Water properties from first principles: Simulations by a general-purpose quantum mechanical polarizable force field
A. G. Donchev, N. G. Galkin, A. A. Illarionov, O. V. Khoruzhii, M. A. Olevanov, V. D. Ozrin, M. V. Subbotin, and V. I. Tarasov *
Algodign, LLC, Bolshaya Sadovaya 8-1, Moscow 123001, Russia
Communicated by Michael Levitt, Stanford University School of Medicine, Stanford, CA, April 14, 2006;
Author contributions: A.G.D., O.V.K., and V.I.T. designed research; A.G.D., N.G.G., A.A.I., O.V.K., M.A.O., V.D.O., M.V.S., and V.I.T. performed research; A.G.D., N.G.G., A.A.I., O.V.K., M.A.O., V.D.O., and V.I.T. contributed new reagents/analytic tools; A.G.D., N.G.G., O.V.K., M.A.O., V.D.O., and V.I.T. analyzed data; and A.G.D., O.V.K., and V.I.T. wrote the paper.
Received February 20, 2006.
We have recently introduced a quantum mechanical polarizable force field (QMPFF) fitted solely to high-level quantum mechanical data for simulations of biomolecular systems. Here, we present an improved form of the force field, QMPFF2, and apply it to simulations of liquid water. The results of the simulations show excellent agreement with a variety of experimental thermodynamic and structural data, as good or better than that provided by specialized water potentials. In particular, QMPFF2 is the only ab initio force field to accurately reproduce the anomalous temperature dependence of water density to our knowledge. The ability of the same force field to successfully simulate the properties of both organic molecules and water suggests it will be useful for simulations of proteins and protein–ligand interactions in the aqueous environment.
Proc Natl Acad Sci U S A. 2006 June 6; 103(23): 8613–8617.
General-purpose force fields, from Levitt’s early protein potential (1) to modern models such as charmm, opls-aa, mmff, and amber (2–5), which approximate molecular potentials by simple analytical formulas, are in wide use for computational studies of biological systems ranging from the simplest molecular clusters to large complexes involving proteins. In the latter case, the investigations encounter serious computational problems, primarily related to proper conformational sampling and adequate treatment of the long-range intermolecular interactions; however, with advancements in simulation methodologies and the increase in computer speed these difficulties are alleviated so the accuracy of the underlying models becomes the dominant factor.
Protein and protein–ligand interactions usually take place in an aqueous environment, which contributes critically to their energetics, e.g., by hydrogen bonding and the hydrophobic effect. Hence, a force field should accurately reproduce the properties of both organic compounds and water if it is to be used for precise calculations of protein–ligand binding, as required for example in drug-design applications. Moreover, the quality of the applications of a force field to water can be considered as a criterion for the accuracy of the approach as a whole. Hence, it is disconcerting that no general-purpose force field has previously succeeded in accurately describing key properties of liquid water.
On the other hand, impressive progress has been made in theoretical studies using specialized water potentials. Many of these potentials are empirical, i.e., they have been fitted to experimental data on the thermodynamics and kinetics of liquid water and in some cases ice. The most advanced of these models, such as the pairwise additive tip5p (6) and polarizable (7–9) potentials, generally provide an accurate description of the most important properties of water and/or ice. However, no one model is yet able to reproduce in detail the diversity of thermodynamic and kinetic experimental data on both gas and condensed phases under a range of conditions. Moreover, these empirical water potentials cannot be transferred to more general molecular systems such as proteins because of the assumptions incorporated and the lack of data on which to calibrate them.
Given these limitations, it would seem preferable to perform simulations by using potentials fitted to high-quality ab initio quantum mechanical (QM) data. Such calculations are now possible because of major advances in methods and vast increases in computer speed. However, because of the complicated functional form of advanced ab initio potentials, their direct use for many-particle systems is very computationally intensive, impeding their applicability to liquid-phase simulations (10–13). Moreover, such studies have generally been performed by using classical molecular dynamics (MD) applied to the QM potentials; application of quantum statistics via the path integral MD (PIMD) technique is even more time-consuming and rare (14). Yet quantum effects in water are non-negligible because of the strong hydrogen-bond interactions that depend sensitively on the positions of H atoms. These positions, in turn, are sensitive to quantum zero-point vibrations caused by the relatively small H atom mass. Thus, quantum effects must be taken into account to obtain a proper assessment of the accuracy of the ab initio approach. By contrast, the empirical potentials, which use classical MD, implicitly include the quantum effects in their parameterization.
We had previously presented a general-purpose ab initio QM polarizable force field (QMPFF) (referred to here as QMPFF1), which is based on physically well grounded considerations of intermolecular interactions and is fitted to an extensive set of high-quality vacuum QM data on properties of simple molecules and their dimers. QMPFF1 accurately simulates the interactions in many organic complexes (15). In this article we present the results of classical and PIMD simulations of liquid water by using a second, more refined version of the force field, QMPFF2. The parameterization process used in QMPFF2 for the atom types and bonds that appear in a water molecule is exactly the same as that used for the types appearing in other molecules. Moreover, in QMPFF there is no separate water model as such because the parameters of the atom and bond types for water are fitted to QM data on interactions in both homodimers of water molecules and their heterodimers with other molecules.
Hence, the high accuracy of the water simulations described below represents crucial validation of the overall QMPFF concept and suggests that the same force field can be applied to both the simulation of biomolecular interactions occurring in water and the study of water itself.