The development of a "first principles" water potential with flexible monomers (MB-pol) for molecular simulations of water systems from gas to condensed phases is described. MB-pol is built upon the many-body expansion of the intermolecular interactions, and the specific focus of this study is on the two-body term (V2B) representing the full-dimensional intermolecular part of the water dimer potential energy surface. V2B is constructed by fitting 40,000 dimer energies calculated at the CCSD(T)/CBS level of theory and imposing the correct asymptotic behavior at long-range as predicted from "first principles". The comparison of the calculated vibration-rotation tunneling (VRT) spectrum and second virial coefficient with the corresponding experimental results demonstrates the accuracy of the MB-pol dimer potential energy surface.

A full-dimensional potential energy function (MB-pol) for simulations of water from the dimer to bulk phases is developed entirely from "first principles" by building upon the many-body expansion of the interaction energy. Specifically, the MB-pol potential is constructed by combining a highly accurate dimer potential energy surface [J. Chem. Theory Comput. 2013, 9, 5395] with explicit three-body and many-body polarization terms. The three-body contribution, expressed as a combination of permutationally invariant polynomials and classical polarizability, is derived from a fit to more than 12000 three-body energies calculated at the CCSD(T)/aug-cc-pVTZ level of theory, imposing the correct asymptotic behavior as predicted from "first principles". Here, the accuracy of MB-pol is demonstrated through comparison of the calculated third virial coefficient with the corresponding experimental data as well as through analysis of the relative energy differences of small clusters.

The MB-pol full-dimensional water potential introduced in the first two papers of this series [J. Chem. Theory Comput. 2013, 9, 5395 and J. Chem. Theory Comput. 2014, 10, 1599] is employed here in classical and quantum simulations of liquid water under ambient conditions. Comparisons with the available experimental data for several structural, thermodynamic, and dynamical properties indicate that MB-pol provides a highly accurate description of the liquid phase. Combined with previous analyses of the dimer vibration-rotation tunneling spectrum, second and third virial coefficients, and cluster structures and energies, the present results demonstrate that MB-pol represents a major step toward the long-sought "universal model" capable of describing the properties of water from the gas to the condensed phases.

We present an Adaptively Biased Molecular Dynamics (ABMD) method for the computation of the free energy surface of a reaction coordinate using non-equilibrium dynamics. The ABMD method belongs to the general category of umbrella sampling methods with an evolving biasing potential, and is inspired by the metadynamics method. The ABMD method has several useful features, including a small number of control parameters, and an O(t) numerical cost with molecular dynamics time t. The ABMD method naturally allows for extensions based on multiple walkers and replica exchange, where different replicas can have different temperatures and/or collective variables. This is beneficial not only in terms of the speed and accuracy of a calculation, but also in terms of the amount of useful information that may be obtained from a given simulation. The workings of the ABMD method are illustrated via a study of the folding of the Ace-GGPGGG-Nme peptide in a gaseous and solvated environment.

A full-dimensional model of water, HBB2-pol, derived entirely from "first-principles", is introduced and employed in computer simulations ranging from the dimer to the liquid. HBB2-pol provides excellent agreement with the measured second and third virial coefficients and, by construction, reproduces the dimer vibration-rotation-tunneling spectrum. The model also predicts the relative energy differences between isomers of small water clusters within the accuracy of highly correlated electronic structure methods. Importantly, when combined with simulation methods that explicitly include zero-point energy and quantum thermal motion, HBB2-pol accurately describes both structural and dynamical properties of the liquid phase.