This document discusses analyzing data from molecular dynamics simulations using GROMACS tools. It provides instructions for using commands like gmx energy and gmx rdf to extract data from simulation output files for analysis. It also discusses analyzing the radial distribution function, which provides information about the probability of finding particles at different distances from each other. The radial distribution function analysis can reveal differences between solids, liquids and gases based on their structural organization.

1. MDS Data Analysis

2. MDS Data Analysis
A range of simulation data analysis can be performed using GROMACS tools such
as gmx energy, gmx distance, gmx rdf, gmx sasa, etc.
For e.g., details from .edr file can be extracted and analyzed using following
commands
gmx energy –f eqm.edr (or prd.edr) –o anyname.xvg
The .xvg file can be plotted using the xmgrace plotting tool
xmgrace anyname.xvg

3. MDS
Data
Analysis
https://manual.gromacs.org/current/user-guide/cmdline.html#gmx-distance

4. MDS Data Analysis
OR
Analyze the data by writing code using any programming language…..

6. Radial Distribution Function

7. Radial Distribution Function
The radial distribution function (RDF) denoted in equations by g(r) defines the
probability of finding a particle at a distance r from another tagged particle.
https://en.wikibooks.org/wiki/Molecular_Simulation/Radial_Distribution_Functions
https://people.bath.ac.uk/chsscp/teach/md.bho/Theory/rdf.html

8. Radial Distribution Function
To construct an RDF g(r), choose an atom in the system and draw around it a
series of concentric spheres, set at a small fixed distance (∆r) apart (see figure
below). At regular time intervals, the number of atoms found in each shell n(r) is
counted and stored. At the end of the simulation, the average number of atoms in
each shell is calculated. This is then divided by the volume of each shell (4p r2Dr)
and the average density r of atoms in the system.
Mathematically the formula is:
𝒈 𝒓 =
n(r)
(4p r2Dr × r)

9. Radial Distribution Function - Normalization
𝒈 𝒓 =
n(r)
(4p r2Dr × r)
In RDF, n(r) is the mean number of atoms in a shell of width Dr at distance r.
The method need not be restricted to one atom. All the atoms in the system
can be treated in this way, leading to an improved determination of the RDF
as an average over many atoms.
https://w3.iams.sinica.edu.tw/lab/jlli/thesis_andy/node14.html
Normalization by
bin (shell) volume

10. Radial Distribution Function - Normalization
𝒈 𝒓 =
n(r)
(4p r2Dr × r)
Number Density

11. Radial Distribution Function - Normalization
Normalization is a scaling technique in which values are shifted and rescaled so
that they end up ranging between 0 and 1. This helps to compare different
plots by bringing them to the same levels.
𝒈 𝒓 =
n(r)
(4p r2Dr × r)
𝒈 𝒓 =
n(r)
(4p r2Dr)
Not Normalized by
average density
Normalized to 1 by
average density
https://mathematica.stackexchange.com/questions/110743/radial-distribution-function
https://www.analyticsvidhya.com/blog/2020/04/feature-scaling-machine-learning-normalization-standardization/
Crystal
image
At very long range every RDF tends to a value of 1.
(One of the important features of RDF)
https://manual.gromacs.org/documentation/5.1/onlinehelp/gmx-rdf.html

12. Radial Distribution Function
Firstly, at short separations (small r) the RDF is zero.
A typical RDF plot (below) shows a number of important features.

13. Radial Distribution Function
Firstly, at short separations (small r) the RDF is zero. This indicates the effective
width of the atoms, since they cannot approach any more closely. This is due to
the strong repulsive forces.
A typical RDF plot (below) shows a number of important features.

14. Radial Distribution Function
A typical RDF plot (below) shows a number of important features.
Secondly, a number of obvious peaks appear, which indicate that the atoms
pack around each other in ‘shells’ of neighbours. The occurrence of peaks at
long range indicates a high degree of ordering (e.g. solids). Usually, at high
temperature the peaks are broad, indicating thermal motion, while at low
temperature they are sharp. They are particularly sharp in crystalline materials,
where atoms are strongly confined in their positions.

15. Radial Distribution Function
https://www.scielo.br/j/mr/a/ttCnWGvJbr9KJkRF3MPv34C/?lang=en
https://www.globalsino.com/EM/page3097.html

16. Radial Distribution Function
The RDF is strongly dependent on the type of matter so will vary greatly for
solids, gases, and liquids.

17. Radial Distribution Function - Gases
Gases do not have a regular structure which heavily influences their RDF. The
RDF of a real gas will have only a single coordination sphere which will rapidly
decay to the normal bulk density of a gas, g(r)=1. The RDF of a real gas is fairly
simplistic, with values of g(r) as follows:
https://en.wikibooks.org/wiki/Molecular_Simulation/Radial_Distribution_Functions

18. Radial Distribution Function - Liquids
Due to their ability to move dynamically liquids do not maintain a constant structure and
lose all of their long-range structure. The first coordination sphere for a liquid will occur at
~σ. At large values of r, the molecules become independent of each other, and the
distribution returns to the bulk density (g(r)=1). The first peak will be the sharpest and
indicates the first coordination sphere of the liquid. Subsequent peaks will occur roughly
in intervals of σ but be much smaller than the first. Liquids are more loosely packed than
solids and therefore do not have exact intervals. Although it is possible for there to be
multiple coordination spheres, there is a depleted probability of finding particles outside
the first sphere due to repulsion caused by the first sphere.
https://en.wikibooks.org/wiki/Molecular_Simulation/Radial_Distribution_Functions

19. Radial Distribution Function - Solids
Solids have regular, periodic structures, with molecules fluctuating near their lattice
positions. The structure is very specific over a long-range, therefore it is rare to see
defects in solids. Discrete peaks at values of σ, √2σ, √3σ, etc. can be seen in the RDF of
a solid. Each peak has a broadened shape which is caused by particles vibrating around
their lattice sites. There is zero probability of finding a particle in regions between
these peaks (perfectly crystalline) as all molecules are packed regularly to fill the space
most efficiently. Each peak represents a coordination shell for the solid, with the
nearest neighbours being found in the first coordination shell, the second nearest
neighbours being found in the second, and so on.
https://en.wikibooks.org/wiki/Molecular_Simulation/Radial_Distribution_Functions

20. Radial Distribution Function
https://en.wikibooks.org/wiki/Molecular_Simulation/Radial_Distribution_Functions
The radial distribution functions of solid (T = 50 K),
liquid (T = 80 K), and gaseous argon (T = 300 K).

21. Radial Distribution Function
https://en.wikibooks.org/wiki/Molecular_Simulation/Radial_Distribution_Functions
The radial distribution functions of solid (T = 50 K),
liquid (T = 80 K), and gaseous argon (T = 300 K).

22. Radial Distribution Function
The radial distribution analysis can be performed using
GROMACS tool gmx rdf.
The RDF is useful in other ways. For example, it is something that can be
deduced experimentally from x-ray or neutron diffraction studies, thus
providing a direct comparison between experiment and simulation.
https://aip.scitation.org/doi/abs/10.1063/1.4960175
https://manual.gromacs.org/documentation/5.1/onlinehelp/gmx-rdf.html
Normalization and other
instructions