We present an accurate and efficient method to obtain Kirkwood-Buff (KB) integrals in the thermodynamic limit from small-sized molecular dynamics simulations. By introducing finite size effects into integral equations of statistical mechanics, we derive an analytical expression connecting the KB integrals of the bulk system with the fluctuations of the number of molecules in the corresponding closed system. We validate the method by calculating the activity coefficients of aqueous urea mixtures and the KB integrals of Lennard-Jones fluids. Moreover, our results demonstrate how to identify simulation conditions under which computer simulations reach the thermodynamic limit.

Abstract:The spatial block analysis (SBA) method has been introduced to efficiently extrapolate thermodynamic quantities from finite-size computer simulations of a large variety of physical systems. In the particular case of simple liquids and liquid mixtures, by subdividing the simulation box into blocks of increasing size and calculating volume-dependent fluctuations of the number of particles, it is possible to extrapolate the bulk isothermal compressibility and Kirkwood-Buff integrals in the thermodynamic limit. Only by explicitly including finite-size effects, ubiquitous in computer simulations, into the SBA method, the extrapolation to the thermodynamic limit can be achieved. In this review, we discuss two of these finite-size effects in the context of the SBA method due to (i) the statistical ensemble and (ii) the finite integration domains used in computer simulations. To illustrate the method, we consider prototypical liquids and liquid mixtures described by truncated and shifted Lennard-Jones (TSLJ) potentials. Furthermore, we show some of the most recent developments of the SBA method, in particular its use to calculate chemical potentials of liquids in a wide range of density/concentration conditions.

Many popular methods for the calculation of chemical potentials rely on the insertion of test particles into the target system. In the case of liquids and liquid mixtures, this procedure increases in difficulty upon increasing density or concentration, and the use of sophisticated enhanced sampling techniques becomes inevitable. In this work, we propose an alternative strategy, spatially resolved thermodynamic integration, or SPARTIAN for short. Here, molecules are described with atomistic resolution in a simulation subregion and as ideal gas particles in a larger reservoir. All molecules are free to diffuse between subdomains adapting their resolution on the fly. To enforce a uniform density profile across the simulation box, a single-molecule external potential is computed, applied, and identified with the difference in chemical potential between the two resolutions. Since the reservoir is represented as an ideal gas bath, this difference exactly amounts to the excess chemical potential of the target system. The present approach surpasses the high density/concentration limitation of particle insertion methods because the ideal gas molecules entering the target system region spontaneously adapt to the local environment. The ideal gas representation contributes negligibly to the computational cost of the simulation, thus allowing one to make use of large reservoirs at minimal expenses. The method has been validated by computing excess chemical potentials for pure Lennard-Jones liquids and mixtures, SPC and SPC/E liquid water, and aqueous solutions of sodium chloride. The reported results well reproduce literature data for these systems.

We present an efficient method to obtain bulk isothermal compressibilities (κ T) and Kirkwood-Buff (KB) integrals of single-and multicomponent liquids using fluctuations of the number of molecules obtained from small-sized molecular dynamics simulations. We write finite-size versions of the Ornstein-Zernike and the KB integral equations and include there finite size effects related to the statistical ensemble and the finite integration volumes required in computer simulations. Consequently, we obtain analytical expressions connecting κ T and the KB integrals in the thermodynamic limit (TL) with density fluctuations in the simulated system. We validate the method by calculating various thermodynamic quantities, including the chemical potentials of SPC/E water as a function of the density, and of aqueous urea solutions as a function of the mole fraction. The reported results are in excellent agreement with calculations obtained by using the best computational methods available, thus validating the method as a tool to compute the chemical potentials of dense molecular liquids and mixtures. Furthermore, the present method identifies conditions in which computer simulations can be effectively considered in the TL.

Shape and size are known to determine a nanoparticle's properties. Hardly ever studied in synthesis, the internal crystal structure (i.e., particle defects, crystallinity, and symmetry) is just as critical as shape and size since it directly impacts catalytic efficiency, plasmon resonance, and orients anisotropic growth of metallic nanoparticles. Hence, its control cannot be ignored any longer in today's research and applications in nanotechnology. This study implemented an unprecedented reliable measurement combining these three structural aspects. The unified small-angle X-ray scattering and diffraction measurement (SAXS/XRD) was coupled with molecular dynamics to allow simultaneous determination of nanoparticles' shape, size, and crystallinity at the atomic scale. Symmetry distribution (icosahedra-Ih, decahedra-Dh, and truncated octahedra-TOh) of 2-6 nm colloidal gold nanoparticles synthesized in organic solvents was quantified. Nanoparticle number density showed the predominance of Ih, followed by Dh, and little, if any, TOh. This result contradicts some theoretical predictions and highlights the strong effect of the synthesis environment on structure stability. We foresee that this unified SAXS/XRD analysis, yielding both statistical and quantitative counts of nanoparticles' symmetry distribution, will provide new insights into nanoparticle formation, growth, and assembly.