Quantum steam tables. Free energy calculations for H2O, D2O, H2S, and H2Se by adaptively optimized Monte Carlo Fourier path integrals

Abstract

Converged quantum mechanical vibrational–rotational partition functions and free energies are calculated using realistic potential energy surfaces for several chalcogen dihydrides (H2O, D2O, H2S, H2Se) over a wide range of temperatures (600–4000 K). We employ an adaptively optimized Monte Carlo integration scheme for computing vibrational–rotational partition functions by the Fourier path-integral method. The partition functions and free energies calculated in this way are compared to approximate calculations that assume the separation of vibrational motions from rotational motions. In the approximate calculations, rotations are treated as those of a classical rigid rotator, and vibrations are treated by perturbation theory methods or by the harmonic oscillator model. We find that the perturbation theory treatments yield molecular partition functions which agree closely overall (within ∼7%) with the fully coupled accurate calculations, and these treatments reduce the errors by about a factor of 2 compared to the independent-mode harmonic oscillator model (with errors of ∼16%). These calculations indicate that vibrational anharmonicity and mode–mode coupling effects are significant, but that they may be treated with useful accuracy by perturbation theory for these molecules. The quantal free energies for gaseous water agree well with previously available approximate values for this well studied molecule, and similarly accurate values are also presented for the less well studied D2O, H2S, and H2Se.

Ab Initio Thermochemistry Beyond Chemical Accuracy for First-and Second-Row Compounds

“…The second method, due to Topper and coworkers [100], is based on Feynman path integrals, and works best in the high temperature limit. Therefore the two methods are complementary.…”

Direct Computation of the Quantum Partition Function by Path-Integral Nested Sampling

“…[13][14][15][16] Later, not only anharmonicities but also the rotation-vibration coupling was fully included in the path-integral computation of equilibrium isotope effects. 17 In a series of papers [18][19][20][21][22] Truhlar and co-workers elaborated on the Monte Carlo Fourier path integral method which gives access to the absolute rotational-vibrational partition function of molecules (with the full inclusion of anharmonicities and rotation-vibration coupling). The separable rotations approximation was found to be in an error of 7 % with respect to the exact result for small triatomic molecules.…”

“…The separable rotations approximation was found to be in an error of 7 % with respect to the exact result for small triatomic molecules. 20 Most recently, further developments of this method made it possible to compute the rovibrational partition function of the methane molecule up to 3000 K. 23,24 Ref. 25 presented a path-integral Monte Carlo computation of the quantum mechanical rovibrational partition function and numerical results for the diatomic hydrogen molecule.…”

“…The separable rotations approximation was found to be in an error of 7% with respect to the exact result for small triatomic molecules. 20 Most recently, further developments of this method made it possible to compute the rovibrational partition function of the methane molecule up to 3000 K. 23,24 Reference 25 presented a path-integral Monte As to van der Waals complexes, in which contributions from unbound states are significant already at moderate temperatures, a highly efficient path-integral Monte Carlo approach was developed for the second virial coefficient, 26 which is related to the ratio of the dimer's to the monomers' partition function. Recent applications of this method include the H 2 • CO dimer using a flexible spectroscopic potential energy surface (PES).…”

A Direct Evaluation of the Partition Function and Thermodynamic Data for Water at High Temperatures

“…20,23 Because of relatively simple and fundamental characteristics of water, there are many predictions of its partition function and thermodynamic properties, 7,8,[10][11][12][13][14]18,20,23,31 including the more recent and accurate estimation obtained by Vidler and Tennyson. 32 This will allow a detailed test of our method.…”