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

journal contribution

posted on 23.04.2009 by Steven L. Mielke, Donald G. Truhlar#### journal contribution

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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.