Analysis of two common algorithms to compute self-diffusion coefficients in infinite dilution from molecular dynamics simulations and application to n-alkanes (C₁ to C₃₅) in water

In this study the order-n algorithm and the linear regression algorithm used to obtain self-diffusion coefficients from molecular dynamics simulations are compared using theoretical analysis and Monte Carlo simulations. This analysis shows that the order-n algorithm allows decreasing the uncertainty in self-diffusion coefficients without increased computational effort. Both algorithms are used to calculate self-diffusion coefficients of linear n-alkanes in infinite dilution in water. Using the same trajectories the results obtained by the order-n algorithm had an average deviation from the experimental value of 2%, whereas using the linear regression algorithm the deviation was 12.5%. A guideline for selecting an optimal frequency, in which the center of mass trajectories from the molecular dynamics simulations should be written out, is given for the order-n algorithm.