# Calculate Root-mean-square deviation (RMSD) of Two Molecules Using Rotation

The root-mean-square deviation (RMSD) is calculated, using Kabsch algorithm (1976) or Quaternion algorithm (1991) for rotation, between two Cartesian coordinates in either `.xyz` or `.pdb` format, resulting in the minimal RMSD.

## Motivation

You have molecule A and B and want to calculate the structural difference between those two. If you just calculate the RMSD straight-forward you might get a too big of a value as seen below. You would need to first recenter the two molecules and then rotate them unto each other to get the true minimal RMSD. This is what this script does.

No Changes Re-centered Rotated   RMSD 2.50 RMSD 1.07 RMSD 0.25

## Citation

• Implementation:
Calculate Root-mean-square deviation (RMSD) of Two Molecules Using Rotation, GitHub, https://awesomeopensource.com/project/charnley/rmsd, <git commit hash or version number>
• Kabsch algorithm:
Kabsch W., 1976, A solution for the best rotation to relate two sets of vectors, Acta Crystallographica, A32:922-923, doi: http://dx.doi.org/10.1107/S0567739476001873
• Quaternion algorithm:
Michael W. Walker and Lejun Shao and Richard A. Volz, 1991, Estimating 3-D location parameters using dual number quaternions, CVGIP: Image Understanding, 54:358-367, doi: http://dx.doi.org/10.1016/1049-9660(91)90036-o

Please cite this project when using it for scientific publications.

## Installation

Easiest is to get the program vis PyPi under the package name `rmsd`,

```pip install rmsd
```

```git clone https://github.com/charnley/rmsd
```

There is only one Python file, so you can also download calculate_rmsd.py and put it in your bin folder.

```wget -O calculate_rmsd https://raw.githubusercontent.com/charnley/rmsd/master/rmsd/calculate_rmsd.py
chmod +x calculate_rmsd
```

## Usage examples

Use `calculate_rmsd --help` to see all the features. Usage is pretty straight forward, call `calculate_rmsd` with two structures in either `.xyz` or `.pdb`. In this example Ethane has the exact same structure, but is translated in space, so the RMSD should be zero.

```calculate_rmsd tests/ethane.xyz tests/ethane_translate.xyz
```

It is also possible to ignore all hydrogens (useful for larger molecules where hydrogens move around indistinguishable) and print the rotated structure for visual comparison. The output will be in XYZ format.

```calculate_rmsd --no-hydrogen --print tests/ethane.xyz tests/ethane_mini.xyz
```

If the atoms are scrambled and not aligned you can use the `--reorder` argument which will align the atoms from structure B unto A. Use `--reorder-method` to select what method for reordering. Choose between Hungarian (default), distance (very approximate) and brute force (slow).

```calculate_rmsd --reorder tests/water_16.xyz tests/water_16_idx.xyz
```

It is also possible to use RMSD as a library in other scripts, see example.py for example usage.

## Problems?

Submit issues or pull requests on GitHub.

## Contributions

Please note that we are using `black` with line length of 99. Easiest way to abide to the code standard is to install the following package.

```pip install pre-commit
```

and run the following command in your repository

```pre-commit install
```

This will install a hook in your git and re-format your code to adhere to the standard. As well as check for code quality.

Get A Weekly Email With Trending Projects For These Topics
No Spam. Unsubscribe easily at any time.
Python (819,784
Bash (18,782
Structure (10,142
Atom Editor (8,173
Rotation (5,094
Molecule (2,272
Pdb (1,049
Reordering (355
Assignment (290
Xyz (44
Rmsd (18