This repository contains Python scripts for analyzing the local geometrical relationship between I⁻ ions and PS₄³⁻ tetrahedra in Li₂S–P₂S₅–LiI glass trajectories.

For each P atom, nearby I⁻ ions are classified according to the number of S atoms from the same PS₄³⁻ tetrahedron located within a specified I–S cutoff distance.

The resulting I⁻ spatial-density distributions are exported as Gaussian cube files and visualized as three-dimensional isosurfaces using Mayavi.

Analysis Concept

For a given I⁻ ion and a given PS₄³⁻ tetrahedron, the number of nearby S atoms is defined as:

s_count = number of S atoms within 4.7 Å from I⁻

The I⁻ configuration is classified as follows:

Classification	s_count	Geometrical interpretation
Zero-type	0	I⁻ is not close to any S atom of the reference PS₄³⁻ unit.
Corner-type	1	I⁻ is located near one S vertex of the PS₄³⁻ tetrahedron.
Edge-type	2	I⁻ is located near two S atoms forming one tetrahedral edge.
Three-type	3	I⁻ is located near three S atoms of the same PS₄³⁻ unit.

The terms corner-type and edge-type describe geometrical proximity only. They do not imply bond sharing or atom sharing between I⁻ and PS₄³⁻ units.

Workflow

LAMMPS trajectory
      |
      v
dump2cube_edge_corner.py
      |
      +-- PS₄_I_All.cube
      +-- PS₄_I_zero.cube
      +-- PS₄_I_corner.cube
      +-- PS₄_I_edge.cube
      +-- PS₄_I_three.cube
      |
      v
cube2mayavi_edge_corner.py
      |
      v
Colored 3D isosurface visualization

Files

File	Description
`dump2cube_edge_corner.py`	Reads a LAMMPS trajectory, aligns PS₄³⁻ units, classifies nearby I⁻ ions, and generates cube files.
`cube2mayavi_edge_corner.py`	Visualizes multiple classified I⁻ cube files using different colors.
`050Li3PS4-050LiI.lammpstrj`	Example LAMMPS trajectory for a Li₂S–P₂S₅–LiI glass.
`050Li3PS4-050LiI_PS4_I_All.cube`	Spatial density of the four nearest I⁻ ions around each P atom.
`050Li3PS4-050LiI_PS4_I_zero.cube`	Spatial density of zero-type I⁻ configurations.
`050Li3PS4-050LiI_PS4_I_corner.cube`	Spatial density of corner-type I⁻ configurations.
`050Li3PS4-050LiI_PS4_I_edge.cube`	Spatial density of edge-type I⁻ configurations.
`050Li3PS4-050LiI_PS4_I_three.cube`	Spatial density of three-type I⁻ configurations.

Requirements

Python packages

The scripts require Python 3 and the following packages:

NumPy
Mayavi
VTK
Traits
PyQt5 or PySide6

Mayavi is generally easiest to install through conda-forge.

conda create -n ps4-iodide python=3.10
conda activate ps4-iodide
conda install -c conda-forge numpy mayavi pyqt

Alternatively, NumPy can be installed with pip:

pip install numpy

Input Trajectory Format

dump2cube_edge_corner.py expects a LAMMPS trajectory containing the following atom columns:

ITEM: ATOMS id type element xu yu zu mol

The trajectory must contain at least the following elements:

The script assumes that P and S atoms belonging to the same PS₄³⁻ tetrahedron have the same molecule ID (mol).

Periodic boundary conditions are applied when calculating relative atomic positions.

Analysis Procedure

For every trajectory frame, the following procedure is performed.

Each P atom is selected as the center of a reference PS₄³⁻ tetrahedron.
The nearest I⁻ ion is used to define the orientation of the PS₄³⁻ unit.
The S atom farthest from the nearest I⁻ ion is aligned with the z axis.
A second S atom is used to fix the rotation around the z axis.
The closest I⁻ ions are rotated into the common PS₄³⁻ reference frame.
I⁻ ions are classified using the number of S atoms within 4.7 Å.
The classified I⁻ coordinates are accumulated over all P atoms and trajectory frames.
Three-dimensional histograms are exported as Gaussian cube files.

Normalization

The density fields for zero-type, corner-type, edge-type, and three-type I⁻ configurations are normalized by the total number of I⁻ coordinates used for the overall I⁻ distribution.

Therefore, the relative density of each classified field reflects both:

the spatial distribution of the configuration, and
the relative occurrence of that configuration.

Usage

Generate Cube Files

python dump2cube_edge_corner.py \
  -i 050Li3PS4-050LiI.lammpstrj \
  -m 160 160 160 \
  -cut 8

Arguments:

Argument	Description
`-i`, `--trjfile`	Input LAMMPS trajectory file.
`-m`, `--mesh`	Number of grid points along the x, y, and z directions.
`-cut`, `--cutoff`	Spatial cutoff distance around the reference P atom in Å.

Expected output files:

050Li3PS4-050LiI_PS4_I_All.cube
050Li3PS4-050LiI_PS4_I_zero.cube
050Li3PS4-050LiI_PS4_I_corner.cube
050Li3PS4-050LiI_PS4_I_edge.cube
050Li3PS4-050LiI_PS4_I_three.cube

Visualize Classified I⁻ Density Fields

python cube2mayavi_edge_corner.py \
  -i 050Li3PS4-050LiI_PS4_I_zero.cube \
     050Li3PS4-050LiI_PS4_I_corner.cube \
     050Li3PS4-050LiI_PS4_I_edge.cube \
     050Li3PS4-050LiI_PS4_I_three.cube \
  -iso 1.2e-09

The script assigns colors based on the file name:

Classification	Color
Zero-type	Blue
Corner-type	Green
Edge-type	Red
Three-type	Yellow

The reference PS₄³⁻ tetrahedron is shown with:

Object	Color
P atom	Purple
S atoms	Yellow
P–S bonds	Gray

Output

Each Gaussian cube file contains:

A reference PS₄³⁻ tetrahedron
- P atom at the origin
- Four S atoms in the aligned coordinate system
A three-dimensional spatial-density field of the selected I⁻ category

The cube files can be visualized using:

Mayavi
VMD
ParaView
PyMOL
Other software supporting Gaussian cube files

Notes and Limitations

The I–S cutoff for classification is fixed at 4.7 Å in the script.
The cube files represent accumulated spatial-density distributions.
The current analysis uses the nearest I⁻ ion to define the orientation of each PS₄³⁻ tetrahedron.
The script searches the 15 nearest I⁻ ions around each P atom when classifying zero-, corner-, edge-, and three-type configurations.
The output filename is generated from the input trajectory name. The current implementation expects an input filename containing LiI.
The current trajectory parser is primarily intended for orthorhombic simulation cells.
The Mayavi visualization requires a GUI-capable Python environment.

License

This repository is intended for academic and research use.

README.org Unescape Escape

PS₄³⁻-Centered I⁻ Geometry Analysis in Li₂S–P₂S₅–LiI Glasses

Overview