Third year simulation experiment/Structural properties and the radial distribution function

This is the sixth section of the third year simulation experiment. You can return to the previous page, Running simulations under specific conditions, or jump ahead to the next section, Dynamical properties and the diffusion coefficient.

We can characterise the structure of systems that we simulate using radial distribution functions, which we denote $g(r)$. Calculating the RDF for a simulation is very useful — it can tell us the distances from an atom at which we will find it's nearest neighbour, second nearest neighbour, and so on; it is also a quantity that can be accessed experimentally, and so provides a good check that the forcefield in our simulation is correctly reproducing the structural features.

In this section, you are going to use VMD to calculate the radial distribution function for the solid, liquid, and vapour phases of the Lennard-Jones fluid.

Calculating $g(r)$ in VMD

1. Start VMD as before and load the trajectory that you want to analyse.
2. Select Extensions -> Analysis -> Radial Pair Distribution Function g(r)
3. Set Selection 1 to all and Selection 2 to all
4. Change delta r to 0.05 — this is the distance between points in the generated RDF.
5. Ensure that Use PBC, Display g(r), Display Int(g(r)), and Save to File are checked
6. Click Compute g(r)

After a short pause while it performs the calculation, VMD will display both the RDF, and its running integral. You will then be prompted to save this data — choose a location for the file that you will be able to find easily later.

Simulations in this section

The RDF subfolder contains an example input script that you can use to record an atomic trajectory to generate RDFs for the solid, liquid, and vapour phase Lennard Jones systems. Make three copies of that script (one for each phase), and modify the density and temperature parameters to give the phase that you want (a phase diagram for the Lennard-Jones system can be found here). Note: when simulating the solid, you will need to change the lattice type in the lattice command to fcc, rather than sc.

TASK 17: perform simulations of the Lennard-Jones system in the three phases. When each is complete, download the trajectory and calculate $g(r)$ and $\int g(r)\mathrm{d}r$. Plot the RDFs for the three systems on the same axes, and attach a copy to your report. Discuss qualitatively the differences between the three RDFs, and what this tells you about the structure of the system in each phase. In the solid case, illustrate which lattice sites the first three peaks correspond to. What is the lattice spacing? What is the coordination number for each of the first three peaks? [15 marks]

This is the sixth section of the third year simulation experiment. You can return to the previous page, Running simulations under specific conditions, or jump ahead to the next section, Dynamical properties and the diffusion coefficient.