MB-pol
© 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].
MB-pol(2023)
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.
References
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