(Version 0.7 - May 23, 2022)
MBX is a C++ library that provides an interface for MD drivers, such as the i-PI wrapper and LAMMPS, to perform classical and path-integral molecular dynamics simulations using our many-body potential energy functions. The current version of MBX includes our MB-pol many-body water potential (see references below) and our MB-nrg many-body potentials for neat CO2 and mixed CO2/H2O mixtures (see references below), and neat CH4 and mixed CH4/H2O mixtures (see references below). MBX also includes the TTM-nrg potentials for halide and alkali-metal ions in water (see references below). MBX is periodically updated with performance improvements and the addition of other many-body potentials.
MBX acts as a client that returns MB-pol and MB-nrg energies and forces while the actual molecular dynamics is controlled by the MD driver. In the case of i-PI, the communication between MBX and i-PI can be established in two ways: Internet and Unix domain sockets. Please refer to the i-PI manual for more details. For LAMMPS, the MBX interface is added through the combination of specific FIX and PAIR_STYLE commands. Please refer to the LAMMPS manual for more details.
You can download MBX from: https://github.com/paesanilab/MBX. The installation instructions are in the README file.
Please post questions on the MBX Google Group: https://groups.google.com/g/mbx-users.
We recommend using LAMMPS since it provides better performance with MBX. Since MBX is parallelized using both OpenMP and MPI, the specific combination of OMP threads and MPI tasks is sensitive to the system's size. MBX is under continued development and optimization. Please check this page for periodic updates.
Notes about the MB-pol many-body potential energy function for water
The development of MB-pol started with a detailed analysis of the two- and three-body water interactions evaluated at the CCSD(T) level to quantitatively assess the accuracy of current force fields, DFT models, and ab initio based interaction potentials that are commonly used in molecular simulations . On the basis of this analysis and the results obtained with the HBB2-pol potential , the full-dimensional MB-pol potential was developed entirely from "first principles" building upon the many-body expansion of the interaction energy between water molecules [3-5].
MB-pol explicitly treats the one-body (intramolecular distortion energy) term and the short-ranged two- and three-body terms. MB-pol can thus be viewed as a classical polarizable potential supplemented by short-range two- and three-body terms that effectively represent quantum-mechanical interactions arising from the overlap of the monomer electron densities. Specifically, at all separations, the total MB-pol two-body term includes (damped) dispersion forces derived from ab initio computed asymptotic expansions of the dispersion energy along with electrostatic contributions due to the interactions between the molecular permanent and induced moments. At short-range, this two-body term is supplemented by a 4th-degree permutationally invariant polynomial that smoothly switches to zero as the oxygen-oxygen separation in the dimer approaches 6.5 Å. Similarly, the MB-pol three-body term includes a three-body polarization term at all separations, which is supplemented by a short-range 4th-degree permutationally invariant polynomial that effectively corrects for the deficiencies of a purely classical representation of the three-body interactions in regions where the electron densities of the three monomers overlap. This short-range three-body contribution is smoothly switched off once the oxygen-oxygen separation between any water molecule and the other two water molecules of a trimer reaches a value of 4.5 Å. In MB-pol, all induced interactions are described through many-body polarization. MB-pol thus contains many-body effects at all monomer separations as well as at all orders, in an explicit way up to the third order and in a mean-field fashion at all higher orders.
Without containing any empirical parameters, MB-pol accurately describes the properties of gas-phase clusters, including the dimer vibration-rotation tunneling spectrum , the second and third virial coefficients [3-4], cluster structures and energies . Simulations carried out with path-integral molecular dynamics (PIMD) and centroid molecular dynamics (CMD) demonstrate that MB-pol provides a highly accurate description of the liquid water at ambient conditions in comparison with experiments for several structural, thermodynamic, and dynamical properties .
Molecular dynamics (MD) simulations carried out with MB-pol in combination with many-body representations of the dipole moment and polarizability predict infrared (IR) and Raman spectra of liquid water [6-7] as well as the vibrational sum-frequency generation spectrum of the air/water interface [8-9] in excellent agreement with the experimental results. MD simulations with MB-pol were used to characterize electrostatic, intramolecular and intermolecular couplings in the vibrational spectra of liquid water [10-11].
MB-pol was also used to characterize the isomeric quantum equilibria of water clusters , the vapor/liquid equilibrium , the structure and thermodynamic response functions of supercooled water , and the energetics and vibrational spectra of several ice phases [15-17]. Combined with electronic structure calculations carried out using many-body perturbation theory, MB-pol enabled theoretical calculations of the electron affinity of bulk and interfacial water  as well as the modeling of the X-ray absorption  and emission  spectra of liquid water.
Through systematic comparisons with CCSD(T) reference data, MB-pol was used to characterize the role played by individual many-body effects in determining the properties of water from the gas to the condensed phase [21-22]. Extensive comparisons with CCSD(T) and quantum Monte Carlo reference data as well as experimental data for water across all phases demonstrated that MB-pol achieves higher accuracy than existing water models based on either molecular mechanics or density functional theory, which are commonly used in ab initio molecular dynamics simulations of water [23-24].
Although MB-pol was originally developed using permutationally invariant polynomials, it was demonstrated that identical accuracy is obtained when the individual low-order terms of the many-body expansion of the energy are represented using neural networks or Gaussian approximation potentials .
MB-pol was also used in simulations to determine the smallest possible ice crystals , the mechanisms of ice formation at the interface of antifreeze proteins , the structure and dynamics of water at the interface of organic monolayers [28-29], the mechanisms of water adsorption in metal-organic frameworks for applications in water harvesting from air [30-32].
Notes about the MB-nrg many-body potential energy functions of generic molecules
Building upon the demonstrated accuracy of MB-pol for water, we developed an integrated theoretical and computational framework, MB-nrg, for data-driven many-body potential energy functions for atomic ions [33-34], and molecular fluids [35-36].
The MB-nrg potentials representing the interactions between halide and alkali metal ions with water have been shown to achieve higher accuracy than both polarizable force fields and DFT models [33-34, 36-38]. When employed in computer simulations, the MB-nrg models have enabled the identification of both tunneling pathways and splittings in halide-water dimers  and halide-dihydrate complexes [40-41], the characterization of isomeric equilibria and vibrational spectra of small ion-water complexes [42-43], and accurate modeling of the hydration structure and EXAFS spectra of ions in solution [44-45]. Similarly, the MB-nrg potentials for small molecules have been shown to accurately reproduce CCSD(T) reference energies as well as structural and thermodynamic properties of molecular fluids, such as neat CO2 and CH4, and binary CO2/H2O [35,46] and CH4/H2O [36,47] mixtures.
Also available in MBX, are the TTM-nrg potentials for halide  and alkali-metal  ions in water. The TTM-nrg potentials use MB-pol to describe water-water interactions, while ion-water interactions are described by polarizable models.
We have recently introduced MB-Fit, an integrated software infrastructure that enables the automated development of fully transferable, data-driven many-body potentials for generic molecules within both MB-nrg and TTM-nrg theoretical/computational frameworks .
1) G.R. Medders, V. Babin, F. Paesani, A critical assessment of two-body and three-body interactions in water, J.
Chem. Theory Comput. 9, 1103 (2013).
2) V. Babin, G.R. Medders, F. Paesani, Toward a universal water model: First principles simulations from the dimer
to the liquid phase, J. Phys. Chem. Lett. 3, 3765 (2012).
3) V. Babin, C. Leforestier, 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,
4) V. Babin, G.R. Medders, 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
5) G.R. Medders, V. Babin, F. Paesani, Development of a “first principles" water potential with flexible monomers.
III: Liquid phase properties, J. Chem. Theory Comput. 10, 2906 (2014).
6) G.R. Medders, F. Paesani, Infrared and Raman spectroscopy of liquid water through “first principles" many-body
molecular dynamics, J. Chem. Theory Comput. 11, 1145 (2015).
7) S.K. Reddy, D.R. Moberg, S.C. Straight, 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).
8) G.R. Medders, 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 (2016).
9) D.R. Moberg, S.C. Straight, F. Paesani, Temperature dependence of the air/water interface revealed by
polarization sensitive sum-frequency generation spectroscopy, J. Phys. Chem. B 122, 4356 (2018).
10) S.C. Straight, F. Paesani, Exploring electrostatic effects on the hydrogen bond network of liquid water through
many-body molecular dynamics, J. Phys. Chem. B 120, 8539 (2016).
11) K.M. Hunter, F.A. Shakib, F. Paesani, Disentangling coupling effects in the infrared spectra of liquid water,
J. Phys. Chem. B 122, 10754 (2018).
12) S.E. Brown, A.W. Götz, X. Cheng, R.P. Steele, V.A. Mandelshtam, F. Paesani, Monitoring water clusters “melt”
through vibrational spectroscopy, J. Am. Chem. Soc. 139, 7082 (2017).
13) M.C. Muniz, T.E. Gartner III, M. Riera, C. Knight, S. Yue, F. Paesani, A.Z. Panagiotopoulos, Vapor-liquid
equilibrium of water with the MB-pol many-body potential, J. Chem. Phys. 154, 211103 (2021).
14) T.E. Gartner III, K.M. Hunter, E. Lambros, A. Caruso, M. Riera, G.R. Medders, A.Z. Panagiotopoulos,
P.G. Debenedetti, F. Paesani, Anomalies and local structure of liquid water from boiling to the supercooled
regime as predicted by the many-body MB-pol model, J. Phys. Chem. Lett. 13, 3652 (2022).
15) C.H. Pham, S.K. Reddy, K. Chen, C. Knight, F. Paesani, Many-body interactions in ice, J. Chem. Theory Comput.
13, 1778 (2017).
16) D.R. Moberg, S.C. Straight, C. Knight, F, Paesani, Molecular origin of the vibrational structure of ice Ih, J. Phys.
Chem. Lett. 81, 2579 (2017).
17) D.R. Moberg, P.J. Sharp, F. Paesani, Molecular-level interpretation of vibrational spectra of ordered ice phases,
J. Phys. Chem. B 122, 10572 (2018).
18) A.P. Gaiduk, T.A. Pham, M. Govoni, F. Paesani, G. Galli, Electron affinity of liquid water, Nat. Commun. 9, 247
19) Z. Sun, L. Zheng, M. Chen, M.L. Klein, F. Paesani, 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).
20) V.W.D. Cruzeiro, A.P. Wildman, X. Li, F. Paesani, On the relationship between hydrogen-bonding motifs and the
1b1 splitting in the X-ray emission spectrum of liquid water, J. Phys. Chem. Lett. 12, 3996 (2021).
21) G.R. Medders, A.W. Götz, M.A. Morales, F. Paesani, On the representation of many-body interactions in
water, J. Chem. Phys. 143, 104102 (2015).
22) M. Riera, E. Lambros, T.T. Nguyen, A.W. Goetz, F. Paesani, Low-order many-body interactions determine the local
structure of liquid water, Chem. Sci. 10, 8211 (2019).
23) S.K. Reddy, S.C. Straight, P. Bajaj, C.H. Pham, M. Riera, D.R. Moberg, M.A. Morales, C. Knight, A.W. Götz,
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).
24) 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 (2016).
25) T.T. Nguyen, E. Székely, G. Imbalzano, J. Behler, G. Csányi, M. Ceriotti, A.W. Götz, F. Paesani, Comparison of
permutationally invariant polynomials, neural networks, and Gaussian approximation potentials in representing
water interactions through many-body expansions, J. Chem. Phys. 148, 241725 (2018).
26) D.R. Moberg, D. Becker, C.W. Dierking, F. Zurheide, B. Bandow, U. Buck, A. Hudait, V. Molinero, F. Paesani,
T. Zeuch, The end of ice I, Proc. Natl. Acad. Sci. U.S.A. 116, 24413 (2019).
27) A. Hudait, D.R. Moberg, Y. Qiu, N. Odendahl, F. Paesani, V. Molinero, Preordering of water is not needed for ice
recognition by hyperactive antifreeze proteins, Proc. Natl. Acad. Sci. U.S.A. 115, 8266 (2018).
28) S.K Reddy, R. Thiraux, B.A. Wellen Rudd, L. Lin, T. Adel, T. Joutsuka, F.M. Geiger, H.C. Allen, A. Morita,
F. Paesani, Bulk contributions modulate the sum-frequency generation spectra of water on model sea-spray
aerosols, Chem 4, 1629 (2018).
29) D.R. Moberg, Q. Li, S.K. Reddy, F. Paesani, Water structure at the interface of alcohol monolayers as determined
by molecular dynamics simulations and computational vibrational sum-frequency generation spectroscopy,
J. Chem. Phys. 150, 034701 (2019).
30) A.J. Rieth, K.M. Hunter, M. Dincă, F. Paesani, Hydrogen bonding structure of confined water templated by a
metal-organic framework with open metal sites, Nat. Commun. 10, 4771 (2019).
31) K.M. Hunter, J.C. Wagner, M. Kalaj, S.M. Cohen, W. Xiong, F. Paesani, Simulation meets experiment: Unraveling
the properties of water in metal-organic frameworks through vibrational spectroscopy, J. Phys. Chem. C. 125,
32) J.C. Wagner, K.M. Hunter, F. Paesani, W. Xiong, Water capture mechanisms at zeolitic imidazolate framework
interfaces, J. Am. Chem. Soc. 143, 21189 (2021).
33) P. Bajaj, A.W. Götz, 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,
34) M. Riera, N. Mardirossian, P. Bajaj, A.W. Götz, 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).
35) M. Riera, E.P. Yeh, F. Paesani, Data-driven many-body models for molecular fluids: CO2/H2O mixtures as a case
study, J. Chem. Theory Comput. 16, 2246 (2020).
36) M. Riera, A. Hirales, R. Ghosh, F. Paesani, Data-driven many-body models with chemical accuracy for CH4/H2O
mixtures, J. Phys. Chem. B 124, 11207 (2020).
36) B.B. Bizzarro, C.K. Egan, F. Paesani, Nature of halide–water interactions: Insights from many-body
representations and density functional theory, J. Chem. Theory Comput. 15, 2983 (2019).
37) C.K. Egan, B.B. Bizzarro, M. Riera, F. Paesani, Nature of alkali ion–water interactions: Insights from many-body
representations and density functional theory, J. Chem. Theory Comput. 16, 3055 (2020).
38) F. Paesani, P. Bajaj, M. Riera, Chemical accuracy in modeling halide ion hydration from many-body
representations, Adv. Phys. X 4, 1631212 (2019).
39) P. Bajaj, X.-G. Wang, T. Carrington, Jr., 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).
40) P. Bajaj, J.O. Richardson, F. Paesani, Ion-mediated hydrogen-bond rearrangement through tunnelling in the
iodide–dihydrate complex, Nat. Chem. 11, 367 (2019).
41) P. Bajaj, D. Zhuang, F. Paesani, Specific ion effects on hydrogen-bond rearrangements in the halide–dihydrate
complexes, J. Phys. Chem. Lett. 10, 2823 (2019).
42) M. Riera, S.E. Brown, 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,
43) P. Bajaj, M. Riera, J.K. Lin, Y.E. Mendoza Montijo, J. Gazca, F. Paesani, Halide ion microhydration: Structure,
energetics, and spectroscopy of small halide–water clusters, J. Phys. Chem. A 123, 2843 (2019).
44) D. Zhuang, M. Riera, G.K. Schenter, J.L. Fulton, F. Paesani, Many-body effects determine the local hydration
structure of Cs+ in solution, J. Phys. Chem. Lett. 10, 406 (2019).
45) A. Caruso, F. Paesani, Data-driven many-body models enable a quantitative description of chloride hydration
from clusters to bulk, J. Chem. Phys. 155, 064502 (2021).
46) S. Yue, M. Riera, R. Ghosh, A.Z. Panagiotopoulos, F. Paesani, Transferability of data-driven many-body models
for CO2 simulations in the vapor and liquid phases, J. Chem. Phys. 156, 104503 (2022).
47) V. Naden Robinson, R. Ghosh, C.K. Egan, M. Riera, C. Knight, F. Paesani, A. Hassanali, The behavior of
methane-water mixtures under elevated pressures using many-body potentials, J. Chem. Phys. 156, 194504
48) D.J. Arismendi-Arrieta, M. Riera, P. Bajaj, R. Prosmiti, 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 (2016).
49) M. Riera, A.W. Götz, F. Paesani, 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 (2016).
50) E.F. Bull-Vulpe, M. Riera, A.W. Götz, F. Paesani, MB-Fit: Software infrastructure for data-driven many-body
potential energy functions, J. Chem. Phys. 155, 124801 (2021).
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