4 bigger the discrepancy also increases suggesting that ori- entational ordering of water molecules around the atoms is playing an important role and a density-only descrip- tion is not enough. Exp. (eV) V kT (eV) V min (eV) Helium 0 . 12 0 . 12 0 . 09 Neon 0 . 12 0 . 11 0 . 07 Argon 0 . 09 0 . 22 0 . 17 Krypton 0 . 07 0 . 25 0 . 18 3 4 5 R (Angstrom) -10 0 10 20 30 40 Interaction Energy (meV) Ar-water data Thermal average Minimum Energy TABLE II: Solvation energies of inert gas atoms FIG. 3: Interaction of Argon and a water molecule. Each diamond correspond to a specific orientation. Also presented are the Boltzmann average potential (solid line) and the min- imum potential (dot-dashed line). CONCLUSIONS AND FUTURE DIRECTIONS This work presents a simple density-functional theory for water which gives reasonable overall agreement with molecular dynamics simulation data for the solvation of hard spheres in water, with quite good agreement for smaller spheres (radius less than 2.5 ˚ A). However, as we move to look at simple solutes, such as inert gasses, we find mixed results. While we are able to reproduce the counter-intuitive trend of decreasing energy with increas- ing size in the inert gas sequence when going from He to Ne, we fail to do so for the larger atoms. Thus, although solvation of hard spheres, whose interaction with water molecules is generally taken to involve only the location of the oxygen nucleus and thus contains no orientation dependence, may be well described by density-only the- ories, such theories do not necessarily describe well the solvation of even simple solutes such as inert gases. It thus appears that treatment of orientation in some form is needed to attain results approaching chemical accu- racy for realistic solutes. This work was funded by NSF GRANT #CHE–0113670. We determined the potential energy of interaction be- tween a water molecule and an atom of each of the in- ert gasses in Table II directly through ab initio density- functional theory calculations within the generalized gra- dient approximation (GGA) [23]. For these calculations we take ⃗ r to be the displacement between the nucleus of the inert gas and the nucleus of the oxygen atom and con- sidered one hundred different orientations for the water molecule, with these orientations optimized to sample the angular dependence evenly according to the procedure of Womersley and Sloan[24]. Figure 3 summarizes the re- sults for argon, which was typical of all of the inert gasses considered in this work. The scatter in the interaction energy at each distance r shows a strong dependence on the orientation of the wa- ter molecule, particularly at closer distances. The ques- tion then immediately arises of how to couple to any con- tinuum theory based solely on the molecular density N ( r ) with no information about the orientations of the solute. As the coupling in such density-only functional theories takes the form ∫ V ( ⃗ r ) n ( ⃗ r ) d⃗ r , a choice must be make to to define a unique value for the potential V ( ⃗ r ) for each point ⃗ r . One approach would be to assume that each water molecule independently assumes its most favored orientation for a given distance, thereby defining V ( r ) as the minimum energy envelop ( V$_{min}$ ) of the data in Fig- ure 3. Another approach would be to take the thermal average interaction under the assumption that the water molecules choose their orientations independently of each other, thereby defining V ( r ) as the Boltzmann weighted average ( V$_{kT}$ ) of the data at each distance. Table II summarizes the results of the minimum free energy of our functional for both of these approaches. For helium and neon experimental and theoretical results agree quite well. Also the difference between using V$_{min}$ and V$_{kT}$ is less than 0 . 04 eV . As the size of atoms gets [10] S. X. Sun, Phys. Rev. E 64 , 021512 (2001). [9] B. Roux and T. Simonson, Bioph. Chem. 78 , 1 (1999). [8] J. Tomasi and M. Persico, Chem. Rev. 94 , 2027 (1994). [7] W. Curtin and N. W. Ashcroft, Phys. Rev. A 32 , 2909 (1985). [6] E. A. Carter, G. Ciccotti, J. T. Hynes, and R. Kapral, Chem. Phys. Lett. 156 , 472 (1989). [5] G. M. Torrie and J. Valleau, J. Comput. Phys. 23 , 187 (1977). [4] P. Kollman, Chem. Rev. 93 , 2395 (1993). [3] W. Jorgensen, J.Chandrasekhar, J. Madura, R. Impey, and M. Klein, J. Chem. Phys. 79 , 926 (1983). [2] H. J. C. Berendsen, J. P. M. Postma, W. F. van Gun- steren, and J. Hermans, Intermolecular Forces (Reidel, Dordrecht, 1981). [1] J. P. Hansen and I. R. McDonald, Theory of Simple Liq- uids (Academic Press, 1989).