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

Abstract

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

On the proper use of the Bigeleisen–Mayer equation and corrections to it in the calculation of isotopic fractionation equilibrium constants

“…We tested the HIR of ethane by Gaussian 03 program and found it is equal to the unity (means no correction). The same result was also obtained by many other researchers with similar methods (e.g., Lynch et al, 2005;Ellingson et al, 2006). The general treatment of these methods is to relate the barrier height, the effective moment of inertia and the frequency of torsional mode as…”

Exploring the effect of anharmonicity of molecular vibrations on thermodynamic properties

“…Both are in very good agreement with the 1.008 value predicted by Truhlar et al This is to be expected at room temperature, since, as noted by Truhlar et al, the rigid-rotor-harmonic-oscillator approximation is already very close to the accurate rotovibrational partition function due to the lack of floppy modes in CH 4 . For H 2 O 2 , the calculated ZPE͑0͒ ELC = 16.46 kcal/ mol is in very good agreement with the value of ϳ16.37 kcal/ mol estimated by Lynch et al 30 Finally, the calculated room temperature standard-state Gibbs free energy of 13.64 kcal/ mol underestimates by less than 0.5 kcal/ mol the more accurate values obtained by Lynch et al 29 and Dorofeeva et al…”

Converged vibrational energy levels and quantum mechanical vibrational partition function of ethane

“…The only previous molecule with a torsion for which converged vibrational or rovibrational partition functions have been obtained is H 2 O 2 ͑and several of its isotopomers͒, 11,12 with four atoms as compared to eight atoms here. The only previous molecule of any type with more than four atoms for which converged vibrational and rotational partition function have been calculated is CH 4 , 10 with five atoms, again considerably smaller than the present eightatom case.…”

“…[1][2][3] All thermodynamic variables of a system, for example, internal energy, free energy, and entropy, can be expressed in terms of the partition function and its derivatives. An alternative to the harmonic oscillator approximation is to include the anharmonic effects in the partition function calculation, [5][6][7][8][9][10][11][12] which is the objective of the present work. [1][2][3][4] The internal partition function of a polyatomic system is often computed by making a series of approximations.…”