Two Faces of the Two-Phase Thermodynamic Model.

Ádám Madarász,Andrea Hamza,Imre Bakó,Dávid Ferenc

doi:10.1021/acs.jctc.1c00156

Abstract

The quantum harmonic model and the two-phase thermodynamic method (2PT) are widely used to obtain quantum-corrected properties such as isobaric heat capacities or molar entropies. 2PT heat capacities were calculated inconsistently in the literature. For water, the classical heat capacity was also considered, but for organic liquids, it was omitted. We reanalyzed the performance of different quantum corrections on the heat capacities of common organic solvents against experimental data. We have pointed out serious flaws in previous 2PT studies. The vibrational density of states was calculated incorrectly causing a 39% relative error in diffusion coefficients and 45% error in the 2PT heat capacities. The wrong conversion of isobaric and isochoric heat capacities also caused about 40% error but in the other direction. We have introduced the concept of anharmonic correction (AC), which is simply the deviation of the classical heat capacity from that of the harmonic oscillator model. This anharmonic contribution is around +30 to 40 J/(mol K) for water depending on the water model and −8 to −10 J/(mol K) for hydrocarbons and halocarbons. AC is unrealistically large, +40 J/(K mol) for alcohols and amines, indicating some deficiency of the OPLS force field. The accuracy of the computations was also assessed with the determination of the self-diffusion coefficients.

Highlights

Accounting for nuclear quantum effects is essential to obtain meaningful thermodynamic properties that are comparable to experimental observations.[1]
We have introduced the concept of anharmonic correction (AC), which is the deviation of the classical heat capacity from that of the harmonic oscillator model
We showed that the 1PT+AC heat capacity can be significantly overestimated if the left Riemann sum is used instead of the trapezoidal rule in the computation of vibrational density of states (VDOS) in eq 2.60 To check whether this numerical error can occur in the calculation of the 2PT heat capacities, we thoroughly tested the “dos” analysis tool of GROMACS that was used in ref 20

Summary

Introduction

Accounting for nuclear quantum effects is essential to obtain meaningful thermodynamic properties that are comparable to experimental observations.[1] The most typical example is that zero point energies are indispensable for the determination of reaction free energies. The quantum harmonic oscillator model works quite well for small molecules and solid states, but the anharmonicity becomes significant in macromolecules, interfaces, and liquids, and the potential energy surfaces must be mapped using molecular dynamics or Monte Carlo simulation. Berens proposed to add quantum correction to the classically calculated properties using the harmonic oscillator model.[2] Goddard improved this by the separation of different motions like translation rotations and vibrations and using different partition functions for each of them.[3,4] This was abbreviated as the two-phase thermodynamic (2PT) model referring to the gas-phase and solid-phase motions in contrast to the one-phase thermodynamic (1PT) method where only vibrations were considered. An anharmonic correction was included in Berens’ original idea, and we refer to that method as onephase-thermodynamics with anharmonic correction (1PT +AC)

Methods

Results

Conclusion