Evaluation of Different Methods for Computation of Kirkwood-Buff Integrals in the Thermodynamic Limit from Molecular Dynamics Simulations
Master thesis
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http://hdl.handle.net/11250/2562299Utgivelsesdato
2018Metadata
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- Institutt for kjemi [1404]
Sammendrag
The total correlation integrals can provide useful information about the local structure of fluids, both for mixtures and for pure materials. These integrals are commonly referred to as Kirkwood-Buff integrals, due to their central role in the solution theory derived by Kirkwood and Buff. The solution theory was originally derived from molecular distribution functions in the grand canonical ensemble, but several methods exist for the purpose of the computation of Kirkwood-Buff integrals using other ensembles. The purpose of this master's thesis is therefore to evaluate the efficiency of different methods available for computation of Kirkwood-Buff integrals from finite size computer simulations. To determine the method with the best overall performance, four factors are considered: accuracy, precision, availability and computational cost. All methods analyzed here are based on extracting the Kirkwood-Buff integrals in the thermodynamic limit from the ones computed for different-sized finite volumes. The finite-size Kirkwood-Buff integrals are either calculated from a running integral over the radial distribution function, or from fluctuations of number of particles in small subsystems inside a larger reservoir. Both methods give finite-size Kirkwood-Buff integrals that scale linearly with the inverse system size, making the values in the thermodynamic limit readily available. Recently, a scaling equation taking the finite size of the system into account was formulated (J Chem Phys. 2016;145(14):141103), and two ways of defining the subvolumes are available. The first is by placing the subvolumes at random locations inside the simulation box, while the second defines the subvolumes as lattice cells of a superimposed grid on the total simulation box. In this study, all different alternatives are investigated in detail in order to determine their effect on the Kirkwood-Buff integrals in the thermodynamic limit.
It was found that the superimposed lattice does not provide enough data points to precisely extract the Kirkwood-Buff integral in the thermodynamic limit, since the number available subvolume sizes is constrained by the total simulation box. In addition, the fluctuations are directly correlated for subvolumes placed right next to each other. The different techniques to extract the thermodynamic limit value of the Kirkwood-Buff integrals mainly resulted in similar values, but the ones involving fewer rounds of curve fitting were more precise. The randomly positioned spheres is the most flexible method. Combined with linear scaling it also provided the best overall accuracy, provided that the system is sufficiently far from the critical point. The radial distribution function is less sensitive to the critical point and the ensemble of the reservoir. The fluctuating volume in the isobaric-isothermal ensemble results in unwanted contributions to the fluctuations in the largest subsystems, and should therefore be avoided.