High-Precision Quantum Thermochemistry on Nonquasiharmonic Potentials:  Converged Path-Integral Free Energies and a Systematically Convergent Family of Generalized Pitzer−Gwinn Approximations

Accurate quantum mechanical (QM) vibrational−rotational partition functions for HOOD, D<sub>2</sub>O<sub>2</sub>, H<sup>18</sup>OOH,\nH<sub>2</sub><sup>18</sup>O<sub>2</sub>, D<sup>18</sup>OOH, and H<sup>18</sup>OOD are determined using a realistic potential energy surface for temperatures\nranging from 300 to 2400 K by using the TT-FPI-ESPE path-integral Monte Carlo method. These data, together\nwith our prior results for H<sub>2</sub>O<sub>2</sub>, provide benchmarks for testing approximate methods of estimating isotope\neffects for systems with torsional motions. Harmonic approximations yield poor accuracy for these systems,\nand although the well-known Pitzer−Gwinn (PG) approximation provides better results for absolute partition\nfunctions, it yields the same results as the harmonic approximation for isotope effects because these are\nintrinsically quantal phenomena. We present QM generalizations of the PG approximation that can provide\nhigh accuracy for both isotope effects and absolute partition functions. These approximations can be\nsystematically improved until they approach the accurate result and converge rapidly. These methods can\nalso be used to obtain affordable estimates of zero-point energies from accurate partition functionseven\nthose at relatively high temperatures.