Benchmark results for the Lennard-Jones fluid
The purpose of these pages is to provide some explicit results from molecular dynamics and Monte Carlo simulations for the Lennard-Jones fluid. It is intended to provide guides for testing codes. Reproducing these results is a test of the correctness of codes, either written by the user or obtained elsewhere. The explicit conditions for each of the sets of results are supplied so that meaningful comparisons of your results with the ones listed here are possible.
The information presented here has been organized into eight different pages. It is available as web pages or as a single excel file.
As is usually the case, temperature, density (number density), pressure, etc., are given in reduced units (denoted by *). That is, these properties are expressed in terms of the characteristic energy, ε, and length scale, σ, defined by the Lennard-Jones potential:
Therefore, the reduced temperature T*, density ρ*, and pressure p* are kBT/ε, ρσ3, pσ3/ε, respectively. The critical parameters for the pure LJ fluid have been determined to be Tc* = 1.3120(7), ρc* = 0.316(1), and pc* = 0.1279(6) .
For computational expediency, the potential and force are usually truncated at some cutoff distance rc. That is, the effective potential V(r) is
In this work, the cutoff distance is taken to be 3σ, unless noted otherwise. An approximate correction for this truncation to the energy and pressure of the system can be obtained by assuming the spatial correlations beyond the cutoff distance are unity. The reader is referred to Refs.  and  for these so-called “standard long range corrections” (sLRC). It should be noted that this not a good assumption in inhomogeneous fluids. For completeness, the working expressions for obtaining the long range corrections to the potential energy per particle and virial pressure are provided below:
where ρ is the bulk number density, VLJ(r) is the Lennard-Jones potential energy, and rc is the truncation (cutoff) distance. A subtle point to note is that the above pressure correction does not account for impulsive effects at rc where the potential energy (and therefore the force) changes discontinuously. This is particularly important when trying to simulate directly interfacial phenomena . Finally, it should be mentioned that other truncation and long range correction schemes for dealing with non-bonded interactions exist [4-8]. In some cases, the truncation schemes can yield critical properties that differ from those quoted above .
In future versions, coordinate sets will be available for which the potential energy per particle and the virial are specified. This information can be used to test energy/force routines.
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