An overview is provided on the development and status of potential energy functions that are used in atomic-level statistical mechanics and molecular dynamics simulations of water and of organic and biomolecular systems. Some topics that are considered are the form of force fields, their parameterization and performance, simulations of organic liquids, computation of free energies of hydration, universal extension for organic molecules, and choice of atomic charges. The discussion of water models covers some history, performance issues, and special topics such as nuclear quantum effects.T he last 30 years have witnessed remarkable progress in condensed-phase theory. Before that time, atomic-level computer simulations of fluids were largely restricted to atomic and diatomic systems. The first simulation of liquid water was not reported until 1969 and was a Monte Carlo (MC) effort (1), which was followed by the molecular dynamics (MD) studies of Rahman and Stillinger (2, 3) in the early 1970s. The state-of-the-art simulations of water in 1974 were performed for 216 molecules for Ͻ10 ps (3). Even by 1990, there had been almost no MD simulations for a protein in aqueous solution covering 100 ps (4), whereas today MD simulations for a protein with Ϸ10,000 water molecules for many nanoseconds or mixed quantum and molecular mechanics (QM͞ MM) simulations for an enzymatic reaction are not problematic. Of course, performing longer simulations for larger systems does not guarantee the production of useful results. Key underlying issues for accuracy are adequate configurational sampling and the quality of the description of the intramolecular and intermolecular energetics. Progress on the former issue has been aided greatly by massive increases in computing power, although the substantial technical developments in the latter area are the focus of this overview. The topic also has received attention in comprehensive, recent reviews for the treatment of water (5) and biomolecular systems (6-10) that go far beyond the present page limitations. So, the presentation here will be more condensed with a focus on force-field development, water, and aqueous solutions and with some emphasis on our personal experiences and viewpoint.
Force FieldsA force field consists of classical potential energy expressions and the associated adjustable parameters. The large majority of condensed-phase simulations have invoked pairwise additivity such that the total potential energy for a collection of molecules and͞or ions (components) with coordinates X ជ is given by the sum of the intermolecular interaction energies between all components plus the sum of the intramolecular energies of the components (Eq. 1).The intramolecular potential energy is typically represented by harmonic terms for bond stretching and angle bending, a Fourier series for each torsional angle, and Coulomb and Lennard-Jones interactions between atoms separated by three or more bonds (Eqs. 2-5). The latter ''nonbonded'' interactions also are evaluated between intermolecular at...