We present a near-linear scaling formulation of the explicitly correlated coupled-cluster singles and doubles with the perturbative triples method [CCSD] for high-spin states of open-shell species. The approach is based on the conventional open-shell CCSD formalism [M. Saitow et al., J. Chem. Phys. 146, 164105 (2017)] utilizing the domain local pair-natural orbitals (DLPNO) framework. The use of spin-independent set of pair-natural orbitals ensures exact agreement with the closed-shell formalism reported previously, with only marginally impact on the cost (e.g., the open-shell formalism is only 1.5 times slower than the closed-shell counterpart for the C160H322 n-alkane, with the measured size complexity of ≈1.2). Evaluation of coupled-cluster energies near the complete-basis-set (CBS) limit for open-shell systems with more than 550 atoms and 5000 basis functions is feasible on a single multi-core computer in less than 3 days. The aug-cc-pVTZ DLPNO-CCSD contribution to the heat of formation for the 50 largest molecules among the 348 core combustion species benchmark set [J. Klippenstein et al., J. Phys. Chem. A 121, 6580–6602 (2017)] had root-mean-square deviation (RMSD) from the extrapolated CBS CCSD(T) reference values of 0.3 kcal/mol. For a more challenging set of 50 reactions involving small closed- and open-shell molecules [G. Knizia et al., J. Chem. Phys. 130, 054104 (2009)], the aug-cc-pVQ(+d)Z DLPNO-CCSD yielded a RMSD of ∼0.4 kcal/mol with respect to the CBS CCSD(T) estimate.
REFERENCES
1.
K.
Raghavachari
, G. W.
Trucks
, J. A.
Pople
, and M.
Head-Gordon
, “A fifth-order perturbation comparison of electron correlation
,” Chem. Phys. Lett.
157
, 479
(1989
).2.
O.
Sinanoǧlu
, “Many-electron theory of atoms, molecules and their interactions
,” Adv. Chem. Phys.
6
, 315
(1964
).3.
R. K.
Nesbet
, “Electronic correlation in atoms and molecules
,” Adv. Chem. Phys.
9
, 321
(1965
).4.
P.
Pulay
, “Localizability of dynamic electron correlation
,” Chem. Phys. Lett.
100
, 151
–154
(1983
).5.
S.
Saebø
and P.
Pulay
, “Fourth-order Møller–Plesset perturbation theory in the local correlation treatment. I. Method
,” J. Chem. Phys.
86
, 914
–922
(1986
).6.
S.
Saebo
and P.
Pulay
, “Local treatment of electron correlation
,” Annu. Rev. Phys. Chem.
44
, 213
–236
(1993
).7.
M.
Schütz
, G.
Hetzer
, and H.-J.
Werner
, “Linear scaling local electron correlation methods. I. Linear scaling local MP2
,” J. Chem. Phys.
111
, 5691
–5705
(1999
).8.
G.
Hetzer
, M.
Schütz
, H.
Stoll
, and H.-J.
Werner
, “Low-order scaling local correlation methods. II: Splitting the Coulomb operator in linear scaling local second-order Møller–Plesset perturbation theory
,” J. Chem. Phys.
113
, 9443
–9455
(2000
).9.
M.
Schütz
, “Low-order scaling local electron correlation methods. III. Linear scaling local perturbative triples correction (T)
,” J. Chem. Phys.
113
, 9986
–10001
(2000
).10.
M.
Schütz
and H.-J.
Werner
, “Low-order scaling local correlation methods. IV. Linear scaling local coupled-cluster (LCCSD)
,” J. Chem. Phys.
114
, 661
–681
(2001
).11.
M.
Schütz
, “Low-order scaling local electron correlation methods. V. Connected triples beyond (T): Linear scaling local CCSDT-1b
,” J. Chem. Phys.
116
, 8772
–8785
(2002
).12.
C.
Riplinger
, B.
Sandhoefer
, A.
Hansen
, and F.
Neese
, “Natural triple excitations in local coupled cluster calculations with pair natural orbitals
,” J. Chem. Phys.
139
, 134101
(2013
).13.
P.
Pinski
, C.
Riplinger
, E. F.
Valeev
, and F.
Neese
, “SparseMaps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals
,” J. Chem. Phys.
143
, 034108
(2015
).14.
H.-J.
Werner
, G.
Knizia
, C.
Krause
, M.
Schwilk
, and M.
Dornbach
, “Scalable electron correlation methods I.: PNO-LMP2 with linear scaling in the molecular size and near-inverse-linear scaling in the number of processors
,” J. Chem. Theory Comput.
11
, 484
–507
(2015
).15.
H. R.
McAlexander
and T. D.
Crawford
, “A comparison of three approaches to the reduced-scaling coupled cluster treatment of non-resonant molecular response properties
,” J. Chem. Theory Comput.
12
, 209
–222
(2016
).16.
C.
Edmiston
and M.
Krauss
, “Pseudonatural orbitals as a basis for the superposition of configurations. I. He2+
,” J. Chem. Phys.
45
, 1833
–1839
(1966
).17.
W.
Meyer
, “PNO-CI studies of electron correlation effects. I. Configuration expansion by means of nonorthogonal orbitals, and application of the ground state and ionized states of methane
,” J. Chem. Phys.
58
, 1017
(1973
).18.
W.
Meyer
, “PNO-CI and CEPA studies of electron correlation effects
,” Theor. Chim. Acta
35
, 277
–292
(1974
).19.
R.
Ahlrichs
, H.
Lischka
, V.
Staemmler
, and W.
Kutzelnigg
, “PNO-CI (pair natural orbital configuration interaction) and CEPA-PNO (coupled cluster pair approximation with pair natural orbitals) calculations of molecular systems. I. Outline of the method for closed-shell states
,” J. Chem. Phys.
62
, 1225
–1234
(1975
).20.
F.
Neese
, F.
Wennmohs
, and A.
Hansen
, “Efficient and accurate local approximations to coupled-electron pair approaches: An attempt to revive the pair natural orbital method
,” J. Chem. Phys.
130
, 114108
(2009
).21.
F.
Neese
, A.
Hansen
, and D. G.
Liakos
, “Efficient and accurate approximations to the local coupled cluster singles doubles method using a truncated pair natural orbital basis
,” J. Chem. Phys.
131
, 064103
(2009
).22.
C.
Riplinger
and F.
Neese
, “An efficient and near linear scaling pair natural orbital based local coupled cluster method
,” J. Chem. Phys.
138
, 034106
(2013
).23.
C.
Riplinger
, P.
Pinski
, U.
Becker
, E. F.
Valeev
, and F.
Neese
, “SparseMaps—A systematic infrastructure for reduced-scaling electronic structure methods. II. Linear scaling domain based pair natural orbital coupled cluster theory
,” J. Chem. Phys.
144
, 024109
(2016
).24.
Q.
Ma
and H.-J.
Werner
, “Scalable electron correlation methods. 2. Parallel PNO-LMP2-F12 with near linear scaling in the molecular size
,” J. Chem. Theory Comput.
11
, 5291
–5304
(2015
).25.
D. P.
Tew
, B.
Helmich
, and C.
Hättig
, “Local explicitly correlated second-order Møller–Plesset perturbation theory with pair natural orbitals
,” J. Chem. Phys.
135
, 074107
(2011
).26.
C.
Hättig
, D. P.
Tew
, and B.
Helmich
, “Local explicitly correlated second- and third-order Møller–Plesset perturbation theory with pair natural orbitals
,” J. Chem. Phys.
136
, 204105
(2012
).27.
M. S.
Frank
, G.
Schmitz
, and C.
Hättig
, “The PNO–MP2 gradient and its application to molecular geometry optimisations
,” Mol. Phys.
115
, 343
–356
(2017
).28.
P.
Pinski
and F.
Neese
, “Analytical gradient for the domain-based local pair natural orbital second order Møller–Plesset perturbation theory method (DLPNO-MP2)
,” J. Chem. Phys.
150
, 164102
(2019
).29.
B.
Helmich
and C.
Hättig
, “A pair natural orbital implementation of the coupled cluster model CC2 for excitation energies
,” J. Chem. Phys.
139
, 084114-1
–084114-13
(2013
).30.
B.
Helmich
and C.
Hättig
, “A pair natural orbital based implementation of ADC(2)-x: Perspectives and challenges for response methods for singly and doubly excited states in large molecules
,” Comput. Theor. Chem.
1040-1041
, 35
–44
(2014
).31.
M. S.
Frank
and C.
Hättig
, “A pair natural orbital based implementation of CCSD excitation energies within the framework of linear response theory
,” J. Chem. Phys.
148
, 134102
(2018
).32.
A. K.
Dutta
, M.
Nooijen
, F.
Neese
, and R.
Izsák
, “Exploring the accuracy of a low scaling similarity transformed equation of motion method for vertical excitation energies
,” J. Chem. Theory Comput.
14
, 72
–91
(2017
).33.
D.
Mester
, P. R.
Nagy
, and M.
Kállay
, “Reduced-scaling correlation methods for the excited states of large molecules: Implementation and benchmarks for the second-order algebraic-diagrammatic construction approach
,” J. Chem. Theory Comput.
15
, 6111
–6126
(2019
).34.
A.
Dittmer
, R.
Izsák
, F.
Neese
, and D.
Maganas
, “Accurate band gap predictions of semiconductors in the framework of the similarity transformed equation of motion coupled cluster theory
,” Inorg. Chem.
58
, 9303
–9315
(2019
).35.
C. A. M.
Salla
, J.
Teixeira dos Santos
, G.
Farias
, A. J.
Bortoluzi
, S. F.
Curcio
, T.
Cazati
, R.
Izsák
, F.
Neese
, B.
de Souza
, and I. H.
Bechtold
, “New boron(III) blue emitters for all-solution processed OLEDs: Molecular design assisted by theoretical modeling
,” Eur. J. Inorg. Chem.
2019
, 2247
–2257
.36.
A. K.
Dutta
, M.
Saitow
, C.
Riplinger
, F.
Neese
, and R.
Izsák
, “A near-linear scaling equation of motion coupled cluster method for ionized states
,” J. Chem. Phys.
148
, 244101
(2018
).37.
A. K.
Dutta
, M.
Saitow
, B.
Demoulin
, F.
Neese
, and R.
Izsák
, “A domain-based local pair natural orbital implementation of the equation of motion coupled cluster method for electron attached states
,” J. Chem. Phys.
150
, 164123
(2019
).38.
S.
Haldar
, C.
Riplinger
, B.
Demoulin
, F.
Neese
, R.
Izsak
, and A. K.
Dutta
, “Multilayer approach to the IP-EOM-DLPNO-CCSD method: Theory, implementation, and application
,” J. Chem. Theory Comput.
15
, 2265
–2277
(2019
).39.
T. D.
Crawford
, A.
Kumar
, A. P.
Bazanté
, and R.
Di Remigio
, “Reduced-scaling coupled cluster response theory: Challenges and opportunities
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci.
9
, e1406
(2019
).40.
O.
Demel
, J.
Pittner
, and F.
Neese
, “A local pair natural orbital-based multireference Mukherjee’s coupled cluster method
,” J. Chem. Theory Comput.
11
, 3104
–3114
(2015
).41.
F.
Menezes
, D.
Kats
, and H.-J.
Werner
, “Local complete active space second-order perturbation theory using pair natural orbitals (PNO-CASPT2)
,” J. Chem. Phys.
145
, 124115
(2016
).42.
Y.
Guo
, K.
Sivalingam
, E. F.
Valeev
, and F.
Neese
, “SparseMaps—A systematic infrastructure for reduced-scaling electronic structure methods. III. Linear-scaling multireference domain-based pair natural orbital N-electron valence perturbation theory
,” J. Chem. Phys.
144
, 094111
(2016
).43.
J.
Brabec
, J.
Lang
, M.
Saitow
, J.
Pittner
, F.
Neese
, and O.
Demel
, “Domain-based local pair natural orbital version of Mukherjee’s state-specific coupled cluster method
,” J. Chem. Theory Comput.
14
, 1370
–1382
(2018
).44.
G. D.
Purvis
and R. J.
Bartlett
, “A full coupled-cluster singles and doubles model: The inclusion of disconnected triples
,” J. Chem. Phys.
76
, 1910
–1918
(1982
).45.
M.
Rittby
and R. J.
Bartlett
, “An open-shell spin-restricted coupled cluster method: Application to ionization potentials in N2
,” J. Phys. Chem.
92
, 3033
–3036
(1988
).46.
J. D.
Watts
and R. J.
Bartlett
, “The coupled-cluster single, double and triple excitation model for open-shell single reference functions
,” J. Chem. Phys.
93
, 6104
–6105
(1990
).47.
C. L.
Janssen
and H. F.
Schaefer
III, “The automated solution of second quantization equations with applications to the coupled cluster approach
,” Theor. Chem.
79
, 1
–42
(1991
).48.
J. D.
Watts
, J.
Gauss
, and R. J.
Bartlett
, “Coupled-cluster methods with noniterative triple excitations for restricted open-shell Hartree–Fock and other general single determinant reference functions. Energies and analytical gradients
,” J. Chem. Phys.
98
, 8718
–8733
(1993
).49.
X.
Li
and J.
Paldus
, “Automation of the implementation of spin-adapted open-shell coupled-cluster theories relying on the unitary group formalism
,” J. Chem. Phys.
101
, 8812
–8826
(1994
).50.
R. J.
Bartlett
and M.
Musiał
, “Coupled-cluster theory in quantum chemistry
,” Rev. Mod. Phys.
79
, 291
–352
(2007
).51.
A. I.
Krylov
, “Equation-of-motion coupled-cluster methods for open-shell and electronically excited species: The Hitchhiker’s guide to Fock space
,” Annu. Rev. Phys. Chem.
59
, 433
–462
(2008
).52.
R. J.
Bartlett
, “The coupled-cluster revolution
,” Mol. Phys.
108
, 2905
–2920
(2010
).53.
R. J.
Bartlett
, “Coupled-cluster theory and its equation-of-motion extensions
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci.
2
, 126
–138
(2012
).54.
F.
Neese
, “Importance of direct spin–spin coupling and spin-flip excitations for the zero-field splittings of transition metal complexes: A case study
,” J. Am. Chem. Soc.
128
, 10213
–10222
(2006
).55.
A.
Hansen
, D. G.
Liakos
, and F.
Neese
, “Efficient and accurate local single reference correlation methods for high-spin open-shell molecules using pair natural orbitals
,” J. Chem. Phys.
135
, 214102
(2011
).56.
M.
Saitow
, U.
Becker
, C.
Riplinger
, E. F.
Valeev
, and F.
Neese
, “A new near-linear scaling, efficient and accurate, open-shell domain-based local pair natural orbital coupled cluster singles and doubles theory
,” J. Chem. Phys.
146
, 164105
(2017
).57.
Y.
Guo
, C.
Riplinger
, D. G.
Liakos
, U.
Becker
, M.
Saitow
, and F.
Neese
, “Linear scaling perturbative triples correction approximations for open-shell domain-based local pair natural orbital coupled cluster singles and doubles theory [DLPNO-CCSD(T0/T)]
,” J. Chem. Phys.
152
, 024116
(2020
).58.
C.
Krause
and H.-J.
Werner
, “Scalable electron correlation methods. 6. Local spin-restricted open-shell second-order Møller–Plesset perturbation theory using pair natural orbitals: PNO-RMP2
,” J. Chem. Phys.
15
, 987
–1005
(2019
).59.
Q.
Ma
and H.-J.
Werner
, “Scalable electron correlation methods. 7. Local open-shell coupled-cluster methods using pair natural orbitals: PNO-RCCSD and PNO-UCCSD
,” J. Chem. Theory Comput.
16
, 3135
(2020
).60.
W.
Kutzelnigg
and J. D.
Morgan
, “Rates of convergence of the partial-wave expansions of atomic correlation energies
,” J. Chem. Phys.
96
, 4484
(1992
).61.
W.
Kutzelnigg
, “r12-dependent terms in the wave function as closed sums of partial wave amplitudes for large l
,” Theor. Chim. Acta
68
, 445
–469
(1985
).62.
W.
Klopper
and C. C. M.
Samson
, “Explicitly correlated second-order Møller–Plesset methods with auxiliary basis sets
,” J. Chem. Phys.
116
, 6397
–6410
(2002
).63.
F. R.
Manby
, “Density fitting in second-order linear-r12 Møller–Plesset perturbation theory
,” J. Chem. Phys.
119
, 4607
(2003
).64.
S.
Ten-no
, “Explicitly correlated second order perturbation theory: Introduction of a rational generator and numerical quadratures
,” J. Chem. Phys.
121
, 117
–129
(2004
).65.
S.
Ten-no
, “Initiation of explicitly correlated Slater-type geminal theory
,” Chem. Phys. Lett.
398
, 56
–61
(2004
).66.
E. F.
Valeev
, “Improving on the resolution of the identity in linear R12 ab initio theories
,” Chem. Phys. Lett.
395
, 190
–195
(2004
).67.
S.
Kedžuch
, M.
Milko
, and J.
Noga
, “Alternative formulation of the matrix elements in MP2-R12 theory
,” Int. J. Quantum Chem.
105
, 929
–936
(2005
).68.
H.
Fliegl
, W.
Klopper
, and C.
Hättig
, “Coupled-cluster theory with simplified linear-r12 corrections: The CCSD (R12) model
,” J. Chem. Phys.
122
, 084107
(2005
).69.
H.-J.
Werner
, T. B.
Adler
, and F. R.
Manby
, “General orbital invariant MP2-F12 theory
,” J. Chem. Phys.
126
, 164102
(2007
).70.
E. F.
Valeev
, “Coupled-cluster methods with perturbative inclusion of explicitly correlated terms: A preliminary investigation
,” Phys. Chem. Chem. Phys.
10
, 106
–113
(2008
).71.
J.
Zhang
and E. F.
Valeev
, “Prediction of reaction barriers and thermochemical properties with explicitly correlated coupled-cluster methods: A basis set assessment
,” J. Chem. Theory Comput.
8
, 3175
–3186
(2012
).72.
However, further numerical approximations like the resolution of identity in the F12 methods can sometimes slow down this convergence. Furthermore, precise analysis of the basis set convergence of correlation energy for molecules is more phenomenological than for atoms.
73.
D. G.
Liakos
, R.
Izsák
, E. F.
Valeev
, and F.
Neese
, “What is the most efficient way to reach the canonical MP2 basis set limit?
,” Mol. Phys.
111
, 2653
–2662
(2013
).74.
J.
Yang
, G. K.-L.
Chan
, F. R.
Manby
, M.
Schütz
, and H.-J.
Werner
, “The orbital-specific-virtual local coupled cluster singles and doubles method
,” J. Chem. Phys.
136
, 144105-1
–144105-16
(2012
).75.
C.
Krause
and H.-J.
Werner
, “Comparison of explicitly correlated local coupled-cluster methods with various choices of virtual orbitals
,” Phys. Chem. Chem. Phys.
14
, 7591
–7604
(2012
).76.
D. P.
Tew
and C.
Hättig
, “Pair natural orbitals in explicitly correlated second-order Møller–Plesset theory
,” Int. J. Quantum Chem.
113
, 224
–229
(2013
).77.
G.
Schmitz
, C.
Hättig
, and D. P.
Tew
, “Explicitly correlated PNO-MP2 and PNO-CCSD and their application to the S66 set and large molecular systems
,” Phys. Chem. Chem. Phys.
16
, 22167
–22178
(2014
).78.
Q.
Ma
and H.-J.
Werner
, “Scalable electron correlation methods. 5. Parallel perturbative triples correction for explicitly correlated local coupled cluster with pair natural orbitals
,” J. Chem. Theory Comput.
14
, 198
–215
(2018
).79.
F.
Pavošević
, P.
Pinski
, C.
Riplinger
, F.
Neese
, and E. F.
Valeev
, “SparseMaps—A systematic infrastructure for reduced-scaling electronic structure methods. IV. Linear-scaling second-order explicitly correlated energy with pair natural orbitals
,” J. Chem. Phys.
144
, 144109
(2016
).80.
F.
Pavošević
, C.
Peng
, P.
Pinski
, C.
Riplinger
, F.
Neese
, and E. F.
Valeev
, “SparseMaps—A systematic infrastructure for reduced scaling electronic structure methods. V. Linear scaling explicitly correlated coupled-cluster method with pair natural orbitals
,” J. Chem. Phys.
146
, 174108
(2017
).81.
E. F.
Valeev
and T.
Daniel Crawford
, “Simple coupled-cluster singles and doubles method with perturbative inclusion of triples and explicitly correlated geminals: The CCSD(T)R12 model
,” J. Chem. Phys.
128
, 244113
(2008
).82.
F.
Neese
, “The ORCA program system
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci.
2
, 73
–78
(2011
).83.
L.
Kong
, F. A.
Bischoff
, and E. F.
Valeev
, “Explicitly correlated R12/F12 methods for electronic structure
,” Chem. Rev.
112
, 75
–107
(2012
).84.
T.
Helgaker
, P.
Jørgensen
, and J.
Olsen
, Molecular Electronic-Structure Theory
, 1st ed. (John Wiley & Sons, Ltd.
, Chichester, UK
, 2000
).85.
J. F.
Stanton
, “Why CCSD(T) works: A different perspective
,” Chem. Phys. Lett.
281
, 130
(1997
).86.
A. G.
Taube
and R. J.
Bartlett
, “Improving upon CCSD(T): ΛCCSD(T). I. Potential energy surfaces
,” J. Chem. Phys.
128
, 044110
(2008
).87.
H.
Fliegl
, C.
Hättig
, and W.
Klopper
, “Inclusion of the (T) triples correction into the linear-r12 corrected coupled-cluster model CCSD(R12)
,” Int. J. Quantum Chem.
106
, 2306
–2317
(2006
).88.
T. B.
Adler
, G.
Knizia
, and H.-J.
Werner
, “A simple and efficient CCSD(t)-F12 approximation
,” J. Chem. Phys.
127
, 221106
(2007
).89.
D. P.
Tew
, W.
Klopper
, and C.
Hättig
, “A diagonal orbital-invariant explicitly-correlated coupled-cluster method
,” Chem. Phys. Lett.
452
, 326
–332
(2008
).90.
T.
Shiozaki
, M.
Kamiya
, S.
Hirata
, and E. F.
Valeev
, “Equations of explicitly-correlated coupled-cluster methods
,” Phys. Chem. Chem. Phys.
10
, 3358
–3370
(2008
).91.
C.
Hättig
, D. P.
Tew
, and A.
Köhn
, “Communications: Accurate and efficient approximations to explicitly correlated coupled-cluster singles and doubles, CCSD-F12
,” J. Chem. Phys.
132
, 231102-1
–231102-4
(2010
).92.
D.
Kats
and D. P.
Tew
, “Orbital-optimized distinguishable cluster theory with explicit correlation
,” J. Chem. Theory Comput.
15
, 13
–17
(2019
).93.
F.
Pavošević
, F.
Neese
, and E. F.
Valeev
, “Geminal-spanning orbitals make explicitly correlated reduced-scaling coupled-cluster methods robust, yet simple
,” J. Chem. Phys.
141
, 054106
(2014
).94.
D. P.
Tew
and W.
Klopper
, “New correlation factors for explicitly correlated electronic wave functions
,” J. Chem. Phys.
123
, 074101
(2005
).95.
A. J.
May
, E.
Valeev
, R.
Polly
, and F. R.
Manby
, “Analysis of the errors in explicitly correlated electronic structure theory
,” Phys. Chem. Chem. Phys.
7
, 2710
–2713
(2005
).96.
K. A.
Peterson
, T. B.
Adler
, and H.-J.
Werner
, “Systematically convergent basis sets for explicitly correlated wavefunctions: The atoms H, He, B–Ne, and Al–Ar
,” J. Chem. Phys.
128
, 084102
(2008
).97.
M.
Torheyden
and E. F.
Valeev
, “Variational formulation of perturbative explicitly-correlated coupled-cluster methods
,” Phys. Chem. Chem. Phys.
10
, 3410
–3420
(2008
).98.
J. M.
Foster
and S. F.
Boys
, “Canonical configurational interaction procedure
,” Rev. Mod. Phys.
32
, 300
–302
(1960
).99.
K. G.
Dyall
, “The choice of a zeroth-order Hamiltonian for second-order perturbation theory with a complete active space self-consistent-field reference function
,” J. Chem. Phys.
102
, 4909
–4918
(1995
).100.
D. E.
Woon
and T. H.
Dunning
, Jr., “Gaussian basis sets for use in correlated molecular calculations. III. The atoms aluminum through argon
,” J. Chem. Phys.
98
, 1358
–1371
(1993
).101.
F.
Weigend
and R.
Ahlrichs
, “Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy
,” Phys. Chem. Chem. Phys.
7
, 3297
–3305
(2005
).102.
F.
Weigend
, A.
Köhn
, and C.
Hättig
, “Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations
,” J. Chem. Phys.
116
, 3175
–3183
(2002
).103.
F.
Weigend
, “Accurate Coulomb-fitting basis sets for H to Rn
,” Phys. Chem. Chem. Phys.
8
, 1057
–1065
(2006
).104.
C.
Hättig
, “Optimization of auxiliary basis sets for RI-MP2 and RI-CC2 calculations: Core–valence and quintuple-ζ basis sets for H to Ar and QZVPP basis sets for Li to Kr
,” Phys. Chem. Chem. Phys.
7
, 59
(2005
).105.
K. E.
Yousaf
and K. A.
Peterson
, “Optimized auxiliary basis sets for explicitly correlated methods
,” J. Chem. Phys.
129
, 184108
(2008
).106.
R.
Izsák
and F.
Neese
, “An overlap fitted chain of spheres exchange method
,” J. Chem. Phys.
135
, 144105
(2011
).107.
S. J.
Klippenstein
, L. B.
Harding
, and B.
Ruscic
, “Ab initio computations and active thermochemical tables hand in hand: Heats of formation of core combustion species
,” J. Phys. Chem. A
121
, 6580
–6602
(2017
).108.
G.
Knizia
, T. B.
Adler
, and H.-J.
Werner
, “Simplified CCSD(T)-F12 methods: Theory and benchmarks
,” J. Chem. Phys.
130
, 054104
(2009
).109.
M. C.
Clement
, J.
Zhang
, C. A.
Lewis
, C.
Yang
, and E. F.
Valeev
, “Optimized pair natural orbitals for the coupled cluster methods
,” J. Chem. Theory Comput.
14
, 4581
–4589
(2018
).110.
H.-J.
Werner
, “Eliminating the domain error in local explicitly correlated second-order Møller–Plesset perturbation theory
,” J. Chem. Phys.
129
, 101103
(2008
).111.
The equation displayed in Ref. 107 has a small sign-related typo: The sign before the group with should be positive instead of negative.
112.
B.
Ruscic
, R. E.
Pinzon
, M. L.
Morton
, G.
von Laszevski
, S. J.
Bittner
, S. G.
Nijsure
, K. A.
Amin
, M.
Minkoff
, and A. F.
Wagner
, “Introduction to active thermochemical tables: several “key” enthalpies of formation revisited
,” J. Phys. Chem. A
108
, 9979
–9997
(2004
).113.
Y.
Guo
, C.
Riplinger
, U.
Becker
, D. G.
Liakos
, Y.
Minenkov
, L.
Cavallo
, and F.
Neese
, “Communication: An improved linear scaling perturbative triples correction for the domain based local pair-natural orbital based singles and doubles coupled cluster method [DLPNO-CCSD(T)]
,” J. Chem. Phys.
148
, 011101
(2018
).114.
D. G.
Liakos
, Y.
Guo
, and F.
Neese
, “Comprehensive benchmark results for the domain based local pair natural orbital coupled cluster method (DLPNO-CCSD(T)) for closed- and open-shell systems
,” J. Phys. Chem. A
124
, 90
–100
(2019
).115.
T.
Helgaker
, W.
Klopper
, H.
Koch
, and J.
Noga
, “Basis-set convergence of correlated calculations on water
,” J. Chem. Phys.
106
, 9639
–9646
(1997
).116.
S.
Ye
, C.
Riplinger
, A.
Hansen
, C.
Krebs
, J. M.
Bollinger
, Jr., and F.
Neese
, “Electronic structure analysis of the oxygen-activation mechanism by FeII- and α-ketoglutarate (αKG)-dependent dioxygenases
,” Chem. - Eur. J.
18
, 6555
–6567
(2012
).117.
T.
Krämer
, M.
Kampa
, W.
Lubitz
, M.
van Gastel
, and F.
Neese
, “Theoretical spectroscopy of the NiII intermediate states in the catalytic cycle and the activation of [NiFe] hydrogenases
,” ChemBioChem
14
, 1898
–1905
(2013
).118.
F.
Müh
and A.
Zouni
, “The nonheme iron in photosystem II
,” Photosynth. Res.
116
, 295
–314
(2013
).119.
T.
Yanai
, D. P.
Tew
, and N. C.
Handy
, “A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP)
,” Chem. Phys. Lett.
393
, 51
–57
(2004
).© 2020 Author(s).
2020
Author(s)
You do not currently have access to this content.
