%0 DATA
%A Steven L., Mielke
%A Donald G., Truhlar
%D 2009
%T Improved Methods for Feynman Path Integral Calculations of Vibrational−Rotational Free Energies and Application to Isotopic Fractionation of Hydrated Chloride Ions
%U https://acs.figshare.com/articles/Improved_Methods_for_Feynman_Path_Integral_Calculations_of_Vibrational_Rotational_Free_Energies_and_Application_to_Isotopic_Fractionation_of_Hydrated_Chloride_Ions/2862073
%R 10.1021/jp900834u.s001
%2 https://ndownloader.figshare.com/files/4559899
%K HORR
%K Feynman Path Integral Calculations
%K sequential sectioning scheme
%K Feynman path integrals
%K equilibrium constants
%K H 2O reaction
%K HDO
%K Keq
%K ion cyclotron resonance experiments
%K multireference configuration interaction calculations
%K H 2O D 2O
%K Hydrated Chloride IonsWe
%K Cl
%K vibrational perturbation theory
%X 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 H_{2}O, D_{2}O, and HDO. Ion cyclotron resonance experiments indicate that the equilibrium constant, *K*_{eq}, for the reaction Cl(H_{2}O)^{−} + D_{2}O ⇌ Cl(D_{2}O)^{−} + H_{2}O is 0.76, whereas the three theoretical predictions are 0.946, 0.979, and 1.20. Similarly, the experimental *K*_{eq} for the Cl(H_{2}O)^{−} + HDO ⇌ Cl(HDO)^{−} + H_{2}O reaction is 0.64 as compared to theoretical values of 0.972, 0.998, and 1.10. Although Cl(H_{2}O)^{−} has a large degree of anharmonicity, *K*_{eq} 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.