The Many-Body Expansion (MBE) is a useful tool to simulate condensed phase chemical systems, often avoiding the steep computational cost of usual electronic structure methods. However, it often requires higher than 2-body terms to achieve quantitative accuracy. In this work, we propose the Polarized MBE (PolBE) method where each MBE energy contribution is treated as an embedding problem. In each energy term, a smaller fragment is embedded into a larger, polarized environment and only a small region is treated at the high-level of theory using embedded mean-field theory. The role of polarized environment was found to be crucial in providing quantitative accuracy at the 2-body level. PolBE accurately predicts noncovalent interaction energies for a number of systems, including CO2, water, and hydrated ion clusters, with a variety of interaction mechanisms, from weak dispersion to strong electrostatics considered in this work. We further demonstrate that the PolBE interaction energy is predominantly pairwise unlike the usual vacuum MBE that requires higher-order terms to achieve similar accuracy. We numerically show that PolBE often performs better than other widely used embedded MBE methods such as the electrostatically embedded MBE. Owing to the lack of expensive diagonalization of Fock matrices and its embarrassingly parallel nature, PolBE is a promising way to access condensed phase systems with hybrid density functionals that are difficult to treat with currently available methods.
REFERENCES
1.
J.
Yang
, W.
Hu
, D.
Usvyat
, D.
Matthews
, M.
Schütz
, and G. K.-L.
Chan
, “Ab initio determination of the crystalline benzene lattice energy to sub-kilojoule/mole accuracy
,” Science
345
, 640
–643
(2014
).2.
G. J.
Beran
, “Modeling polymorphic molecular crystals with electronic structure theory
,” Chem. Rev.
116
, 5567
–5613
(2016
).3.
A. D.
Boese
and J.
Sauer
, “Embedded and DFT calculations on the crystal structures of small alkanes, notably propane
,” Cryst. Growth Des.
17
, 1636
–1646
(2017
).4.
O.
Demerdash
, E.-H.
Yap
, and T.
Head-Gordon
, “Advanced potential energy surfaces for condensed phase simulation
,” Annu. Rev. Phys. Chem.
65
, 149
–174
(2014
).5.
D.
Zgid
and G. K.-L.
Chan
, “Dynamical mean-field theory from a quantum chemical perspective
,” J. Chem. Phys.
134
, 094115
(2011
).6.
T. N.
Lan
and D.
Zgid
, “Generalized self-energy embedding theory
,” J. Phys. Chem. Lett.
8
, 2200
–2205
(2017
).7.
H.
Ishida
, “Surface-embedded Green-function method: A formulation using a linearized-augmented-plane-wave basis set
,” Phys. Rev. B
63
, 165409
(2001
).8.
W.
Chibani
, X.
Ren
, M.
Scheffler
, and P.
Rinke
, “Self-consistent Green’s function embedding for advanced electronic structure methods based on a dynamical mean-field concept
,” Phys. Rev. B
93
, 165106
(2016
).9.
P.
Elliott
, K.
Burke
, M. H.
Cohen
, and A.
Wasserman
, “Partition density-functional theory
,” Phys. Rev. A
82
, 24501
(2010
).10.
C.
Huang
, “Extending the density functional embedding theory to finite temperature and an efficient iterative method for solving for embedding potentials
,” J. Chem. Phys.
144
, 124106
(2016
).11.
C.
Huang
and E. A.
Carter
, “Potential-functional embedding theory for molecules and materials
,” J. Chem. Phys.
135
, 194104
(2011
).12.
M. E.
Fornace
, J.
Lee
, K.
Miyamoto
, F. R.
Manby
, and T. F.
Miller
, “Embedded mean-field theory
,” J. Chem. Theory Comput.
11
, 568
–580
(2015
).13.
F. R.
Manby
, M.
Stella
, J. D.
Goodpaster
, and T. F.
Miller
, “A simple, exact density-functional-theory embedding scheme
,” J. Chem. Theory Comput.
8
, 2564
–2568
(2012
).14.
T. A.
Wesolowski
and A.
Warshel
, “Frozen density functional approach for ab initio calculations of solvated molecules
,” J. Phys. Chem.
97
, 8050
–8053
(1993
).15.
T. A.
Wesolowski
, S.
Shedge
, and X.
Zhou
, “Frozen-density embedding strategy for multilevel simulations of electronic structure
,” Chem. Rev.
115
, 5891
–5928
(2015
).16.
G.
Knizia
and G. K.-L.
Chan
, “Density matrix embedding: A simple alternative to dynamical mean-field theory
,” Phys. Rev. Lett.
109
, 186404
(2012
).17.
S.
Wouters
, C. A.
Jiménez-Hoyos
, Q.
Sun
, and G. K.-L.
Chan
, “A practical guide to density matrix embedding theory in quantum chemistry
,” J. Chem. Theory Comput.
12
, 2706
–2719
(2016
).18.
E.
Prodan
and W.
Kohn
, “Nearsightedness of electronic matter
,” Proc. Natl. Acad. Sci. U. S. A.
102
, 11635
–11638
(2005
).19.
T.
Vreven
and K.
Morokuma
, “Chapter 3 Hybrid Methods: ONIOM(QM: MM) and QM/MM
,” in Annual Reports in Computational Chemistry
, edited by D. C.
Spellmeyer
(Elsevier
, 2006
), Vol. 2, pp. 35
–51
.20.
W.
Guo
, A.
Wu
, and X.
Xu
, “XO: An extended ONIOM method for accurate and efficient geometry optimization of large molecules
,” Chem. Phys. Lett.
498
, 203
–208
(2010
).21.
L. W.
Chung
, W. M.
Sameera
, R.
Ramozzi
, A. J.
Page
, M.
Hatanaka
, G. P.
Petrova
, T. V.
Harris
, X.
Li
, Z.
Ke
, F.
Liu
, H. B.
Li
, L.
Ding
, and K.
Morokuma
, “The ONIOM method and its applications
,” Chem. Rev.
115
, 5678
–5796
(2015
).22.
E. E.
Dahlke
and D.
Truhlar
, “Electrostatically embedded many-body expansion for large systems, with applications to water clusters
,” J. Chem. Theory Comput.
3
, 46
–53
(2007
).23.
E. E.
Dahlke
and D. G.
Truhlar
, “Electrostatically embedded many-body expansion for simulations
,” J. Chem. Theory Comput.
4
, 1
–6
(2008
).24.
E. E.
Dahlke
and D. G.
Truhlar
, “Electrostatically embedded many-body correlation energy, with applications to the calculation of accurate second-order Møller-Plesset perturbation theory energies for large water clusters
,” J. Chem. Theory Comput.
3
, 1342
–1348
(2007
).25.
R. M.
Richard
, K. U.
Lao
, and J. M.
Herbert
, “Aiming for benchmark accuracy with the many-body expansion
,” Acc. Chem. Res.
47
, 2828
–2836
(2014
).26.
P. J.
Bygrave
, N. L.
Allan
, and F. R.
Manby
, “The embedded many-body expansion for energetics of molecular crystals
,” J. Chem. Phys.
137
, 164102
(2012
).27.
J.
Gao
and Y.
Wang
, “Communication: Variational many-body expansion: Accounting for exchange repulsion, charge delocalization, and dispersion in the fragment-based explicit polarization method
,” J. Chem. Phys.
136
, 071101
(2012
).28.
L.
Song
, J.
Han
, Y. L.
Lin
, W.
Xie
, and J.
Gao
, “Explicit polarization (X-poi) potential using ab initio molecular orbital theory and density functional theory
,” J. Phys. Chem. A
113
, 11656
–11664
(2009
).29.
J.
Gao
, “Toward a molecular orbital derived empirical potential for liquid simulations
,” J. Phys. Chem. B
101
, 657
–663
(1997
).30.
J.
Gao
, “A molecular-orbital derived polarization potential for liquid water
,” J. Chem. Phys.
109
, 2346
–2354
(1998
).31.
W.
Xie
and J.
Gao
, “Design of a next generation force field: The X-Pol potential
,” J. Chem. Theory Comput.
3
, 1890
–1900
(2007
).32.
J.
Liu
, B.
Rana
, K.-Y.
Liu
, and J. M.
Herbert
, “Variational formulation of the generalized many-body expansion with self-consistent charge embedding: Simple and correct analytic energy gradient for fragment-based ab initio molecular dynamics
,” J. Phys. Chem. Lett.
10
, 3877
–3886
(2019
).33.
K. U.
Lao
and J. M.
Herbert
, “Accurate intermolecular interactions at dramatically reduced cost: XPol+SAPT with empirical dispersion
,” J. Phys. Chem. Lett.
3
, 3241
–3248
(2012
).34.
A.
Cembran
, P.
Bao
, Y.
Wang
, L.
Song
, D. G.
Truhlar
, and J.
Gao
, “On the interfragment exchange in the X-Pol method
,” J. Chem. Theory Comput.
6
, 2469
–2476
(2010
).35.
K.
Kitaura
, E.
Ikeo
, T.
Asada
, T.
Nakano
, and M.
Uebayasi
, “Fragment molecular orbital method: An approximate computational method for large molecules
,” Chem. Phys. Lett.
313
, 701
–706
(1999
).36.
D. G.
Fedorov
and K.
Kitaura
, “Extending the power of quantum chemistry to large systems with the fragment molecular orbital method
,” J. Phys. Chem. A
111
, 6904
–6914
(2007
).37.
M. S.
Gordon
, D. G.
Fedorov
, S. R.
Pruitt
, and L. V.
Slipchenko
, “Fragmentation methods: A route to accurate calculations on large systems
,” Chem. Rev.
112
, 632
–672
(2012
).38.
D. G.
Fedorov
and K.
Kitaura
, in Modern Methods for Theoretical Physical Chemistry of Biopolymers
, edited by E. B.
Starikov
, J. P.
Lewis
, and S.
Tanaka
(Elsevier Science
Amsterdam
, 2006
), Chap. 1, pp. 3
–38
.39.
H.
Stoll
, G.
Wagenblast
, and H.
Preuss
, “On the use of local basis-sets for localized molecular-orbitals
,” Theor. Chim. Acta
57
, 169
–178
(1980
).40.
E.
Gianinetti
, M.
Raimondi
, and E.
Tornaghi
, “Modification of the Roothaan equations to exclude BSSE from molecular interaction calculations
,” Int. J. Quantum Chem.
60
, 157
–166
(1996
).41.
R. Z.
Khaliullin
, M.
Head-Gordon
, and A. T.
Bell
, “An efficient self-consistent field method for large systems of weakly interacting components
,” J. Chem. Phys.
124
, 204105
(2006
).42.
T.
Nagata
, O.
Takahashi
, K.
Saito
, and S.
Iwata
, “Basis set superposition error free self-consistent field method for molecular interaction in multi-component systems: Projection operator formalism
,” J. Chem. Phys.
115
, 3553
(2001
).43.
J. M.
Cullen
, “An examination of the effects of basis set and charge transfer in hydrogen-bonded dimers with a constrained Hartree-Fock method
,” Int. J. Quantum Chem.
40
, 193
–207
(1991
).44.
R. Z.
Khaliullin
, E. A.
Cobar
, R. C.
Lochan
, A. T.
Bell
, and M.
Head-Gordon
, “Unravelling the origin of intermolecular interactions using absolutely localized molecular orbitals
,” J. Phys. Chem. A
111
, 8753
–8765
(2007
).45.
P. R.
Horn
, E. J.
Sundstrom
, T. A.
Baker
, and M.
Head-Gordon
, “Unrestricted absolutely localized molecular orbitals for energy decomposition analysis: Theory and applications to intermolecular interactions involving radicals
,” J. Chem. Phys.
138
, 134119
(2013
).46.
J.
Thirman
and M.
Head-Gordon
, “An energy decomposition analysis for second-order Møller-Plesset perturbation theory based on absolutely localized molecular orbitals
,” J. Chem. Phys.
143
, 084124
(2015
).47.
Y.
Mo
, J.
Gao
, and S. D.
Peyerimhoff
, “Energy decomposition analysis of intermolecular interactions using a block-localized wave function approach
,” J. Chem. Phys.
112
, 5530
–5538
(2000
).48.
N.
Mardirossian
and M.
Head-Gordon
, “Thirty years of density functional theory in computational chemistry: An overview and extensive assessment of 200 density functionals
,” Mol. Phys.
115
, 2315
(2017
).49.
J.
Gao
, A.
Cembran
, and Y.
Mo
, “Generalized X-Pol theory and charge delocalization states
,” J. Chem. Theory Comput.
6
, 2402
–2410
(2010
).50.
F.
Ding
, F. R.
Manby
, and T. F.
Miller
, “Embedded mean-field theory with block-orthogonalized partitioning
,” J. Chem. Theory Comput.
13
, 1605
–1615
(2017
).51.
N.
Mardirossian
and M.
Head-Gordon
, “B97M-V: A combinatorially optimized, range-separated hybrid, meta-GGA density functional with VV10 nonlocal correlation
,” J. Chem. Phys.
144
, 214110
(2016
).52.
J.
Perdew
, K.
Burke
, and M.
Ernzerhof
, “Generalized gradient approximation made simple
,” Phys. Rev. Lett.
77
, 3865
–3868
(1996
).53.
D.
Rappoport
and F.
Furche
, “Property-optimized Gaussian basis sets for molecular response calculations
,” J. Chem. Phys.
133
, 134105
(2010
).54.
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
).55.
P. M.
Gill
, B. G.
Johnson
, and J. A.
Pople
, “A standard grid for density functional calculations
,” Chem. Phys. Lett.
209
, 506
–512
(1993
).56.
Y.
Shao
, Z.
Gan
, E.
Epifanovsky
, A. T.
Gilbert
, M.
Wormit
, J.
Kussmann
, A. W.
Lange
, A.
Behn
, J.
Deng
, X.
Feng
, D.
Ghosh
, M.
Goldey
, P. R.
Horn
, L. D.
Jacobson
, I.
Kaliman
, R. Z.
Khaliullin
, T.
Kus
, A.
Landau
, J.
Liu
, E. I.
Proynov
, Y. M.
Rhee
, R. M.
Richard
, M. A.
Rohrdanz
, R. P.
Steele
, E. J.
Sundstrom
, H. L.
Woodcock
, P. M.
Zimmerman
, D.
Zuev
, B.
Albrecht
, E.
Alguire
, B.
Austin
, G. J.
Beran
, Y. A.
Bernard
, E.
Berquist
, K.
Brandhorst
, K. B.
Bravaya
, S. T.
Brown
, D.
Casanova
, C. M.
Chang
, Y.
Chen
, S. H.
Chien
, K. D.
Closser
, D. L.
Crittenden
, M.
Diedenhofen
, R. A.
Distasio
, H.
Do
, A. D.
Dutoi
, R. G.
Edgar
, S.
Fatehi
, L.
Fusti-Molnar
, A.
Ghysels
, A.
Golubeva-Zadorozhnaya
, J.
Gomes
, M. W.
Hanson-Heine
, P. H.
Harbach
, A. W.
Hauser
, E. G.
Hohenstein
, Z. C.
Holden
, T. C.
Jagau
, H.
Ji
, B.
Kaduk
, K.
Khistyaev
, J.
Kim
, J.
Kim
, R. A.
King
, P.
Klunzinger
, D.
Kosenkov
, T.
Kowalczyk
, C. M.
Krauter
, K. U.
Lao
, A. D.
Laurent
, K. V.
Lawler
, S. V.
Levchenko
, C. Y.
Lin
, F.
Liu
, E.
Livshits
, R. C.
Lochan
, A.
Luenser
, P.
Manohar
, S. F.
Manzer
, S. P.
Mao
, N.
Mardirossian
, A. V.
Marenich
, S. A.
Maurer
, N. J.
Mayhall
, E.
Neuscamman
, C. M.
Oana
, R.
Olivares-Amaya
, D. P.
Oneill
, J. A.
Parkhill
, T. M.
Perrine
, R.
Peverati
, A.
Prociuk
, D. R.
Rehn
, E.
Rosta
, N. J.
Russ
, S. M.
Sharada
, S.
Sharma
, D. W.
Small
, A.
Sodt
, T.
Stein
, D.
Stück
, Y. C.
Su
, A J.
Thom
, T.
Tsuchimochi
, V.
Vanovschi
, L.
Vogt
, O.
Vydrov
, T.
Wang
, M. A.
Watson
, J.
Wenzel
, A.
White
, C. F.
Williams
, J.
Yang
, S.
Yeganeh
, S. R.
Yost
, Z. Q.
You
, I. Y.
Zhang
, X.
Zhang
, Y.
Zhao
, B. R.
Brooks
, G. K.
Chan
, D. M.
Chipman
, C. J.
Cramer
, W. A.
Goddard
, M. S.
Gordon
, W. J.
Hehre
, A.
Klamt
, H. F.
Schaefer
, M. W.
Schmidt
, C. D.
Sherrill
, D. G.
Truhlar
, A.
Warshel
, X.
Xu
, A.
Aspuru-Guzik
, R.
Baer
, A. T.
Bell
, N. A.
Besley
, J. D.
Chai
, A.
Dreuw
, B. D.
Dunietz
, T. R.
Furlani
, S. R.
Gwaltney
, C. P.
Hsu
, Y.
Jung
, J.
Kong
, D. S.
Lambrecht
, W.
Liang
, C.
Ochsenfeld
, V. A.
Rassolov
, L. V.
Slipchenko
, J. E.
Subotnik
, T.
Van Voorhis
, J. M.
Herbert
, A. I.
Krylov
, P. M.
Gill
, and M.
Head-gordon
, “Advances in molecular quantum chemistry contained in the Q-Chem 4 program package
,” Mol. Phys.
113
, 184
–215
(2015
).57.
J.
Lee
and M.
Head-Gordon
, “Regularized orbital-optimized second-order Møller-Plesset perturbation theory: A reliable fifth-order-scaling electron correlation model with orbital energy dependent regularizers
,” J. Chem. Theory Comput.
14
, 5203
–5219
(2018
).58.
J.
Lee
and M.
Head-Gordon
, “Distinguishing artificial and essential symmetry breaking in a single determinant: Approach and application to the C 60, C 36, and C 20 fullerenes
,” Phys. Chem. Chem. Phys.
21
, 4763
–4778
(2019
).59.
J.
Lee
and M.
Head-Gordon
, “Two single-reference approaches to singlet biradicaloid problems: Complex, restricted orbitals and approximate spin-projection combined with regularized orbital-optimized Møller-Plesset perturbation theory
,” J. Chem. Phys.
150
, 244106
(2019
).60.
L. W.
Bertels
, J.
Lee
, and M.
Head-Gordon
, “Third-order Møller-Plesset perturbation theory made useful? Choice of orbitals and scaling greatly improves accuracy for thermochemistry, kinetics, and intermolecular interactions
,” J. Phys. Chem. Lett.
10
, 4170
–4176
(2019
).61.
R. A.
Mata
and H. J.
Werner
, “Calculation of smooth potential energy surfaces using local electron correlation methods
,” J. Chem. Phys.
125
, 184110
(2006
).62.
J. E.
Subotnik
, A.
Sodt
, and M.
Head-Gordon
, “The limits of local correlation theory: Electronic delocalization and chemically smooth potential energy surfaces
,” J. Chem. Phys.
128
, 034103
(2008
).63.
S. S.
Xantheas
, “Cooperativity and hydrogen bonding network in water clusters
,” Chem. Phys.
258
, 225
–231
(2000
).64.
A.
Sum
and S.
Sandler
, “Ab initio calculations of cooperativity effects on clusters of methanol, ethanol, 1-propanol, and methanethiol
,” J. Phys. Chem. A
104
, 1121
–1129
(2000
).65.
L.
Rincón
, R.
Almeida
, D.
García-Aldea
, and H.
Diez Y Riega
, “Hydrogen bond cooperativity and electron delocalization in hydrogen fluoride clusters
,” J. Chem. Phys.
114
, 5552
–5561
(2001
).66.
W. A.
Luck
, “The importance of cooperativity for the properties of liquid water
,” J. Mol. Struct.
448
, 131
–142
(1998
).67.
D.
Yuan
, Y.
Li
, Z.
Ni
, P.
Pulay
, W.
Li
, and S.
Li
, “Benchmark relative energies for large water clusters with the generalized energy-based fragmentation method
,” J. Chem. Theory Comput.
13
, 2696
–2704
(2017
).68.
B.
Temelso
, C. R.
Renner
, and G. C.
Shields
, “Importance and reliability of small basis set CCSD(T) corrections to MP2 binding and relative energies of water clusters
,” J. Chem. Theory Comput.
11
, 1439
–1448
(2015
).69.
J.
Friedrich
and B.
Fiedler
, “Accurate calculation of binding energies for molecular clusters–assessment of different models
,” Chem. Phys.
472
, 72
–80
(2016
).70.
B.
Temelso
, K. A.
Archer
, and G. C.
Shields
, “Benchmark structures and binding energies of small water clusters with anharmonicity corrections
,” J. Phys. Chem. A
115
, 12034
–12046
(2011
).71.
J. W.
Ponder
, C.
Wu
, P.
Ren
, V. S.
Pande
, J. D.
Chodera
, M. J.
Schnieders
, I.
Haque
, D. L.
Mobley
, D. S.
Lambrecht
, R. A.
Distasio
, M.
Head-Gordon
, G. N.
Clark
, M. E.
Johnson
, and T.
Head-Gordon
, “Current status of the AMOEBA polarizable force field
,” J. Phys. Chem. B
114
, 2549
–2564
(2010
).72.
P.
Ren
and J. W.
Ponder
, “Polarizable atomic multipole water model for molecular mechanics simulation
,” J. Phys. Chem. B
107
, 5933
–5947
(2003
).73.
C. J.
Tainter
, P. A.
Pieniazek
, Y. S.
Lin
, and J. L.
Skinner
, “Robust three-body water simulation model
,” J. Chem. Phys.
134
, 184501
(2011
).74.
V.
Babin
, C.
Leforestier
, and F.
Paesani
, “Development of a “first principles” water potential with flexible monomers: Dimer potential energy surface, VRT spectrum, and second virial coefficient
,” J. Chem. Theory Comput.
9
, 5395
–5403
(2013
).75.
G. A.
Cisneros
, K. T.
Wikfeldt
, L.
Ojamäe
, J.
Lu
, Y.
Xu
, H.
Torabifard
, A. P.
Bartók
, G.
Csányi
, V.
Molinero
, and F.
Paesani
, “Modeling molecular interactions in water: From pairwise to many-body potential energy functions
,” Chem. Rev.
116
, 7501
–7528
(2016
).76.
G. R.
Medders
and F.
Paesani
, “Infrared and Raman spectroscopy of liquid water through “first-principles” many-body molecular dynamics
,” J. Chem. Theory Comput.
11
, 1145
–1154
(2015
).77.
S. K.
Reddy
, S. C.
Straight
, P.
Bajaj
, C.
Huy Pham
, M.
Riera
, D. R.
Moberg
, M. A.
Morales
, C.
Knight
, A. W.
Götz
, and F.
Paesani
, “On the accuracy of the MB-pol many-body potential for water: Interaction energies, vibrational frequencies, and classical thermodynamic and dynamical properties from clusters to liquid water and ice
,” J. Chem. Phys.
145
, 194504
(2016
).78.
L. X.
Dang
and T.-M.
Chang
, “Molecular dynamics study of water clusters, liquid, and liquid-vapor interface of water with many-body potentials
,” J. Chem. Phys.
106
, 8149
–8159
(1997
).79.
C. J.
Burnham
, J.
Li
, S. S.
Xantheas
, and M.
Leslie
, “The parametrization of a thole-type all-atom polarizable water model from first principles and its application to the study of water clusters (n = 2-21) and the phonon spectrum of ice Ih
,” J. Chem. Phys.
110
, 4566
–4581
(1999
).80.
C. C.
Wang
, P.
Zielke
, O. F.
Sigurbjörnsson
, C. R.
Viteri
, and R.
Signorell
, “Infrared spectra of C2H6, C2H4, C2H2, and CO2 aerosols potentially formed in Titan’s atmosphere
,” J. Phys. Chem. A
113
, 11129
–11137
(2009
).81.
J. M.
DeSimone
, “Practical approaches to green solvents
,” Science
297
, 799
–803
(2002
).82.
R.
Bukowski
, J.
Sadlej
, B.
Jeziorski
, P.
Jankowski
, K.
Szalewicz
, S. A.
Kucharski
, H. L.
Williams
, and B. M.
Rice
, “Intermolecular potential of carbon dioxide dimer from symmetry-adapted perturbation theory
,” J. Chem. Phys.
110
, 3785
–3803
(1999
).83.
P. R.
Horn
and M.
Head-Gordon
, “Polarization contributions to intermolecular interactions revisited with fragment electric-field response functions
,” J. Chem. Phys.
143
, 114111
(2015
).84.
P. R.
Horn
, Y.
Mao
, and M.
Head-Gordon
, “Defining the contributions of permanent electrostatics, Pauli repulsion, and dispersion in density functional theory calculations of intermolecular interaction energies
,” J. Chem. Phys.
144
, 114107
(2016
).85.
The CCSD(T) interaction energy reported in this work has been extrapolated to the Complete Basis Set (CBS) limit using the focal point approximation analysis, . The MP2 correlation energy was extrapolated to use the 2-point extrapolation formula114 using the the aug-cc-pVQZ and the aug-cc-pV5Z basis sets.
86.
K. H.
Lemke
and T. M.
Seward
, “Thermodynamic properties of carbon dioxide clusters by M06-2X and dispersion-corrected B2PLYP-D theory
,” Chem. Phys. Lett.
573
, 19
–23
(2013
).87.
K. D.
Jordan
and K.
Sen
, Chemical Modelling: Volume 13
(The Royal Society of Chemistry
, 2017
), Vol. 13, pp. 105
–131
88.
R.
Ludwig
, “Water: From clusters to the bulk
,” Angew. Chem., Int. Ed. Engl.
40
, 1808
–1827
(2001
).89.
J. K.
Gregory
, D. C.
Clary
, K.
Liu
, M. G.
Brown
, and R. J.
Saykally
, “The water dipole moment in water clusters
,” Science
275
, 814
–817
(1997
).90.
Y. S.
Badyal
, M.-L.
Saboungi
, D. L.
Price
, S. D.
Shastri
, D. R.
Haeffner
, and A. K.
Soper
, “Electron distribution in water
,” J. Chem. Phys.
112
, 9206
(2000
).91.
E. R.
Batista
, S. S.
Xantheas
, and H.
Jonsson
, “Molecular multipole moments of water molecules in ice Ih
,” J. Chem. Phys.
109
, 4546
–4551
(1998
).92.
P. L.
Silvestrelli
and M.
Parrinello
, “Structural, electronic, and bonding properties of liquid water from first principles
,” J. Chem. Phys.
111
, 3572
–3580
(1999
).93.
T. K.
Ghanty
and S. K.
Ghosh
, “Polarizability of water clusters: An ab initio investigation
,” J. Chem. Phys.
118
, 8547
–8550
(2003
).94.
R. Z.
Khaliullin
, A. T.
Bell
, and M.
Head-Gordon
, “Electron donation in the water-water hydrogen bond
,” Chem. - Eur. J.
15
, 851
–855
(2009
).95.
E. A.
Cobar
, P. R.
Horn
, R. G.
Bergman
, and M.
Head-Gordon
, “Examination of the hydrogen-bonding networks in small water clusters (n = 2-5, 13, 17) using absolutely localized molecular orbital energy decomposition analysis
,” Phys. Chem. Chem. Phys.
14
, 15328
–15339
(2012
).96.
S.
Maheshwary
, N.
Patel
, N.
Sathyamurthy
, A. D.
Kulkarni
, and S. R.
Gadre
, “Structure and stability of water clusters (H2O)n, n = 8-20: An ab initio investigation
,” J. Phys. Chem. A
105
, 10525
–10537
(2001
).97.
B. S.
González
, J.
Hernández-Rojas
, and D. J.
Wales
, “Global minima and energetics of Li+(H2O)n and Ca2+(H2O)n clusters for n ≤ 20
,” Chem. Phys. Lett.
412
, 23
–28
(2005
).98.
C. K.
Egan
and F.
Paesani
, “Assessing many-body effects of water self-ions. I: OH–(H2O)n clusters
,” J. Chem. Theory Comput.
14
, 1982
–1997
(2018
).99.
R. M.
Richard
, K. U.
Lao
, and J. M.
Herbert
, “Understanding the many-body expansion for large systems. I. Precision considerations
,” J. Chem. Phys.
141
, 014108
(2014
).100.
C. M.
Breneman
and K. B.
Wiberg
, “Determining atom-centered monopoles from molecular electrostatic potentials. The need for high sampling density in formamide conformational analysis
,” J. Comput. Chem.
11
, 361
–373
(1990
).101.
A.
Becke
, “Density functional thermochemistry III. The role of exact exchange
,” J. Chem. Phys.
98
, 5648
–5652
(1993
).102.
C.
Lee
, W.
Yang
, and R. G.
Parr
, “Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density
,” Phys. Rev. B
37
, 785
–789
(1988
).103.
W. J.
Hehre
, R. F.
Stewart
, and J. A.
Pople
, “Self-consistent molecular-orbital methods. I. Use of Gaussian expansions of slater-type atomic orbitals
,” J. Chem. Phys.
51
, 2657
–2664
(1969
).104.
ErgoSCF, 2019, http://www.ergoscf.org/; accessed 13 May 2019.
105.
J.
Almlof
, K.
Faegri
, and K.
Korsell
, “Principles for a direct SCF approach to LCAO-MO ab-initio calculations
,” J. Comput. Chem.
3
, 385
–399
(1982
).106.
S.
Manzer
, P. R.
Horn
, N.
Mardirossian
, and M.
Head-Gordon
, “Fast, accurate evaluation of exact exchange: The occ-RI-K algorithm
,” J. Chem. Phys.
143
, 024113
(2015
).107.
S. F.
Manzer
, E.
Epifanovsky
, and M.
Head-Gordon
, “Efficient implementation of the pair atomic resolution of the identity approximation for exact exchange for hybrid and range-separated density functionals
,” J. Chem. Theory Comput.
11
, 518
–527
(2015
).108.
C.
Ochsenfeld
, J.
Kussmann
, and D. S.
Lambrecht
, Reviews in computational chemistry
(John Wiley & Sons, Ltd.
, 2007
), Chap. 1, pp. 1
–82
.109.
W.
Hu
, L.
Lin
, and C.
Yang
, “DGDFT: A massively parallel method for large scale density functional theory calculations
,” J. Chem. Phys.
143
, 124110
(2015
).110.
N.
Mardirossian
and M.
Head-Gordon
, “Survival of the most transferable at the top of Jacob’s ladder: Defining and testing the ωB97M(2) double hybrid density functional
,” J. Chem. Phys.
148
, 241736
(2018
).111.
R. C.
Lochan
and M.
Head-Gordon
, “Orbital-optimized opposite-spin scaled second-order correlation: An economical method to improve the description of open-shell molecules
,” J. Chem. Phys.
126
, 164101
(2007
).112.
D.
Stück
and M.
Head-Gordon
, “Regularized orbital-optimized second-order perturbation theory
,” J. Chem. Phys.
139
, 244109
(2013
).113.
K.
Raghavachari
, G. W.
Trucks
, J. A.
Pople
, and M.
Head-Gordon
, “A fifth-order perturbation comparison of electron correlation theories
,” Chem. Phys. Lett.
157
, 479
–483
(1989
).114.
T.
Helgaker
, W.
Klopper
, H.
Koch
, and J.
Noga
, “Basis-set convergence of correlated calculations on water
,” J. Chem. Phys.
106
, 9639
–9646
(1997
).© 2019 Author(s).
2019
Author(s)
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