We use ab initio molecular dynamics as a basis for quasichemical theory evaluation of the free energy of water near conventional liquid thermodynamic states. The Perdew-Wang-91 (PW91), Perdew-Burke-Ernzerhof (PBE), and revised PBE (rPBE) functionals are employed. The oxygen radial density distribution using the rPBE functional is in reasonable agreement with current experiments, whereas the PW91 and PBE functionals predict a more structured oxygen radial density distribution. The diffusion coefficient with the rPBE functional is in reasonable accord with experiments. Using a maximum entropy procedure, we obtain $x_0$ from the coordination number distribution $x_n$ for oxygen atoms having n neighbors. Likewise, we obtain $p_0$ from $p_n,$ the probability of observing cavities of specified radius containing n water molecules. The probability $x_0$ is a measure of the local chemical interactions and is central to the quasichemical theory of solutions. The probability $p_0,$ central to the theory of liquids, is a measure of the free energy required to open cavities of defined sizes in the solvent. Using these values and a reasonable model for electrostatic and dispersion effects, the hydration free energy of water in water at 314 K is calculated to be $-5.1\mathrm{k}\mathrm{c}\mathrm{a}\mathrm{l}/\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}$ with the rPBE functional, in encouraging agreement with the experimental value of $-6.1\mathrm{k}\mathrm{c}\mathrm{a}\mathrm{l}/\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}.$

• Received 3 July 2003

DOI:https://doi.org/10.1103/PhysRevE.68.041505