The trajectory file for this example is here on figshare. The trajectory file details the fMSI (flat Monolayer Square Ice) formed when quasi-one-dimensional water at 320 K. In this example, the in-plane RDF of the quasi-two-dimensional fMSI is determined.

The radial distribution function $g(r)$, or pair distribution function. It can be used to illuminate features of short-range and long-range order. The RDF is the probability of finding a particle at a distance of $r$ from a tagged reference particle, relative to that of an ideal gas. For a system of $N$ particles, the pair correlation function for $N(N-1)$ pairs is:

(r-r_i) \delta (r'-r_j) \langle

The C++ backend code essentially bins distances between pairs of particles, and normalizes the resulting histogram. The normalization is done with respect to an ideal gas.

On running the example, an output top-level directory named runOne is created.

## Steps to Run the Example¶

In order to run this example, without making any changes to the example files, please follow the steps below.

• Download the LAMMPS trajectory file from here on figshare. Copy the downloaded trajectory file, entitled dump-320.lammpstrj, into the traj folder inside the top-level directory input. Alternatively, you could change the path to the trajectory file in the conf.yaml file:
trajectory: "path/to/trajectory/file"

• You can obtain the other input files required from example_lua/rdf2D-example folder. Copy the contents of the rdf2D-example into the top-level lua_inputs directory.
• You can change the frames to be analyzed by updating the options in the vars.lua file. The starting and ending frames are inclusive, starting from 1 onwards, irrespective of the timestep number.
• A custom volume slice can also be defined in the vars.lua file.
• The functions.lua file actually contains the Lua functions which interface with the C++ backend.

## Analyzing the Output¶

Inside the output directory, a directory called topoMonolayer is created. Inside the topoMonolayer directory, files called coverageAreaXY.dat, coverageAreaXZ.dat, and coverageAreaYZ.dat contain the number of rings and and the corresponding coverage area% [1], for each frame. Here, the confining sheet is in the XY plane, so the coverageAreaXY.dat contains the coverage area% and quantities of interest. Inside runOne/topoMonolayer/dataFiles, LAMMPS data files which are numbered according to the frame number are created. These data files can be visualized in OVITO or VMD, although OVITO is recommended for optimal type visualization.

The output file rdf.dat contains the values of $r$ and $g(r)$ in each column, and can be plotted to obtain the in-plane radial distribution function. For a better and less grainy plot, you should use more frames for the RDF.

## References¶

1. Goswami, A., & Singh, J. K. (2020). A general topological network criterion for exploring the structure of icy nanoribbons and monolayers. Physical Chemistry Chemical Physics. doi:10.1039/c9cp04902a