Many-body potential energy functions (MB-PEFs), which integrate data-driven representations of many-body short-range quantum mechanical interactions with physics-based representations of many-body polarization and long-range interactions, have recently been shown to provide high accuracy in the description of molecular interactions from the gas to the condensed phase. Here, we present MB-Fit, a software infrastructure for the automated development of MB-PEFs for generic molecules within the TTM-nrg (Thole-type model energy) and MB-nrg (many-body energy) theoretical frameworks. Besides providing all the necessary computational tools for generating TTM-nrg and MB-nrg PEFs, MB-Fit provides a seamless interface with the MBX software, a many-body energy and force calculator for computer simulations. Given the demonstrated accuracy of the MB-PEFs, particularly within the MB-nrg framework, we believe that MB-Fit will enable routine predictive computer simulations of generic (small) molecules in the gas, liquid, and solid phases, including, but not limited to, the modeling of quantum isomeric equilibria in molecular clusters, solvation processes, molecular crystals, and phase diagrams.
REFERENCES
1.
D.
Frenkel
and B.
Smit
, Understanding Molecular Simulation: From Algorithms to Applications
(Elsevier
, 2001
), Vol. 1.2.
M.
Tuckerman
, Statistical Mechanics: Theory and Molecular Simulation
(Oxford University Press
, 2010
).3.
W. F.
Van Gunsteren
and H. J. C.
Berendsen
, “Computer simulation of molecular dynamics: Methodology, applications, and perspectives in chemistry
,” Angew. Chem., Int. Ed.
29
, 992
–1023
(1990
).4.
K.
Binder
, Monte Carlo and Molecular Dynamics Simulations in Polymer Science
(Oxford University Press
, 1995
).5.
A.
Warshel
, “Computer simulations of enzyme catalysis: Methods, progress, and insights
,” Annu. Rev. Biophys. Biomol. Struct.
32
, 425
–443
(2003
).6.
M.
Karplus
and J.
Kuriyan
, “Molecular dynamics and protein function
,” Proc. Natl. Acad. Sci. U. S. A.
102
, 6679
–6685
(2005
).7.
J. D.
Durrant
and J. A.
McCammon
, “Molecular dynamics simulations and drug discovery
,” BMC Biol.
9
, 71
(2011
).8.
K.
Ohno
, K.
Esfarjani
, and Y.
Kawazoe
, Computational Materials Science: From Ab Initio to Monte Carlo Methods
(Springer
, 2018
).9.
S.
Lifson
and A.
Warshel
, “Consistent force field for calculations of conformations, vibrational spectra, and enthalpies of cycloalkane and n-alkane molecules
,” J. Chem. Phys.
49
, 5116
–5129
(1968
).10.
A.
Warshel
and S.
Lifson
, “Consistent force field calculations. II. Crystal structures, sublimation energies, molecular and lattice vibrations, molecular conformations, and enthalpies of alkanes
,” J. Chem. Phys.
53
, 582
–594
(1970
).11.
A. K.
Rappé
, C. J.
Casewit
, K. S.
Colwell
, W. A.
Goddard
III, and W. M.
Skiff
, “UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations
,” J. Am. Chem. Soc.
114
, 10024
–10035
(1992
).12.
T. A.
Halgren
and W.
Damm
, “Polarizable force fields
,” Curr. Opin. Struct. Biol.
11
, 236
–242
(2001
).13.
A. D.
MacKerell
, Jr., “Empirical force fields for biological macromolecules: Overview and issues
,” J. Comput. Chem.
25
, 1584
–1604
(2004
).14.
P. S.
Nerenberg
and T.
Head-Gordon
, “New developments in force fields for biomolecular simulations
,” Curr. Opin. Struct. Biol.
49
, 129
–138
(2018
).15.
J. A.
Harrison
, J. D.
Schall
, S.
Maskey
, P. T.
Mikulski
, M. T.
Knippenberg
, and B. H.
Morrow
, “Review of force fields and intermolecular potentials used in atomistic computational materials research
,” Appl. Phys. Rev.
5
, 031104
(2018
).16.
J.
Behler
, “Perspective: Machine learning potentials for atomistic simulations
,” J. Chem. Phys.
145
, 170901
(2016
).17.
V. L.
Deringer
, M. A.
Caro
, and G.
Csányi
, “Machine learning interatomic potentials as emerging tools for materials science
,” Adv. Mater.
31
, 1902765
(2019
).18.
F.
Noé
, A.
Tkatchenko
, K.-R.
Müller
, and C.
Clementi
, “Machine learning for molecular simulation
,” Annu. Rev. Phys. Chem.
71
, 361
–390
(2020
).19.
T.
Mueller
, A.
Hernandez
, and C.
Wang
, “Machine learning for interatomic potential models
,” J. Chem. Phys.
152
, 050902
(2020
).20.
T. B.
Blank
, S. D.
Brown
, A. W.
Calhoun
, and D. J.
Doren
, “Neural network models of potential energy surfaces
,” J. Chem. Phys.
103
, 4129
–4137
(1995
).21.
H.
Gassner
, M.
Probst
, A.
Lauenstein
, and K.
Hermansson
, “Representation of intermolecular potential functions by neural networks
,” J. Phys. Chem. A
102
, 4596
–4605
(1998
).22.
S.
Lorenz
, A.
Groß
, and M.
Scheffler
, “Representing high-dimensional potential-energy surfaces for reactions at surfaces by neural networks
,” Chem. Phys. Lett.
395
, 210
–215
(2004
).23.
S.
Manzhos
and T.
Carrington
, Jr., “Using neural networks to represent potential surfaces as sums of products
,” J. Chem. Phys.
125
, 194105
(2006
).24.
J.
Behler
and M.
Parrinello
, “Generalized neural-network representation of high-dimensional potential-energy surfaces
,” Phys. Rev. Lett.
98
, 146401
(2007
).25.
S. A.
Ghasemi
, A.
Hofstetter
, S.
Saha
, and S.
Goedecker
, “Interatomic potentials for ionic systems with density functional accuracy based on charge densities obtained by a neural network
,” Phys. Rev. B
92
, 045131
(2015
).26.
J. S.
Smith
, O.
Isayev
, and A. E.
Roitberg
, “ANI-1: An extensible neural network potential with DFT accuracy at force field computational cost
,” Chem. Sci.
8
, 3192
–3203
(2017
).27.
K. T.
Schütt
, H. E.
Sauceda
, P.-J.
Kindermans
, A.
Tkatchenko
, and K.-R.
Müller
, “SchNet—A deep learning architecture for molecules and materials
,” J. Chem. Phys.
148
, 241722
(2018
).28.
L.
Zhang
, J.
Han
, H.
Wang
, R.
Car
, and W.
E
, “Deep potential molecular dynamics: A scalable model with the accuracy of quantum mechanics
,” Phys. Rev. Lett.
120
, 143001
(2018
).29.
O. T.
Unke
and M.
Meuwly
, “PhysNet: A neural network for predicting energies, forces, dipole moments, and partial charges
,” J. Chem. Theory Comput.
15
, 3678
–3693
(2019
).30.
A. P.
Bartók
, M. C.
Payne
, R.
Kondor
, and G.
Csányi
, “Gaussian approximation potentials: The accuracy of quantum mechanics, without the electrons
,” Phys. Rev. Lett.
104
, 136403
(2010
).31.
A. V.
Shapeev
, “Moment tensor potentials: A class of systematically improvable interatomic potentials
,” Multiscale Model. Simul.
14
, 1153
–1173
(2016
).32.
A. P.
Thompson
, L. P.
Swiler
, C. R.
Trott
, S. M.
Foiles
, and G. J.
Tucker
, “Spectral neighbor analysis method for automated generation of quantum-accurate interatomic potentials
,” J. Comput. Phys.
285
, 316
–330
(2015
).33.
R.
Drautz
, “Atomic cluster expansion for accurate and transferable interatomic potentials
,” Phys. Rev. B
99
, 014104
(2019
).34.
M.
Rupp
, A.
Tkatchenko
, K.-R.
Müller
, and O. A.
Von Lilienfeld
, “Fast and accurate modeling of molecular atomization energies with machine learning
,” Phys. Rev. Lett.
108
, 058301
(2012
).35.
S.
Chmiela
, A.
Tkatchenko
, H. E.
Sauceda
, I.
Poltavsky
, K. T.
Schütt
, and K.-R.
Müller
, “Machine learning of accurate energy-conserving molecular force fields
,” Sci. Adv.
3
, e1603015
(2017
).36.
A.
Vitek
, M.
Stachon
, P.
Krömer
, and V.
Snáel
, “Towards the modeling of atomic and molecular clusters energy by support vector regression
,” in 2013 5th International Conference on Intelligent Networking and Collaborative Systems
(IEEE
, 2013
), pp. 121
–126
.37.
B. J.
Braams
and J. M.
Bowman
, “Permutationally invariant potential energy surfaces in high dimensionality
,” Int. Rev. Phys. Chem.
28
, 577
–606
(2009
).38.
Z.
Xie
and J. M.
Bowman
, “Permutationally invariant polynomial basis for molecular energy surface fitting via monomial symmetrization
,” J. Chem. Theory Comput.
6
, 26
–34
(2010
).39.
Y.
Wang
, X.
Huang
, B. C.
Shepler
, B. J.
Braams
, and J. M.
Bowman
, “Flexible, ab initio potential, and dipole moment surfaces for water. I. Tests and applications for clusters up to the 22-mer
,” J. Chem. Phys.
134
, 094509
(2011
).40.
C.
Qu
, Q.
Yu
, and J. M.
Bowman
, “Permutationally invariant potential energy surfaces
,” Annu. Rev. Phys. Chem.
69
, 151
–175
(2018
).41.
A.
Nandi
, C.
Qu
, and J. M.
Bowman
, “Full and fragmented permutationally invariant polynomial potential energy surfaces for trans and cis N-methyl acetamide and isomerization saddle points
,” J. Chem. Phys.
151
, 084306
(2019
).42.
A.
Nandi
, C.
Qu
, P. L.
Houston
, R.
Conte
, and J. M.
Bowman
, “δ-machine learning for potential energy surfaces: A PIP approach to bring a DFT-based PES to CCSD(T) level of theory
,” J. Chem. Phys.
154
, 051102
(2021
).43.
D. R.
Moberg
and A. W.
Jasper
, “Permutationally invariant polynomial expansions with unrestricted complexity
,” J. Chem. Theory Comput.
17
, 5440
–5455
(2021
).44.
B.
Jiang
and H.
Guo
, “Permutation invariant polynomial neural network approach to fitting potential energy surfaces
,” J. Chem. Phys.
139
, 054112
(2013
).45.
J.
Li
, B.
Jiang
, and H.
Guo
, “Permutation invariant polynomial neural network approach to fitting potential energy surfaces. II. Four-atom systems
,” J. Chem. Phys.
139
, 204103
(2013
).46.
B.
Jiang
and H.
Guo
, “Permutation invariant polynomial neural network approach to fitting potential energy surfaces. III. Molecule-surface interactions
,” J. Chem. Phys.
141
, 034109
(2014
).47.
C.
Xie
, X.
Zhu
, D. R.
Yarkony
, and H.
Guo
, “Permutation invariant polynomial neural network approach to fitting potential energy surfaces. IV. Coupled diabatic potential energy matrices
,” J. Chem. Phys.
149
, 144107
(2018
).48.
K. T.
Butler
, D. W.
Davies
, H.
Cartwright
, O.
Isayev
, and A.
Walsh
, “Machine learning for molecular and materials science
,” Nature
559
, 547
–555
(2018
).49.
J.
Behler
, “Four generations of high-dimensional neural network potentials
,” Chem. Rev.
121
, 10037
–10072
(2021
).50.
S.
Manzhos
and T.
Carrington
, Jr., “Neural network potential energy surfaces for small molecules and reactions
,” Chem. Rev.
121
, 10187
–10217
(2021
).51.
T.
Morawietz
and J.
Behler
, “A density-functional theory-based neural network potential for water clusters including van der Waals corrections
,” J. Phys. Chem. A
117
, 7356
–7366
(2013
).52.
C.
Schran
, J.
Behler
, and D.
Marx
, “Automated fitting of neural network potentials at coupled cluster accuracy: Protonated water clusters as testing ground
,” J. Chem. Theory Comput.
16
, 88
–99
(2019
).53.
D.
Rosenberger
, J. S.
Smith
, and A. E.
Garcia
, “Modeling of peptides with classical and novel machine learning force fields: A comparison
,” J. Phys. Chem. B
125
, 3598
–3612
(2021
).54.
S.
Yue
, M. C.
Muniz
, M. F.
Calegari Andrade
, L.
Zhang
, R.
Car
, and A. Z.
Panagiotopoulos
, “When do short-range atomistic machine-learning models fall short?
,” J. Chem. Phys.
154
, 034111
(2021
).55.
J.
Rezac
and P.
Hobza
, “Describing noncovalent interactions beyond the common approximations: How accurate is the ‘gold standard,’ CCSD(T) at the complete basis set limit?
,” J. Chem. Theory Comput.
9
, 2151
–2155
(2013
).56.
D.
Hankins
, J. W.
Moskowitz
, and F. H.
Stillinger
, “Water molecule interactions
,” J. Chem. Phys.
53
, 4544
–4554
(1970
).57.
F.
Paesani
, “Getting the right answers for the right reasons: Toward predictive molecular simulations of water with many-body potential energy functions
,” Acc. Chem. Res.
49
, 1844
–1851
(2016
).58.
F.
Paesani
, “Water: Many-body potential from first principles (from the gas to the liquid phase)
,” in Handbook of Materials Modeling: Methods: Theory and Modeling
(Springer
, 2020
), pp. 635
–660
.59.
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
).60.
V.
Babin
, G. R.
Medders
, and F.
Paesani
, “Development of a ‘first principles’ water potential with flexible monomers. II: Trimer potential energy surface, third virial coefficient, and small clusters
,” J. Chem. Theory Comput.
10
, 1599
–1607
(2014
).61.
G. R.
Medders
, V.
Babin
, and F.
Paesani
, “Development of a ‘first-principles’ water potential with flexible monomers. III. Liquid phase properties
,” J. Chem. Theory Comput.
10
, 2906
–2910
(2014
).62.
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
).63.
J. O.
Richardson
, C.
Pérez
, S.
Lobsiger
, A. A.
Reid
, B.
Temelso
, G. C.
Shields
, Z.
Kisiel
, D. J.
Wales
, B. H.
Pate
, and S. C.
Althorpe
, “Concerted hydrogen-bond breaking by quantum tunneling in the water hexamer prism
,” Science
351
, 1310
–1313
(2016
).64.
W. T. S.
Cole
, J. D.
Farrell
, D. J.
Wales
, and R. J.
Saykally
, “Structure and torsional dynamics of the water octamer from THz laser spectroscopy near 215 μm
,” Science
352
, 1194
–1197
(2016
).65.
J. D.
Mallory
and V. A.
Mandelshtam
, “Diffusion Monte Carlo studies of MB-pol (H2O)2–6 and (D2O)2–6 clusters: Structures and binding energies
,” J. Chem. Phys.
145
, 064308
(2016
).66.
P. E.
Videla
, P. J.
Rossky
, and D.
Laria
, “Communication: Isotopic effects on tunneling motions in the water trimer
,” J. Chem. Phys.
144
, 061101
(2016
).67.
S. E.
Brown
, A. W.
Götz
, X.
Cheng
, R. P.
Steele
, V. A.
Mandelshtam
, and F.
Paesani
, “Monitoring water clusters ‘melt’ through vibrational spectroscopy
,” J. Am. Chem. Soc.
139
, 7082
–7088
(2017
).68.
C. L.
Vaillant
and M. T.
Cvitaš
, “Rotation-tunneling spectrum of the water dimer from instanton theory
,” Phys. Chem. Chem. Phys.
20
, 26809
–26813
(2018
).69.
C. L.
Vaillant
, D. J.
Wales
, and S. C.
Althorpe
, “Tunneling splittings from path-integral molecular dynamics using a Langevin thermostat
,” J. Chem. Phys.
148
, 234102
(2018
).70.
M.
Schmidt
and P.-N.
Roy
, “Path integral molecular dynamic simulation of flexible molecular systems in their ground state: Application to the water dimer
,” J. Chem. Phys.
148
, 124116
(2018
).71.
K. P.
Bishop
and P.-N.
Roy
, “Quantum mechanical free energy profiles with post-quantization restraints: Binding free energy of the water dimer over a broad range of temperatures
,” J. Chem. Phys.
148
, 102303
(2018
).72.
P. E.
Videla
, P. J.
Rossky
, and D.
Laria
, “Isotopic equilibria in aqueous clusters at low temperatures: Insights from the MB-pol many-body potential
,” J. Chem. Phys.
148
, 084303
(2018
).73.
N. R.
Samala
and N.
Agmon
, “Temperature dependence of intramolecular vibrational bands in small water clusters
,” J. Phys. Chem. B
123
, 9428
–9442
(2019
).74.
M. T.
Cvitaš
and J. O.
Richardson
, “Quantum tunnelling pathways of the water pentamer
,” Phys. Chem. Chem. Phys.
22
, 1035
–1044
(2020
).75.
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
).76.
S. C.
Straight
and F.
Paesani
, “Exploring electrostatic effects on the hydrogen bond network of liquid water through many-body molecular dynamics
,” J. Phys. Chem. B
120
, 8539
–8546
(2016
).77.
S. K.
Reddy
, D. R.
Moberg
, S. C.
Straight
, and F.
Paesani
, “Temperature-dependent vibrational spectra and structure of liquid water from classical and quantum simulations with the MB-pol potential energy function
,” J. Chem. Phys.
147
, 244504
(2017
).78.
K. M.
Hunter
, F. A.
Shakib
, and F.
Paesani
, “Disentangling coupling effects in the infrared spectra of liquid water
,” J. Phys. Chem. B
122
, 10754
–10761
(2018
).79.
Z.
Sun
, L.
Zheng
, M.
Chen
, M. L.
Klein
, F.
Paesani
, and X.
Wu
, “Electron-hole theory of the effect of quantum nuclei on the x-ray absorption spectra of liquid water
,” Phys. Rev. Lett.
121
, 137401
(2018
).80.
A. P.
Gaiduk
, T. A.
Pham
, M.
Govoni
, F.
Paesani
, and G.
Galli
, “Electron affinity of liquid water
,” Nat. Commun.
9
, 247
(2018
).81.
V. W. D.
Cruzeiro
, A.
Wildman
, X.
Li
, and F.
Paesani
, “Relationship between hydrogen-bonding motifs and the 1b1 splitting in the x-ray emission spectrum of liquid water
,” J. Phys. Chem. Lett.
12
, 3996
–4002
(2021
).82.
G. R.
Medders
and F.
Paesani
, “Dissecting the molecular structure of the air/water interface from quantum simulations of the sum-frequency generation spectrum
,” J. Am. Chem. Soc.
138
, 3912
–3919
(2016
).83.
D. R.
Moberg
, S. C.
Straight
, and F.
Paesani
, “Temperature dependence of the air/water interface revealed by polarization sensitive sum-frequency generation spectroscopy
,” J. Phys. Chem. B
122
, 4356
–4365
(2018
).84.
S.
Sun
, F.
Tang
, S.
Imoto
, D. R.
Moberg
, T.
Ohto
, F.
Paesani
, M.
Bonn
, E. H. G.
Backus
, and Y.
Nagata
, “Orientational distribution of free OH groups of interfacial water is exponential
,” Phys. Rev. Lett.
121
, 246101
(2018
).85.
S.
Sengupta
, D. R.
Moberg
, F.
Paesani
, and E.
Tyrode
, “Neat water–vapor interface: Proton continuum and the nonresonant background
,” J. Phys. Chem. Lett.
9
, 6744
–6749
(2018
).86.
M. C.
Muniz
, T. E.
Gartner
III, M.
Riera
, C.
Knight
, S.
Yue
, F.
Paesani
, and A. Z.
Panagiotopoulos
, “Vapor-liquid equilibrium of water with the MB-pol many-body potential
,” J. Chem. Phys.
154
, 211103
(2021
).87.
C. H.
Pham
, S. K.
Reddy
, K.
Chen
, C.
Knight
, and F.
Paesani
, “Many-body interactions in ice
,” J. Chem. Theory Comput.
13
, 1778
–1784
(2017
).88.
D. R.
Moberg
, S. C.
Straight
, C.
Knight
, and F.
Paesani
, “Molecular origin of the vibrational structure of ice Ih
,” J. Phys. Chem. Lett.
8
, 2579
–2583
(2017
).89.
D. R.
Moberg
, P. J.
Sharp
, and F.
Paesani
, “Molecular-level interpretation of vibrational spectra of ordered ice phases
,” J. Phys. Chem. B
122
, 10572
–10581
(2018
).90.
D. R.
Moberg
, D.
Becker
, C. W.
Dierking
, F.
Zurheide
, B.
Bandow
, U.
Buck
, A.
Hudait
, V.
Molinero
, F.
Paesani
, and T.
Zeuch
, “The end of ice I
,” Proc. Natl. Acad. Sci. U. S. A.
116
, 24413
–24419
(2019
).91.
L.
del Rosso
, M.
Celli
, D.
Colognesi
, S.
Rudic
, N. J.
English
, and L.
Ulivi
, “Density of phonon states in cubic ice Ic
,” ChemRxiv:14769987.v1 (2021
).92.
D. J.
Arismendi-Arrieta
, M.
Riera
, P.
Bajaj
, R.
Prosmiti
, and F.
Paesani
, “i-TTM model for ab initio-based ion–water interaction potentials. 1. Halide–water potential energy functions
,” J. Phys. Chem. B
120
, 1822
–1832
(2015
).93.
P.
Bajaj
, A. W.
Götz
, and F.
Paesani
, “Toward chemical accuracy in the description of ion–water interactions through many-body representations. I. Halide–water dimer potential energy surfaces
,” J. Chem. Theory Comput.
12
, 2698
–2705
(2016
).94.
B. B.
Bizzarro
, C. K.
Egan
, and F.
Paesani
, “Nature of halide–water interactions: Insights from many-body representations and density functional theory
,” J. Chem. Theory Comput.
15
, 2983
–2995
(2019
).95.
M.
Riera
, A. W.
Götz
, and F.
Paesani
, “The i-TTM model for ab initio-based ion–water interaction potentials. II. Alkali metal ion–water potential energy functions
,” Phys. Chem. Chem. Phys.
18
, 30334
–30343
(2016
).96.
M.
Riera
, N.
Mardirossian
, P.
Bajaj
, A. W.
Götz
, and F.
Paesani
, “Toward chemical accuracy in the description of ion–water interactions through many-body representations. Alkali-water dimer potential energy surfaces
,” J. Chem. Phys.
147
, 161715
(2017
).97.
C. K.
Egan
, B. B.
Bizzarro
, M.
Riera
, and F.
Paesani
, “Nature of alkali ion–water interactions: Insights from many-body representations and density functional theory. II
,” J. Chem. Theory Comput.
16
, 3055
–3072
(2020
).98.
M.
Riera
, E. P.
Yeh
, and F.
Paesani
, “Data-driven many-body models for molecular fluids: CO2/H2O mixtures as a case study
,” J. Chem. Theory Comput.
16
, 2246
–2257
(2020
).99.
M.
Riera
, A.
Hirales
, R.
Ghosh
, and F.
Paesani
, “Data-driven many-body models with chemical accuracy for CH4/H2O mixtures
,” J. Chem. Phys. B
124
, 11207
–11221
(2020
).100.
V. W. D.
Cruzeiro
, E.
Lambros
, M.
Riera
, R.
Roy
, F.
Paesani
, and A. W.
Götz
, “Highly accurate many-body potentials for simulations of N2O5 in water: Benchmarks, development, and validation
,” J. Chem. Theory Comput.
17
, 3931
(2021
).101.
P.
Bajaj
, X.-G.
Wang
, T.
Carrington
, Jr., and F.
Paesani
, “Vibrational spectra of halide–water dimers: Insights on ion hydration from full-dimensional quantum calculations on many-body potential energy surfaces
,” J. Chem. Phys.
148
, 102321
(2018
).102.
M.
Riera
, S. E.
Brown
, and F.
Paesani
, “Isomeric equilibria, nuclear quantum effects, and vibrational spectra of M+(H2O)n=1–3 clusters, with M = Li, Na, K, Rb, and Cs, through many-body representations
,” J. Phys. Chem. A
122
, 5811
–5821
(2018
).103.
P.
Bajaj
, M.
Riera
, J. K.
Lin
, Y. E.
Mendoza Montijo
, J.
Gazca
, and F.
Paesani
, “Halide ion microhydration: Structure, energetics, and spectroscopy of small halide–water clusters
,” J. Phys. Chem. A
123
, 2843
–2852
(2019
).104.
P.
Bajaj
, J. O.
Richardson
, and F.
Paesani
, “Ion-mediated hydrogen-bond rearrangement through tunnelling in the iodide–dihydrate complex
,” Nat. Chem.
11
, 367
(2019
).105.
P.
Bajaj
, D.
Zhuang
, and F.
Paesani
, “Specific ion effects on hydrogen-bond rearrangements in the halide–dihydrate complexes
,” J. Phys. Chem. Lett.
10
, 2823
–2828
(2019
).106.
D.
Zhuang
, M.
Riera
, G. K.
Schenter
, J. L.
Fulton
, and F.
Paesani
, “Many-body effects determine the local hydration structure of Cs+ in solution
,” J. Phys. Chem. Lett.
10
, 406
–412
(2019
).107.
M.
Riera
, J. J.
Talbot
, R. P.
Steele
, and F.
Paesani
, “Infrared signatures of isomer selectivity and symmetry breaking in the Cs+(H2O)3 complex using many-body potential energy functions
,” J. Chem. Phys.
153
, 044306
(2020
).108.
A.
Caruso
and F.
Paesani
, “Data-driven many-body models enable a quantitative description of chloride hydration from clusters to bulk
,” J. Chem. Phys.
155
, 064502
(2021
).109.
MBX: A many-body energy and force calculator, http://paesanigroup.ucsd.edu/software/mbx.html.
110.
LAMMPS molecular dynamics simulator, http://lammps.sandia.gov.
111.
i-PI: A universal force engine, http://ipi-code.org.
112.
A. J.
Stone
, The Theory of Intermolecular Forces
(Oxford University Press
, Oxford
, 2013
).113.
K. T.
Tang
and J. P.
Toennies
, “An improved simple model for the van der Waals potential based on universal damping functions for the dispersion coefficients
,” J. Chem. Phys.
80
, 3726
–3741
(1984
).114.
C. J.
Burnham
, D. J.
Anick
, P. K.
Mankoo
, and G. F.
Reiter
, “The vibrational proton potential in bulk liquid water and ice
,” J. Chem. Phys.
128
, 154519
(2008
).115.
Maplesoft Development Team
, Maple 2019 Maplesoft, a division of Waterloo Maple, Inc., Waterloo, Ontario, https://www.maplesoft.com.116.
PostgreSQL Development Team
, PostgreSQL, version 11.3.0, https://www.postgresql.org.117.
T. P. Team
, Postgresql driver for python–psycopg, https://www.psycopg.org/.118.
S. E.
Brown
, “From ab initio data to high-dimensional potential energy surfaces: A critical overview and assessment of the development of permutationally invariant polynomial potential energy surfaces for single molecules
,” J. Chem. Phys.
151
, 194111
(2019
).119.
K.
Shoemake
, “Uniform random rotations
,” in Graphics Gems III
, edited by D.
Kirk
(Academic Press, Inc.
, 1992
).120.
Y.
Zhai
, A.
Caruso
, S.
Gao
, and F.
Paesani
, “Active learning of many-body configuration space: Application to the Cs+–water MB-nrg potential energy function as a case study
,” J. Chem. Phys.
152
, 144103
(2020
).121.
R.
Pordes
, D.
Petravick
, B.
Kramer
, D.
Olson
, M.
Livny
, A.
Roy
, P.
Avery
, K.
Blackburn
, T.
Wenaus
, F.
Würthwein
, I.
Foster
, R.
Gardner
, M.
Wilde
, A.
Blatecky
, J.
McGee
, and R.
Quick
, “The open science grid
,” J. Phys.: Conf. Ser.
78
, 012057
(2007
).122.
E.
Epifanovsky
,A. T. B.
Gilbert
,X.
Feng
,J.
Lee
,Y.
Mao
,N.
Mardirossian
,P.
Pokhilko
,A. F.
White
,M. P.
Coons
,A. L.
Dempwolff
,Z.
Gan
,D.
Hait
,P. R.
Horn
,L. D.
Jacobson
,I.
Kaliman
,J.
Kussmann
,A. W.
Lange
,K. U.
Lao
,D. S.
Levine
,J.
Liu
,S. C.
McKenzie
,A. F.
Morrison
,K. D.
Nanda
,F.
Plasser
,D. R.
Rehn
,M. L.
Vidal
,Z.-Q.
You
,Y.
Zhu
,B.
Alam
,B. J.
Albrecht
,A.
Aldossary
,E.
Alguire
,J. H.
Andersen
,V.
Athavale
,D.
Barton
,K.
Begam
,A.
Behn
,N.
Bellonzi
,Y. A.
Bernard
,E. J.
Berquist
,H. G. A.
Burton
,A.
Carreras
,K.
Carter-Fenk
,R.
Chakraborty
,A. D.
Chien
,K. D.
Closser
,V.
Cofer-Shabica
,S.
Dasgupta
,M.
de Wergifosse
,J.
Deng
,M.
Diedenhofen
,H.
Do
,S.
Ehlert
,P.-T.
Fang
,S.
Fatehi
,Q.
Feng
,T.
Friedhoff
,J.
Gayvert
,Q.
Ge
,G.
Gidofalvi
,M.
Goldey
,J.
Gomes
,C. E.
González-Espinoza
,S.
Gulania
,A. O.
Gunina
,M. W. D.
Hanson-Heine
,P. H. P.
Harbach
,A.
Hauser
,M. F.
Herbst
,M.
Hernández Vera
,M.
Hodecker
,Z. C.
Holden
,S.
Houck
,X.
Huang
,K.
Hui
,B. C.
Huynh
,M.
Ivanov
,Á.
Jász
,H.
Ji
,H.
Jiang
,B.
Kaduk
,S.
Kähler
,K.
Khistyaev
,J.
Kim
,G.
Kis
,P.
Klunzinger
,Z.
Koczor-Benda
,J. H.
Koh
,D.
Kosenkov
,L.
Koulias
,T.
Kowalczyk
,C. M.
Krauter
,K.
Kue
,A.
Kunitsa
,T.
Kus
,I.
Ladjànszki
,A.
Landau
,K. V.
Lawler
,D.
Lefrancois
,S.
Lehtola
,R. R.
Li
,Y.-P.
Li
,J.
Liang
,M.
Liebenthal
,H.-H.
Lin
,Y.-S.
Lin
,F.
Liu
,K.-Y.
Liu
,M.
Loipersberger
,A.
Luenser
,A.
Manjanath
,P.
Manohar
,E.
Mansoor
,S. F.
Manzer
,S.-P.
Mao
,A. V.
Marenich
,T.
Markovich
,S.
Mason
,S. A.
Maurer
,P. F.
McLaughlin
,M. F. S. J.
Menger
,J.-M.
Mewes
,S. A.
Mewes
,P.
Morgante
,J. W.
Mullinax
,K. J.
Oosterbaan
,G.
Paran
,A. C.
Paul
,S. K.
Paul
, F.
Pavošević
,Z.
Pei
,S.
Prager
,E. I.
Proynov
,Á.
Ràk
,E.
Ramos-Cordoba
,B.
Rana
,A. E.
Rask
,A.
Rettig
,R. M.
Richard
,F.
Rob
,E.
Rossomme
,T.
Scheele
,M.
Scheurer
,M.
Schneider
,N.
Sergueev
,S. M.
Sharada
,W.
Skomorowski
,D. W.
Small
,C. J.
Stein
,Y.-C.
Su
,E. J.
Sundstrom
,Z.
Tao
,J.
Thirman
,G. J.
Tornai
,T.
Tsuchimochi
,N. M.
Tubman
,S. P.
Veccham
,O.
Vydrov
,J.
Wenzel
,J.
Witte
,A.
Yamada
,K.
Yao
,S.
Yeganeh
,S. R.
Yost
,A.
Zech
, I. Y.
Zhang
,X.
Zhang
,Y.
Zhang
,D.
Zuev
,A.
Aspuru-Guzik
,A. T.
Bell
,N. A.
Besley
,K. B.
Bravaya
,B. R.
Brooks
,D.
Casanova
,J.-D.
Chai
,S.
Coriani
,C. J.
Cramer
,G.
Cserey
,A. E.
DePrince
III,R. A.
DiStasio
, Jr.,A.
Dreuw
,B. D.
Dunietz
,T. R.
Furlani
,W. A.
Goddard
III,S.
Hammes-Schiffer
,T.
Head-Gordon
,W. J.
Hehre
,C.-P.
Hsu
,T.-C.
Jagau
,Y.
Jung
,A.
Klamt
,J.
Kong
,D. S.
Lambrecht
,W.
Liang
,N. J.
Mayhall
,C. W.
McCurdy
,J. B.
Neaton
,C.
Ochsenfeld
,J. A.
Parkhill
,R.
Peverati
,V. A.
Rassolov
,Y.
Shao
,L. V.
Slipchenko
,T.
Stauch
,R. P.
Steele
,J. E.
Subotnik
,A. J. W.
Thom
,A.
Tkatchenko
,D. G.
Truhlar
,T.
Van Voorhis
,T. A.
Wesolowski
,K. B.
Whaley
,H. L.
Woodcock
III,P. M.
Zimmerman
,S.
Faraji
,P. M. W.
Gill
,M.
Head-Gordon
,J. M.
Herbert
, and A. I.
Krylov
, “Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package
,” J. Chem. Phys.
155
, 084801
(2021
).123.
D. G. A.
Smith
, L. A.
Burns
, A. C.
Simmonett
, R. M.
Parrish
, M. C.
Schieber
, R.
Galvelis
, P.
Kraus
, H.
Kruse
, R.
Di Remigio
, A.
Alenaizan
, A. M.
James
, S.
Lehtola
, J. P.
Misiewicz
, M.
Scheurer
, R. A.
Shaw
, J. B.
Schriber
, Y.
Xie
, Z. L.
Glick
, D. A.
Sirianni
, J. S.
O’Brien
, J. M.
Waldrop
, A.
Kumar
, E. G.
Hohenstein
, B. P.
Pritchard
, B. R.
Brooks
, H. F.
Schaefer
III, A. Y.
Sokolov
, K.
Patkowski
, A. E.
DePrince
III, U.
Bozkaya
, R. A.
King
, F. A.
Evangelista
, J. M.
Turney
, T. D.
Crawford
, and C. D.
Sherrill
, “PSI4 1.4: Open-source software for high-throughput quantum chemistry
,” J. Chem. Phys.
152
, 184108
(2020
).124.
A. V.
Marenich
, S. V.
Jerome
, C. J.
Cramer
, and D. G.
Truhlar
, “Charge model 5: An extension of Hirshfeld population analysis for the accurate description of molecular interactions in gaseous and condensed phases
,” J. Chem. Theory Comput.
8
, 527
–541
(2012
).125.
A. D.
Becke
and E. R.
Johnson
, “Exchange-hole dipole moment and the dispersion interaction
,” J. Chem. Phys.
122
, 154104
(2005
).126.
E. R.
Johnson
and A. D.
Becke
, “A post-Hartree–Fock model of intermolecular interactions
,” J. Chem. Phys.
123
, 024101
(2005
).127.
E. R.
Johnson
and A. D.
Becke
, “A post-Hartree-Fock model of intermolecular interactions: Inclusion of higher-order corrections
,” J. Chem. Phys.
124
, 174104
(2006
).128.
S. F.
Boys
and F.
Bernardi
, “The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors
,” Mol. Phys.
19
, 553
–566
(1970
).129.
Free Software Foundation, Inc., GCC, the GNU compiler collection, https://gcc.gnu.org.
130.
Intel Corporation, Intel Compiler for C++, https://software.intel.com.
131.
M.
Bonomi
, D.
Branduardi
, G.
Bussi
, C.
Camilloni
, D.
Provasi
, P.
Raiteri
, D.
Donadio
, F.
Marinelli
, F.
Pietrucci
, R. A.
Broglia
, and M.
Parrinello
, “PLUMED: A portable plugin for free-energy calculations with molecular dynamics
,” Comput. Phys. Commun.
180
, 1961
–1972
(2009
).132.
G. A.
Tribello
, M.
Bonomi
, D.
Branduardi
, C.
Camilloni
, and G.
Bussi
, “PLUMED 2: New feathers for an old bird
,” Comput. Phys. Commun.
185
, 604
–613
(2014
).133.
GitHub, MB-Fit: Software infrastructure for data-driven many-body potential energy functions, https://github.com/paesanilab/MB-Fit.
134.
D. R.
MacFarlane
, P. V.
Cherepanov
, J.
Choi
, B. H. R.
Suryanto
, R. Y.
Hodgetts
, J. M.
Bakker
, F. M. F.
Vallana
, and A. N.
Simonov
, “A roadmap to the ammonia economy
,” Joule
4
, 1186
–1205
(2020
).135.
A. E.
DePrince
III and C. D.
Sherrill
, “Accuracy and efficiency of coupled-cluster theory using density fitting/Cholesky decomposition, frozen natural orbitals, and at t1-transformed Hamiltonian
,” J. Chem. Theory Comput.
9
, 2687
–2696
(2013
).136.
C.
Adamo
and V.
Barone
, “Toward reliable density functional methods without adjustable parameters: The PBE0 model
,” J. Chem. Phys.
110
, 6158
–6170
(1999
).137.
S.
Grimme
, J.
Antony
, S.
Ehrlich
, and H.
Krieg
, “A consistent and accurate ab initio parameterization of density functional dispersion correction (DFT-D) for the 94 elements H–Pu
,” J. Chem. Phys.
132
, 154104
(2010
).138.
T. H.
Dunning
, Jr., “Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
,” J. Chem. Phys.
90
, 1007
–1023
(1989
).139.
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
).140.
M.
Riera
, E.
Lambros
, T. T.
Nguyen
, A. W.
Götz
, and F.
Paesani
, “Low-order many-body interactions determine the local structure of liquid water
,” Chem. Sci.
10
, 8211
–8218
(2019
).141.
C. K.
Egan
and F.
Paesani
, “Assessing many-body effects of water self-ions. II: H3O+(H2O)n clusters
,” J. Chem. Theory Comput.
15
, 4816
–4833
(2019
).142.
F.
Paesani
, P.
Bajaj
, and M.
Riera
, “Chemical accuracy in modeling halide ion hydration from many-body representations
,” Adv. Phys. X
4
, 1631212
(2019
).143.
G. R.
Medders
, A. W.
Götz
, M. A.
Morales
, P.
Bajaj
, and F.
Paesani
, “On the representation of many-body interactions in water
,” J. Chem. Phys.
143
, 104102
(2015
).144.
E.
Lambros
and F.
Paesani
, “How good are polarizable and flexible models for water: Insights from a many-body perspective
,” J. Chem. Phys.
153
, 060901
(2020
).145.
U.
Góra
, R.
Podeszwa
, W.
Cencek
, and K.
Szalewicz
, “Interaction energies of large clusters from many-body expansion
,” J. Chem. Phys.
135
, 224102
(2011
).146.
J. O.
Hirschfelder
, F. T.
McClure
, and I. F.
Weeks
, “Second virial coefficients and the forces between complex molecules
,” J. Chem. Phys.
10
, 201
–214
(1942
).147.
M. A.
Ricci
, M.
Nardone
, F. P.
Ricci
, C.
Andreani
, and A. K.
Soper
, “Microscopic structure of low temperature liquid ammonia: A neutron diffraction experiment
,” J. Chem. Phys.
102
, 7650
–7655
(1995
).148.
L.
Martínez
, R.
Andrade
, E. G.
Birgin
, and J. M.
Martínez
, “PACKMOL: A package for building initial configurations for molecular dynamics simulations
,” J. Comput. Chem.
30
, 2157
–2164
(2009
).149.
J.
Towns
, T.
Cockerill
, M.
Dahan
, I.
Foster
, K.
Gaither
, A.
Grimshaw
, V.
Hazlewood
, S.
Lathrop
, D.
Lifka
, G. D.
Peterson
, R.
Roskies
, J. R.
Scott
, and N.
Wilkins-Diehr
, “XSEDE: Accelerating scientific discovery
,” Comput. Sci. Eng.
16
, 62
–74
(2014
).© 2021 Author(s). Published under an exclusive license by AIP Publishing.
2021
Author(s)
You do not currently have access to this content.
