A new perspective on the order-n algorithm for computing correlation functions

A method to measure correlations is presented that can be shown to be identical to the original 'order-n algorithm' from Frenkel and Smit (Understanding Molecular Simulation, Academic Press, 2002). In contrast to their work, we present the algorithm without the use of 'block sums of velocities'. We show that the algorithm gives identical results compared to standard correlation methods for the time points at which the correlation is computed. We apply the algorithm to compute diffusion of methane and benzene in the metal-organic framework IRMOF-1 and focus on the computation of the mean-squared displacement, the velocity autocorrelation function (VACF), and the angular VACF. Other correlation functions can readily be computed using the same algorithm. The savings in computer time and memory result from a reduction of the number of time points, as they can be chosen non-uniformly. In addition, the algorithm is significantly easier to implement than standard methods. Source code for the algorithm is given.