5 Minutes Tutorial

System

1. Obtain the trajectory from the molecular dynamics production run.

Note

Example system : 550 TIP3P water molecules with box length of 25.5 Å * 25.5 Å * 25.5 Å

2. Generate the xyz file (input for the order package) from the trajectory with the atoms (O or center of mass) necessary to calculate the local structure.

Note

This xyz file should include all the water Oxygen atoms and all the other atoms that are cosidered as the closest neighbors. Make sure to follow the following file format for the xyz file. In this example the central Oxygen atoms of water are named as “OW”.

Line #1 : Number of atoms

Line #2 : BoxlenghtX(Space)BoxlenghtY(Space)BoxlenghtZ

Line #3 & onwards : Symbol assigned by the user for the central atom and the other atoms that can be considered as the closest neighbors

3. Commands available in the package

$order [input] [-h] [-t TASK] [-c CENTER] [-b BINS] [-f FREQUENCY] [-p PLOT]

input

File name of the xyz file

-h

Show this help message and exit

-t TASK

Specification of the type of task that you need to perform. TASK can
be oto or tto or avc (default: oto).
If you need to perform multiple tasks simultaneously use a "," to
separate the tasks. (Ex : tto,oto)

-c CENTER

Type of center atom (default: 'O')
(In the example mentioned above the center is 'OW')

-b BINS

Number of bins for the parameter (default: 100)

-f FREQUENCY

Compute the parameter every n frame(s) in the xyz file(default: 1)

-p PLOT

Turn on / off of plotting (default: on)

Orientational Tetrahedral Order (OTO)

This is the most common type of tetrahedral ordr paramater that is being used. This order parameter uses the four closest water Oxygen neighbors for the calculation. The value of q can rang from 0 to 1, where 0 is for an ideal gas and 1 is for a regular tetrahedron.

\[q = 1 - \frac{3}{8}\sum_{j=1}^{3}\sum_{k=j+1}^{4}\left ( \cos \psi _{jk}+\frac{1}{3} \right )^{2}\]

q = Orientational tetrahedral order parameter

ψ_jk = Angle formed by the Oxygen atom under consideration & the two nearest neighbor atoms j & k

$order test.xyz -t oto -c 'OW' -f 5

Translational Tetrahedral Order (TTO)

Similar to orientational tetrahedral order. But here, the variance of the radial distnace between the central water Oxygen atom and the four nearest neighbors are calculated. THe value of S_kis close to 1 and quals 1 for the perfect tetrahedron. As the local tetrahedral nature increases, S_kbecomes more closer to 1.

\[S_{k} = 1 - \frac{1}{3}\sum_{k=1}^{4}\frac{(r_{k} - \bar{r})^2}{4\bar{r}^2}\]

S_k = Translational tetrahedral order parameter

r_k = Radial distance from the cental Oxygen atom to the k th peripheral closest neighbor

\(\bar{r}\) = Arithmatic mean of the four radial distances

$order test.xyz -t tto -c 'OW' -f 5

You can get the average S_kvalue for your system by getting the average value of the raw_data output file.

Average value for S_kfor the example is 0.998892128

Asphericity of the Voronoi Cell (AVC)

Asphericity parameter (\(\eta\)) can be used to characterize the shape of the Voronoi polyhedron. This value is independent of the size of the polyhedron. The value of \(\eta\) for a perfect sphere the is 1, for ice is 2.25 and for a regular tetrahedron it is 3.31. [Duboué-Dijon2015]

\[\eta = \frac{A^3}{36\pi V^2}\]

\(\eta\) = Asphericity parameter

A = Area of the polyhedron

V = Volume of the polyhedron

$order test.xyz -t avc -c 'OW' -f 5

[Duboué-Dijon2015]

DOI: 10.1021/acs.jpcb.5b02936

API Reference

order package

Submodules

order.XYZ module

XYZ trajectory reader

class order.XYZ.XYZLoader(filename)

Bases: object

close()

close XYZ file if it was open

read_all_frames()

read all frames of XYZ trajectory

read_n_frames()

get the starting position of each frame

read_next_frame(frame)

read a frame of XYZ trajectory

order.avc module

class order.avc.VoronoiCell(filename, center, bins=100)

Bases: order.oto.Orientational

asphericity of the Voronoi cell

asphericity(freq=1)

compute asphericity of the Voronoi cell

compute_vc(points)

compute the Voronoi cell

polyhedron(coords, j, L)

find the polyhedron for center molecule

wrap_box(c_coord, coords, L)

wrap the simulation box

order.lsi module

order.order module

order.oto module

Orientational Tetrahedral Order q

class order.oto.Orientational(trajectory, center, bins=100)

Bases: object

orientational tetrahedral order parameter

four_neighbors(coords, L)

compute four nearest water oxygen neighbors

orientational_param(freq=1)

compute orientational order parameter

out_put(taskname='oto', param_name='Q')

output raw data and distribution

order.plot module

class order.plot.plot(filename, taskname)

Bases: object

plotting

plot_distribution()

plot distribution

plot_ionic()

plot distribution

order.tto module

Translational Tetrahedral Order Sk

class order.tto.Translational(filename, center, bins=100)

Bases: order.oto.Orientational

translational tetrahedral order parameter

translational_param(freq=1)

compute translational order parameter

order.util module

order.util.cos_angle(v1, v2)

compute the cos angle of two giving vectors

order.util.output_end(t_start, t_end)

print total running time

order.util.output_interface_info(input_info)

print interface task information

order.util.output_ionic_info(input_info)

print ionic conductivity task information

order.util.output_system_info(filename, n_atoms, n_frames)

print system information

order.util.output_task(name, freq, bins, center)

print task information

order.util.output_welcome()

print welcome information

order.util.pbc(dx, dy, dz, L)

periodic boundary conditions

Module contents

Order

Getting started

Installation:

$ pip install iorder

or

$ git clone https://github.com/ipudu/order
$ cd order
$ python setup.py install

Running:

# calculate bar parmeter for center atom of O
$ order foo.xyz -t bar -c 'O' -f 100 -b 100

Feature Support

Order is ready to calculate several geometric order parameters:

• Orientational Tetrahedral Order
• Translational Tetrahedral Order
• Asphericity of the Voronoi Cell
• Ionic Conductivity
• and more

Contributing

Contributions to this library are always welcome and highly appreciated.

License

MIT - See the LICENSE for more information.