However, this approximation breaks down quantitatively for DMF/water (where DMF molecules are considerably larger than water molecules) and even leads to qualitatively incorrect results for n-butanol/water, the latter being a mixture of immiscible liquids. For instance, estimating the combinatorial entropy of mixing from the molar fractions, as given by the expression for a mixture of ideal gases, works reasonably well for the acetonitrile/water and methanol/water mixtures. We show that while the choice of method to perform the solid/gas partition has a sizable impact on the results, it is the expression to estimate the combinatorial entropy of mixing that has the largest effect on the calculated entropy values. In particular, we study the excess entropy of mixing of methanol/water, acetonitrile/water, N, N-dimethylformamide (DMF)/water, and n-butanol/water, where the ratio of molecular weights varies between ∼1.8:1 and ∼4.1:1 (see Fig. In this paper we present and extensively assess new ways to estimate fluidicities and different mixing schemes, applied to liquid mixtures where the size of the constituent molecules is allowed to differ considerably. While this can be a valid assumption for mixtures of fully miscible and similarly sized molecules, it may not hold accurate when studying, e.g., thermodynamic properties of large solvated molecules such as typical outer-sphere electrochemically active complexes, liquid mixtures where the difference in size of the various molecules is pronounced, and fully immiscible or partially immiscible liquids. Their treatment is based upon the assumption of ideal combinatorial mixing.

3 and Pascal and Goddard 4 has dealt with the derivation of 2PT expressions for multicomponent systems, where many expressions are modified by including molar fractions in the definitions. The original 2PT formalism was developed for monocomponent fluids, where the effects of mixing of different molecular species do not need to be taken into account. This partition relies on the critical parameter f, the fluidicity, which is a measure of how the diffusive properties of the real system compare to those of an ideal hard-sphere gas. 2 The central idea of 2PT is to separate the total number of degrees of freedom N of the system under study into (1 – f) N “solid-like” and fN “gas-like” degrees of freedom, for which thermodynamic properties are calculated separately.

The model builds upon the density of states formalism developed by Berens et al. in 2003, 1 has sparked interest in recent years due to its ability to obtain converged thermodynamic properties from relatively short molecular dynamics (MD) runs. The two-phase thermodynamic (2PT) model, introduced by Lin et al. For the mixtures studied, the GAFF force field seems to perform as a slightly better “all-around” force field when compared to OPLS+SPC/E. We tested two popular force fields, GAFF and OPLS with SPC/E water. However, the ability of the 2PT method to succeed in these calculations is strongly influenced by the choice of force field, the fluidicity (hard-sphere) formalism employed to obtain the solid/gas partition, and the assumed combinatorial entropy of mixing. Our analysis shows that results in excellent agreement with experiment can be obtained with little computational effort for some systems. To ensure a meaningful assessment, we perform MD simulations of liquid mixtures of water with several other molecules of varying sizes: methanol, acetonitrile, N, N-dimethylformamide, and n-butanol. The new scheme enables improved convergence of the results with respect to configurational sampling, by up to one order of magnitude, for short MD runs. This problem arises when the effective temperatures of translational, rotational, and vibrational DoF are not equal, either due to poor equilibration or reduced system size/time sampling, which are typical problems for ab initio MD. We also propose a first-order correction to the issue of kinetic energy transfer between degrees of freedom (DoF). and explore new ways to obtain the partition between the gas-like and solid-like parts of the density of states, as well as the effect of the chosen ideal “combinatorial” entropy of mixing, both of which have a large impact on the results. We build upon the two-phase thermodynamic (2PT) model of Lin et al. We explore different schemes for improved accuracy of entropy calculations in aqueous liquid mixtures from molecular dynamics (MD) simulations.

Entropy of mixing