Find Nodal Plane

Find the nodal plane of a helical molecular orbital.

utilities.py contains a function used to read .cube files that is modified from the Atomic Simulation Codebase (ASE) codebase.

The "export" folder contains the source code for the helper file libread_cube.so. It's written in Rust.

Feel free to open an issue if you have any questions regarding the code or its usage!

Example

If we want to analyze the highest occupied molecular orbital (HOMO) of an [8]cumulene, we can use the following command to find the helical nodal plane.

First, we have to make sure that the atom and the MO has been aligned along the z-axis.

Next, we need to setup up the following folder structure:

molecule_folder
└── data
    └── homo.cube

Running the script will then create a folder called molecule_folder_homo with all the analyzed data in it.

Next, we run the following command.

python find_nodal.py 8_cumulene/homo.cube 6 12 2 --carbon-chain 12,11,6,4,2

where "6" is the center atom, "12" is the bottom atom and "2" is the top atom. The atoms listed after the --carbon-chain command is the chain that the slices will be aligned against. This is important for molecules where the helical MO is not following a straight carbon chain (such as dimethyl-spiro[4.4]nonatetraene).

Description of output files

All files that ends with .npy can be loaded with np.load(). The main result lies in angles.npy with a visualization of this data in angles.png. Some secondary visualization lies in jmol_export.spt. The rest of the files are mainly for debugging.

• angles.npy: Contains the angle between each succesive slice in units of degrees.
• angles.png: Plot of the cumulated sum of angles generated from the data in angles.npy
• atom_info.npy: Contains an array of [atoms, top_carbon, bottom_carbon, [center_x, center_y, center_z]]
  • atoms: An Atoms object containing information about the molecular system
  • {top,bottom}_carbon: Index of the top and bottom carbon, respectively.
  • [center_x, center_y, center_z]: A list of the x, y, and z-coordinate of the center atom.
• fitted_{x,y}.npy: Data points for the line that was fitted through the nodal plane. In other words, this data is the estimation of the nodal plane in a given slice.
• homo.cube: .cube file of the analyzed MO.
• jmol_export.spt: Contains information for Jmol to plot a visualization of the molecule, the analyzed MO, the found nodal plane as a yellow plane and the highest and lowest isovalue as a blue and red line, respectively.
• jmol_plane_data.npy: Information to plot the nodal plane in Jmol.
• max_iso.npy: The maximum isovalue in a given radius-filtered slice.
• max_{neg,pos}_iso.npy: Highest negative and positive isovalue in each radius-filtered slice. Is used to generate the Jmol visualization.
• min_iso_val.npy: The minimum isovalue in each radius-filtered slice.
• phis.npy: The angle between (0,0) and the maximum positive isovalue in a given radius-filtered slice.
• planes.npy: A list of planes sorted according to z-coordinate. Each plane contains a list of coordinates which contains x-, y-, z-coordinates and isovalue.
• {x,y}_cross.npy: The x-, and y-coordinates of where each slice goes from positive to negative. Calculated as the midway point between the closest positive and negative number.
• xyz_vec.npy: Contains the unit vectors of each dimension.

Options

--show-slices

Show each slice that has been generated from the .cube file. Default is False. It will open each slice in a new matplotlib instance so be aware that it will not work if you're connected to a remote server. You also have to be aware that if the analyzed MO have been dumped on a fine grid, you'll open a lot of matplotlib-instances which might tank your computer.

It opens all plots at the same time so it will probably tank your computer if the MO have been dumped on a fine grid.

--export-gif

Export the slices as a .gif. Default is False. This option will try to export all slices used in the analysis as a .gif.

Hückel example

The scripthuckel_model.py calculates the helicality of a chosen MO for a Hückel model of an [8]cumulene. The length of the cumulene can be extended by changing dim.