Potential of mean force along the system/reaction coordinate of the system-bath model in Eq. (3.1) (solid line). Also plotted is the polynomial fit to the numerical data [Eq. (4.9); dashed line] and a cut at R = 2.7 Å through the gas-phase potential of the donor-proton-acceptor complex V C (r, R) [Eq. (3.11); dotted line].
Spectral density of the Azzouz-Borgis model calculated at r = 1.34 Å as described in Sec. III.
Classical flux correlation functions for the Azzouz-Borgis proton transfer system. Solid line: original model. Dotted line: mapped system-bath model. Shown is the modified classical flux correlation function as calculated by Eq. (2.10), i.e., . For the system-bath model, agrees with the commonly used form . In each case, the short-time limit gives the classical transition-state theory rate constant and the long-time limit gives the full thermal rate constant.
Quantum flux correlation function for the system-bath mapping of the Azzouz-Borgis model, as calculated by the ML-MCTDH approach described in Sec. II. Shown is the modified flux correlation function as calculated by Eq. (2.9), i.e., .
Classical rate constants for the Azzouz-Borgis model.
Values of some important ML-MCTDH convergence parameters.
Results of previous approximate quantum-mechanical calculations of the proton-transfer rate constant of the Azzouz-Borgis model. Adapted from Refs. 18. Units are 1010 s−1.
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