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clear yet whether the artifact can be fully fixed in nonspherical systems, although it seems likely.

There are other inherent limitations to the finite boundary method. Due to the finite size of the system, water molecules cannot undergo natural unrestricted diffusion, and examination of water dynamics must be restricted to interior positions. Other transport properties may be affected as well by the size constraint. Existing boundary potentials cannot fully prevent artifactual structure and dynamics of the water near the vacuum/ solvent interface, and thus the layer of solvent must be large enough to allow sufficient bulklike solvent about the solute molecule, reducing the cost advantage over periodic boundary conditions. However, these potentials will probably continue to improve, leading to more accurate simulations with minimal solvation.

Periodic boundary conditions have long been a popular choice for simulations using explicit solvent. Using such a simulation, the density and pressure of the system can be easily specified. Furthermore, since the energy of the system is periodic, there are no preferred positions within the simulation cell. Regardless of position within the central cell, an atom is surrounded on all sides by atoms or their images. Unlike finite boundary conditions, there is no vacuum interface to be ‘‘fixed’’ via boundary potentials. Thus it is believed that periodic boundary conditions best model the environment of bulk matter, at least when long-range electrostatics are not involved.

Wood and Parker [50] discuss the possible artifacts due to periodic boundary conditions, in the context of short-range interactions. They suggest the still sensible approach of varying the unit cell size and shape to empirically test for the size of artifacts in finite systems. The implicit assumption is that these artifacts should vanish in the limit of large unit cell sizes. These early simulations established that artifacts due to periodicity in typical simulations (e.g., no phase transitions occurring) are negligible for systems that have only short-range interactions. When electrostatic interactions are involved, there are finite size periodicity artifacts, and the assumption that these artifacts vanish in the limit of large unit cell sizes is not immediately evident, due to the subtleties of conditional convergence discussed above. However, it seems clear from recent work [9,51] that the correct limiting behavior is reached for large unit cell sizes, and thus the question becomes, At what rate do the artifacts vanish?

Smith and Pettitt [52] studied the free energy of rotation of a dipole in an ideal dielectric at various temperatures. They conclude that finite size artifacts are not large in high dielectric solvents such as water at room temperature. Problems may arise in low dielectric solvents. Similar conclusions about the effect of solvent dielectric were reached in studies of charging free energies by Hummer et al. [51]. In the case of simple point ions they were able to correct these artifacts. The consensus at this point is that finite size artifacts due to periodicity are manageable in simulations of molecules in water at room temperature. The artifacts may be much larger in simulations of charged or polar molecules in low dielectric solvents [49]. In any case the suggestion of Wood and Parker [50] that the results be examined as a function of unit cell size is still pertinent.

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