Paesani Research Group

Laboratory for Theoretical and Computational Chemistry at UC San Diego  


© Paesani Research Group. All rights reserved.

The development of the MB-pol data-driven many-body potential energy function (PEF) [1-3] started with a detailed analysis of 2-body and 3-body interactions in water evaluated at the CCSD(T) level of theory, which allowed us to quantitatively assess the accuracy of current force fields, DFT models, and ab initio-based potentials commonly used in molecular simulations [4]. Based on the analyses of Ref. [4] and the results obtained with the HBB2-pol PEF [5], MB-pol was developed entirely fromm the many-body expansion of the interaction energy between water molecules calculated at the CCSD(T) level of theory [1-3].

MB-pol includes explicit representations of 1-body, 2-body and 3-body energies, which are integrated with a classical representation of many-body polarization. MB-pol can thus be viewed as an ab initio-based polarizable potential supplemented by explicit n-body terms that effectively represent quantum-mechanical interactions arising from the overlap of monomer's electron densities (e.g., Pauli repulsion, charge transfer, and charge penetration) [6]. Briefly, MB-pol represents the energy of a system containing N water molecules as

EN = V1B + V2B + V3B + Velec

The explicit 1-body term (V1B) is an analytical potential energy function representing the intramolecular distortion energy. The explicit 2-body (V2B) term is described by a 2-body term represented by a 4th-degree permutationally invariant polynomial that smoothly switches to zero as the oxygen-oxygen separation in the dimer approaches 6.5 Å, and a 2-body dispersion term derived from the asymptotic expansion of the dispersion energy. The explicit 3-body (V3B) term is described by a 3-body term represented by a 4th-degree permutationally invariant polynomial that is smoothly switched off when any of the water molecules moves more than 4.5 Å apart from the other two molecules. Finally, Velec describes permanent electrostatics and many-body polarization based on a modified Thole-type scheme. MB-pol thus represents all many-body effects at all monomer separations and at all orders, in an explicit way up to the 3-body term and in a mean-field fashion for all n-body terms with n>3. All specific details about the functional form adopted by MB-pol are reported in the original papers [1-2].

Without containing any empirical parameters, MB-pol accurately predicts the properties of water from the gas to the condensed phases [6]. In particular, MB-pol quantitatively reproduces the vibration-rotation tunneling spectrum of the water dimer [1], the energetics, quantum isomeric equilibria, tunneling splittings, and vibrational spectra of small water clusters [7-18], the structural, thermodynamic, and dynamical properties [19-20] as well as the infrared and Raman spectra of liquid water [21-24], the sum-frequency generation spectra of the air/water interface [25-28], the vapor-liquid equilibrium properties [29], and the energetics as well as the infrared and Raman spectra of various ice phases [30-34]. MB-pol is the first model that accurately reproduces the phase diagram of water over a wide range of temperature and pressure conditions [35]. 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 [36] as well as the modeling of the X-ray absorption [37] and emission [38] 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 [39]. 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 [39-43].

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 [44].


In 2023, we introduced MB-pol(2023) [45]. Compared to the original MB-pol PEF, MB-pol(2023) uses larger 2-body and 3-body training sets, adopts more sophisticated 2-body and 3-body permutationally invariant polynomials, and includes an explicit 4-body permutationally invariant polynomial. MB-pol(2023) achieves sub-chemical accuracy and provides remarkable agreement with the experimental results for various properties of liquid water, improving upon the original MB-pol PEF and effectively closing the gap with experimental measurements.

Using MB-pol with other force fields

MB-pol can also be used in combination with conventional force fields using standard Lorentz-Berthelot mixing rules. For these simulations, we recommend using the following Lennard-Jones parameters for the oxygen and hydrogen atoms of the MB-pol water molecules: σOO = 3.26393 Å, εOO = 0.26948 kcal/mol, σHH = 2.68354 Å,  εHH = 3.7 x 10-10 kcal/mol. Simulations carried out with MB-pol in combination with conventional force fields were used to characterize the mechanisms of ice formation at the interface of antifreeze proteins [46], the structure and dynamics of water at the interface of organic monolayers [47-48], the mechanisms of water adsorption in metal-organic frameworks for applications in water harvesting from air [49-52].

How to use MB-pol

MB-pol is available in MBX (version 1.0), an open-access many-body energy and force calculator for data-driven many-body simulations. MBX is interfaced to common simulation packages such as LAMMPS and i-PI. MBX can also be used as a standalone software and provides interfaces written in Fortran and Python that can be seamlessly used in combination with third-party software. MBX can be downloaded from our GitHub page. MB-pol(2023) will be available in the next release of MBX.


1)    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,


2)    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


3)    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).

4)    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).

5)    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).

6)   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).

7)   J.O. Richardson, C. Pérez, S. Lobsiger, A.A. Reid, B. Temelso, G.C. Shields, Z. Kisiel, D.J. Wales, B.H. Pate, S.C.

      Althorpe. Concerted hydrogen-bond breaking by quantum tunneling in the water hexamer prism, Science 351, 1310


8)   W.T. Cole, J.D. Farrell, D.J. Wales, R.J. Saykally, Structure and torsional dynamics of the water octamer from THz

      laser spectroscopy near 215 μm, Science 352, 1194 (2016).

9)   J.D. Mallory, 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).

10)  P.E. Videla, P.J. Rossky, D. Laria, Communication: Isotopic effects on tunneling motions in the water trimer, J. Chem.

       Phys. 144, 061101 (2016).

11)  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).

12)  C.L. Vaillant, M.T. Cvitaš, Rotation-tunneling spectrum of the water dimer from instanton theory, Phys. Chem. Chem.

       Phys. 20, 26809 (2018).

13)  C.L. Vaillant, D.J. Wales, S.C. Althorpe, Tunneling splittings from path-integral molecular dynamics using a Langevin

       thermostat, J. Chem. Phys. 148, 234102 (2018).

14)  M. Schmidt, 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).

15)  K.P. Bishop, 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).

16)  P.E. Videla, P.J. Rossky, D. Laria, Isotopic equilibria in aqueous clusters at low temperatures: Insights from the

       MB-pol many-body potential, J. Chem. Phys. 148, 084303 (2018).

17)  N.R. Samala, N. Agmon, Temperature dependence of intramolecular vibrational bands in small water clusters,

      J. Phys. Chem. B 123, 9428 (2019).

18)  M.T. Cvitaš, J.O. Richardson, Quantum tunnelling pathways of the water pentamer, Phys. Chem. Chem. Phys. 22,

       1035 (2020).

19)  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).

20)  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).

21)  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).

22)  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).

23)  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).

24)  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).

25)  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).  

26)  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).

27)  S. Sun, F. Tang, S. Imoto, D.R. Moberg, T. Ohto, F. Paesani, M. Bonn, E.H, Backus, Y. Nagata, Orientational

       distribution of free OH groups of interfacial water is exponential, Phys. Rev. Lett. 121, 246101 (2018).

28)  S. Sengupta, D.R. Moberg, F. Paesani, E. Tyrode, Neat water-vapor interface: Proton continuum and the nonresonant

       background, J. Phys. Chem. Lett. 9, 6744 (2018).

29)  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).

30)  C.H. Pham, S.K. Reddy, K. Chen, C. Knight, F. Paesani, Many-body interactions in ice, J. Chem. Theory Comput.

       13, 1778 (2017).

31)  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).

32)  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).

33)  D.R. Moberg, D. Becker, C.W. Dierking, F. Zurheide, B. Bandow, U. Buck, A. Hudait, V. Molinero, F. Paesani, T. Zeuch,

       End of Ice I, Proc. Natl. Acad. Sci. U.S.A. 116, 24413 (2019).

34)  S. Rasti, E.Ö. Jónsson, H. Jónsson, J. Meyer, New insights into the volume isotope effect of ice Ih from polarizable

       many-body potentials, J. Phys. Chem. Lett. 13, 11831 (2022).

35)  S.L. Bore, F. Paesani, Realistic phase diagram of water from “first principles” data-driven quantum simulations, Nat.

       Commmun. 14, 3349 (2023).

36)  A.P. Gaiduk, T.A. Pham, M. Govoni, F. Paesani, G. Galli, Electron affinity of liquid water, Nat. Commun. 9, 247


37)  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).

38)  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).

39)  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).

40) G.A. Cisneros, K.T. Wikfeldt, L. Ojamäe, J. Lu, Y. Xu, H. Torabifard, A.P. Bartók, G. Csányi, V. Molinero, F. Paesani,

      Modeling molecular interactions in water: From pairwise to many-body potential energy functions, Chem. Rev. 116,

      7501 (2016).

41) E. Lambros, F. Paesani, How good are polarizable and flexible models for water: Insights from a many-body

      perspective, J. Chem. Phys. 153, 060901 (2020).

42)  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).

43)  E. Palos, E. Lambros, S. Swee, J. Hu, S. Dasgupta, F. Paesani, Assessing the interplay between functional-driven

       and density-driven errors in DFT models of water, J. Chem. Theory Comput. 18, 3410 (2022).

44)  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).

45)  X. Zhu, M. Riera, E.F. Bull-Vulpe, F. Paesani, MB-pol(2023): Sub-chemical accuracy for water simulations from the

       gas to the liquid phase, J. Chem. Theory Comput. ASAP (2023).

46)  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).

47)  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).

48)  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).

49)  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).

50)  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,

       12451 (2021).

51)  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).

52)  C.-H. Ho, M.L. Valentine, Z. Chen, H. Xie, O.K. Farha, W. Xiong, F. Paesani, Structure and thermodynamics of

       water adsorption in NU-1500-Cr, Commun. Chem. 6, 70 (2023).