LennardJones Fluid Reference Calculations
In this section, we provide sample configurations of LennardJones atoms and report the internal energy and pair virial for those configurations. These sample configurations and reference calculations can be used to validate the energy and force routines for an existing or new molecular simulation code.
1. Sample Configurations of LennardJones Atoms
Four sample configurations of LennardJones atoms are available for download as a gzipped tarball archive. This archive contains five files: the four sample configuration files and one metadata file that explains the format of the sample configurations. These configurations should be converted to the configuration file format native to a user's simulation software.
2. Reference Calculations for the Internal Energy and Pair Virial
The following table contains calculations of the pair internal energy (U_{pair}), the instantaneous pair virial (W_{pair}), and the appropriate tail correction to the internal energy (U_{LRC}) for the four sample configurations in Section 1, where periodic boundary conditions [1,2] (also known as the minimumimage convention) were applied to all three Cartesian directions. The definition of these energetic terms are given below in Section 3. The reference calculations are for three truncation schemes: (1) potential truncation at a cutoff radius (r_{c}) of 3σ (σ is the LennardJones diameter), with longrange corrections (LRC), (2) potential truncation at r_{c}=4σ, with longrange corrections, and (3) potential truncation at r_{c}=3σ, with the linearforce shift applied at the cutoff radius (LFS). All sample energies and distances are given in appropriate LennardJones reduced units, denoted by the superscript "*".

LRC, r_{c}*=3.0 
LRC, r_{c}*=4.0

LFS, r_{c}*=3.0

Configuration 
U_{pair}* 
W_{pair}* 
U_{LRC}* 
U_{pair}* 
W_{pair}* 
U_{LRC}* 
U_{pair}* 
W_{pair}* 
U_{LRC}* 
1 
4.3515E+03 
5.6867E+02 
1.9849E+02 
4.4675E+03 
1.2639E+03 
8.3769E+01 
3.8709E+03 
3.1754E+02 
0.0000E0 
2 
6.9000E+02 
5.6846E+02 
2.4230E+01 
7.0460E+02 
6.5599E+02 
1.0226E+01 
6.2012E+02 
4.4533E+02 
0.0000E0 
3 
1.1467E+03 
1.1649E+03 
4.9622E+01 
1.1754E+03 
1.3371E+03 
2.0942E+01 
1.0210E+03 
9.3578E+02 
0.0000E0 
4 
1.6790E+01 
4.6249E+01 
5.4517E01 
1.7060E+01 
4.7869E+01 
2.3008E01 
1.5001E+01 
4.3096E+01 
0.0000E0 
3. Definitions
For the reference calculations given here, the following definitions are relevant:
A. The traditional LennardJones Potential is given by:
B. When the "LongRange Correction" (LRC) is applied to the tail of the LennardJones Potential, the actual potential in a molecular simulation is given by:
C. When the "LinearForce Shift" is applied to the tail of the LennardJones Potential, the actual potential in a molecular simulation is given by:
D. The pair internal energy is given by the following equation, where V(r) is the simulated pair potential:
E. The LongRange correction to the LennardJones potential, per particle, is given by [1,2]:
F. The instantaneous pair virial is given by:
References
1. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Oxford University Press, New York, 1989).
2. D. Frenkel and B. Smit, Understanding Molecular Simulation, 2nd ed. (Academic, San Diego, 2002), pp.3738.