2007)
( )n n
ij i j ii j i
E E E E E<
′ ′ ′ ′= − − +∑ ∑
Partial charges thatreproduce the electrostaticpotential around the molecule
N-body (N > 2) Coulomb
with more accurate short-range potentials
Muneaki KamiyaUniversity of Florida
Counterpoise BSSE correction
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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
Fast
Systematic
Easy to implement
BSSE correction
Analytical derivatives
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Fast methods for water clusters Hirata et al. MP (2005)
0.00.0
1.41.0
2.21.7
12.214.4
Binary interaction MP2
Conventional MP2
kcal/mol
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Fast methods for water clusters Hirata et al. MP (2005)
A record
equation-of-motion coupled-
cluster singles and doubles (EOM-CCSD)
calculation with aug-cc-pVDZ
of a 247-
atom cluster
(740 cm–1)
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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.”
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Forces and force constants Hirata et al. MP (2005); Hirata (in preparation)
LRn n
ij ji i
i j i
E EE E Ex x x x xx
E
<
′ ′∂ ∂′ ′⎛ ⎞∂ ∂ ∂= − − +⎜ ⎟∂ ∂ ∂ ∂ ∂⎝
∂+
⎠ ∂∑ ∑
2 22 2 2n nij ji i
i j i
E EE E Ex y x y x y x y x y<
⎛ ⎞′ ′∂ ∂′ ′∂ ∂ ∂= − − +⎜ ⎟⎜ ⎟∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂⎝ ⎠∑ ∑
( )n n
ij i j ii j i
E E E E E<
′ ′ ′ ′= − − +∑ ∑
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Crystalline hydrogen fluoride Sode, Keçeli & Hirata (in preparation)
Olaseni
SodeUniversity of Florida
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Solid formic acid: energetics Hirata (in preparation)
MP2 aug-cc-pVTZ
BSSE CCSD aug-cc-pVDZ
+0.7 kcal/mol
±0.0 kcal/mol ±0.0 kcal/mol
+2.6 kcal/mol
+0.5 kcal/mol
+2.9 kcal/mol
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Solid formic acid: k
= 0
frequencies Hirata (in preparation)
β1
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Solid formic acid: phonon dispersion Hirata (in preparation)
β1 β1
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Solid formic acid: inelastic neutron Hirata (in preparation)
α β1 β2
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Acknowledgements
US Department of EnergyUS National Science FoundationUniversity of Florida Division of Sponsored ResearchHewlett–Packard Company & ACSAmerican Chemical Society PRFJapan Society for the Promotion of Science