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

Abstract

An exponent of 3/2 was omitted from the last factor on the right-hand side of eq 4 and the first factor on the right-hand side of eq 20. The corrected equations are and The results and discussion were not affected by these errors.

Ab Initio Calculations of Thermochemical Properties of Methanol Clusters

“…The state-of-the-art way is to replace the harmonic oscillator contributions of such motions by those of uncoupled 1D hindered rotations (HR). 36−38 The reason for the uncoupled 1D treatment is 2-fold: (1) a fulldimensional treatment is not practical for all but the smallest molecules 40,41 and (2) the 1D approach has proven accurate for some special cases (n-alkanes, alcohols, thiols, ethers, and thioethers) by comparison to the coupled 2D case. 42,43 The largest rigorously tested system is the hydrogen peroxide monomer, 41 which is a demanding test case and probably gives an upper bound for the error of decoupling one HR from all other anharmonic modes.…”

“…This leads to improved vibrational frequencies for relatively rigid molecules, but turned out to be inadequate for the large amplitude motions of intermolecular complexes in some preliminary calculations in the present work. The state-of-the-art way is to replace the harmonic oscillator contributions of such motions by those of uncoupled 1D hindered rotations (HR). − The reason for the uncoupled 1D treatment is 2-fold: (1) a full-dimensional treatment is not practical for all but the smallest molecules , and (2) the 1D approach has proven accurate for some special cases ( n -alkanes, alcohols, thiols, ethers, and thioethers) by comparison to the coupled 2D case. , The largest rigorously tested system is the hydrogen peroxide monomer, which is a demanding test case and probably gives an upper bound for the error of decoupling one HR from all other anharmonic modes. The error in the partition function when using an exact 1D treatment decoupled from all other motions compared to the exact full dimensional case is 24% (averaged from 200 to 5000 K), corresponding to about 0.5 kJ/mol at ambient temperature.…”

Position-Specific and Clumped Stable Isotope Studies: Comparison of the Urey and Path-Integral Approaches for Carbon Dioxide, Nitrous Oxide, Methane, and Propane

“…The Feynman path-integral (PI) formulation of quantum statistical mechanics provides a useful framework for calculating equilibrium isotope effects. By exploiting the mathematical isomorphism between the quantum Boltzmann statistics of a given system and the classical Boltzmann statistics of its ring-polymer representation, − PI methods have been applied to study equilibrium isotope effects, particularly for hydrogen-containing molecules, in both gas-phase − and condensed-phase − systems.…”

Anharmonic Vibrational Properties from Intrinsic n-Mode State Densities

“…20−23 It is also worth noting the recent semiempirical work of Schmatz 24 as well as the thermodynamic method, which relies on experimental data, 25,26 the density correlation function method of Jeffreys et al, 27,28 and the use of path-integral methods to calculate the quantum partition function directly. 29,30 The accurate inclusion of the coupling terms, however, remains an open issue.…”

“…Many attempts have been made to improve on the separable approximation by looking at the specific coupling between different modes. For instance, the coupling of bends to stretches has been studied and empirical models describing this coupling have been constructed, − the role of stretch–stretch coupling has been investigated in triatomic systems, , numerous methods for treating torsional motions have been developed, ,,− and Monte Carlo integration has been applied to calculation of quantum vibrational states using a spectroscopic (e.g., Dunham) expansion, which includes some anharmonic terms. − It is also worth noting the recent semiempirical work of Schmatz as well as the thermodynamic method, which relies on experimental data, , the density correlation function method of Jeffreys et al, , and the use of path-integral methods to calculate the quantum partition function directly. , The accurate inclusion of the coupling terms, however, remains an open issue.…”