Lennard-Jones fluid simulation website

1. Molecular dynamics results

NVE Molecular dynamics results at liquid-like densities along an isotherm of reduced temperature 0.85. Mean values and standard deviations of temperature, energy, pressure, and diffusion coefficient are reported.

METHOD: NVE molecular dynamics
INTEGRATOR: Velocity-Verlet
TIME STEP: 0.005 t*
N: 500
TRUNCATION: 3σ + standard long range corrections
EQUILIBRATION: >50 t*
PRODUCTION: 100 t*
plot of g(r) versus r
The pair functions for the states with density 0.9 (black), 0.84 (red), and 0.776 (green) are shown here. The pair functions for intermediate densities lie between these curves.
T* ρ* U* p* D*
0.851(1) 0.776 -5.517(1) 0.030(6) 0.061
0.853(1) 0.780 -5.533(1) 0.072(5) 0.063
0.852(1) 0.820 -5.803(1) 0.573(5) 0.048
0.851(1) 0.840 -5.909(1) 0.910(6) 0.042
0.849(1) 0.860 -6.027(1) 1.282(5) 0.035
0.851(1) 0.900 -6.234(1) 2.544(6) 0.027

Remarks

The standard uncertainty in the last digit is in (..) and is obtained from block averages of length 2 to 4 time units. Uncertainties correspond to 67% confidence limits. An estimate of the self-diffusion coefficient is based on 10 independent realizations of the mean-square displacement as a function of time and is of order 1 or 2 in the last digit. Both the potential and force are truncated (no splines) at the above indicated value. Standard long range corrections are included in the tabulated values of energy and pressure. The usual Lennard-Jones units are used where ε = 1, σ = 1, m = 1, and t*2 = (m σ2 / ε ) define the units of energy, mass and time, respectively. The reported pressure was calculated using the virial expression.