## Abstract

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.

Original language | English (US) |
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Pages (from-to) | 1084-1097 |

Number of pages | 14 |

Journal | Molecular Simulation |

Volume | 35 |

Issue number | 12-13 |

DOIs | |

State | Published - Oct 2009 |

### Funding

This material is based upon work supported by the National Science Foundation under the following NSF programs: Partnerships for Advanced Computational Infrastructure, Distributed Terascale Facility (DTF) and Terascale Extensions: Enhancements to the Extensible Terascale Facility. This work was also supported by the National Science Foundation (CTS-0507013) and the Defense Threat Reduction Agency.

## Keywords

- Correlation
- Diffusion
- Order-n

## ASJC Scopus subject areas

- General Chemistry
- Condensed Matter Physics
- General Chemical Engineering
- Information Systems
- General Materials Science
- Modeling and Simulation