Improved Methods for Feynman Path Integral Calculations of Vibrational−Rotational Free Energies and Application to Isotopic Fractionation of Hydrated Chloride Ions
MielkeSteven L.
TruhlarDonald G.
2009
We present two enhancements to our methods for calculating vibrational−rotational free energies by Feynman path integrals, namely, a sequential sectioning scheme for efficiently generating random free-particle paths and a stratified sampling scheme that uses the energy of the path centroids. These improved methods are used with three interaction potentials to calculate equilibrium constants for the fractionation behavior of Cl<sup>−</sup> hydration in the presence of a gas-phase mixture of H<sub>2</sub>O, D<sub>2</sub>O, and HDO. Ion cyclotron resonance experiments indicate that the equilibrium constant, <i>K</i><sub>eq</sub>, for the reaction Cl(H<sub>2</sub>O)<sup>−</sup> + D<sub>2</sub>O ⇌ Cl(D<sub>2</sub>O)<sup>−</sup> + H<sub>2</sub>O is 0.76, whereas the three theoretical predictions are 0.946, 0.979, and 1.20. Similarly, the experimental <i>K</i><sub>eq</sub> for the Cl(H<sub>2</sub>O)<sup>−</sup> + HDO ⇌ Cl(HDO)<sup>−</sup> + H<sub>2</sub>O reaction is 0.64 as compared to theoretical values of 0.972, 0.998, and 1.10. Although Cl(H<sub>2</sub>O)<sup>−</sup> has a large degree of anharmonicity, <i>K</i><sub>eq</sub> values calculated with the harmonic oscillator rigid rotator (HORR) approximation agree with the accurate treatment to within better than 2% in all cases. Results of a variety of electronic structure calculations, including coupled cluster and multireference configuration interaction calculations, with either the HORR approximation or with anharmonicity estimated via second-order vibrational perturbation theory, all agree well with the equilibrium constants obtained from the analytical surfaces.