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Solvent Extraction through the Lens of Advanced Modeling and Simulation
Published in Bruce A. Moyer, Ion Exchange and Solvent Extraction: Volume 23, 2019
Aurora E. Clark, Michael J. Servis, Zhu Liu, Ernesto Martinez-Baez, Jing Su, Enrique R. Batista, Ping Yang, Andrew Wildman, Torin Stetina, Xiaosong Li, Ken Newcomb, Edward J. Maginn, Jochen Autschbach, David A. Dixon
However, the two states of interest are often connected by a free-energy barrier. Since classical simulations can only achieve a finite amount of sampling, without proper care, thermodynamic averages will be inaccurate and highly dependent upon initial conditions. In addition, many important chemical properties have an exponential dependence on the free energy. Small errors in the free-energy calculation can, therefore, have a large effect on the accuracy of the computed properties. Special techniques have been developed to overcome this limitation. One widely used technique is the Multistate Bennett Acceptance Ratio (MBAR) method.273 MBAR allows for a free-energy difference to be computed by splitting the process into various simulation windows, run in parallel. The algorithm uses energy information from all of the windows to calculate the overall free-energy change. This provides a vastly improved estimate of the free energy.
Effect of fluorination on the partitioning of alcohols
Published in Molecular Physics, 2019
Mohammad Soroush Barhaghi, Chloe Luyet, Jeffrey J. Potoff
In addition to using only uncorrelated samples, care must be taken to ensure that data used in the free energy calculation are collected from simulations that have reached equilibrium. Prior molecular dynamics simulations have shown, for example, challenges in converging liquid phase densities and free energies of solvation in 1-octanol [77]. In this work, NPT simulations of 3 × 107 MCS were used to equilibrate the system at each prior to the production run, ensuring stability of the density during free energy calculations, as shown in Figure S2 for perfluorooctanol in 1-octanol. Once free energy data were collected, convergence of the data were assessed by calculating free energies of hydration/solvation in both the forward and reverse directions with alchemical-analysis [72]. In the forward direction, the free energy was calculated using data in the order in which they were collected, while in the ‘reverse’ direction, the free energy was calculated from the data ordered in the reverse of which it was collected. As shown in Figure 2 for F2H6, the forward and reverse calculations match within the statistical uncertainty of the data, suggesting convergence of the free energy calculations [72,78]. Free energies were calculated from simulation data using a variety of thermodynamic integration methods (trapezoidal rule (TI) and cubic spline (TI-CUBIC)), and free energy perturbation techniques (Bennett acceptance ratio (BAR) and multi-state Bennett acceptance ratio (MBAR)). MBAR results are discussed in the body of the paper, while results for TI and BAR may be found in Table S5 of the supporting information. For simulations that have high quality sampling, and sufficient overlap between energy difference distributions, it is expected that all methods will produce similar results. As shown in Figure 3, good agreement for all intermediate states was achieved with all methods.