Improved Methods for Feynman Path Integral Calculations of Vibrational−Rotational Free Energies and Application to Isotopic Fractionation of Hydrated Chloride Ions

2009-04-23T00:00:00Z (GMT) by Steven L. Mielke Donald G. Truhlar
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 hydration in the presence of a gas-phase mixture of H2O, D2O, and HDO. Ion cyclotron resonance experiments indicate that the equilibrium constant, Keq, for the reaction Cl(H2O) + D2O ⇌ Cl(D2O) + H2O is 0.76, whereas the three theoretical predictions are 0.946, 0.979, and 1.20. Similarly, the experimental Keq for the Cl(H2O) + HDO ⇌ Cl(HDO) + H2O reaction is 0.64 as compared to theoretical values of 0.972, 0.998, and 1.10. Although Cl(H2O) has a large degree of anharmonicity, Keq 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.