Particle and Energy Pair and Triplet Correlations in Liquids and Liquid Mixtures from Experiment and Simulation

Abstract

Recent advances in fluctuation solution theory (FST) have provided access to information concerning triplet fluctuations and integrals, in addition to the established pair fluctuations and integrals, for liquids and liquid mixtures using both experimental and simulation data. Here, FST is used to investigate pair and triplet correlations for (i) pure water as provided by experiment and simulation using both polarizable and nonpolarizable water models, (ii) liquid mixtures of methanol and water as provided by experiment and simulation, and (iii) native and denatured states of proteins as provided by simulation. The last application is particularly powerful, as it provides exact equations for the volume, enthalpy, compressibility, thermal expansion, and heat capacity of a single protein form provided by a single simulation. In addition, a discussion of the quality of the integrals obtained from experiment and simulation is provided. The results clearly illustrate that FST can be a powerful tool for the analysis and interpretation of both experimental and simulation data in complex liquid mixtures, including biomolecular systems, and that current simulation protocols can provide reliable values for the pair and triplet correlations and integrals.

On static triplet structures in fluids with quantum behavior

“…First, the general questions beyond the conventional pair approaches: (a) effects on the thermodynamic properties; 1,14,15 (b) the connections with the density (or pressure) derivatives of the radial and Fourier pair structures of fluids (i.e., g 2 (r), r = |r 1 − r 2 | ; S (2) (k), k = |k|); 1,[16][17][18][19][20] and (c) the characterization of fluid mixtures. [21][22][23] Second, multiple scattering 1,24 and the early studies of excitations in helium II. 25,26 Third, the density functional theories of freezing, [27][28][29][30] the theories of glass-forming liquids, 6,31 and the large variety of interfacial phenomena.…”

Gaussian and non-Gaussian fluctuations in pure classical fluids

“…Indeed, previous studies have shown that the GCE distributions are not Gaussian (or symmetric) and therefore this assumption is not justified for the present purposes. 14,20 This point will also be discussed further in Sec. III.…”

“…Hence, the excess entropy and enthalpy fluctuations are equal and therefore δS E could be used in place of δH E in the following equations. If we substitute the expressions for δE and δV given by Equation (20) into the expression for S (2) found in Equation (5) and then collect identical terms the result can be written as…”

“…Nevertheless, from the previous results, it would appear that a general distribution valid for multiple ensembles should be available. Again, we use the substitutions denoted in Equation (20) for the S (2) and S (3) terms. The S (2) term remains the same as before and we can use the result presented in Equation (25) or (26).…”

“…14,[18][19][20] FST provides an alternative view of the commonly studied closed system thermodynamic properties in terms of fluctuating quantities occurring in an equivalent Grand Canonical Ensemble (GCE) system. FST represents a generalization of the Kirkwood-Buff theory of solutions, [21][22][23] to include energy fluctuations.…”