This repository has been archived by the owner on Jun 2, 2022. It is now read-only.
Create structure-similarity.md #36
Merged
Conversation
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
tschaume
suggested changes
Jan 24, 2019
| We use a novel method called CrystallNN to find near(est) neighbors in periodic structures. While the method will be introduced shortly[^3], it is already available through the python package [pymatgen](https://github.com/materialsproject/pymatgen). | ||
|
|
||
| ## Site Fingerprints | ||
| The second step of the structure similarity calculation is the computation of a crystal site fingerprint, $v^{site}$, for each site in the two structures. The fingerprint is a 61-dimensional vector in which each element carries information about the local coordination environment computed with the *site* module of the python package [matminer](https://github.com/hackingmaterials/matminer). For example, the first two elements "wt $\ce{CN1}$" and "single bond $\ce{CN1}$" provide estimates of the likelihood (or weight) of how much the given site should be considered 1-fold coordinated (i.e., *w*$|_{CN=1}$). The third element "wt $\ce{CN2}$" provides a 2-fold coordination likelihood, whereas the fourth element "L-shaped $\ce{CN2}$" holds the resemblance similarity to an L-shaped coordination geometry (also called local structure order parameter) given that we find a coordination configuration with 2 atoms ($q_{L}|_{CN=2}$). The local structure order parameters can assume values between 0, meaning that the observed local environment has no resemblance with the target motif to which it is compared, and 1, which stands for perfect motif match. The remaining elements are: "water-like $\ce{CN2}$," "bent 120 degrees $\ce{CN2}$," "bent 150 degrees $\ce{CN2}$," "linear $\ce{CN2}$," "wt $\ce{CN3}$," "trigonal planar $\ce{CN3}$," "trigonal non-coplanar $\ce{CN3}$," "T-shaped $\ce{CN3}$," "wt $\ce{CN4}$," "square co-planar $\ce{CN4}$," "tetrahedral $\ce{CN4}$," "rectangular see-saw-like $\ce{CN4}$," "see-saw-like $\ce{CN4}$," "trigonal pyramidal $\ce{CN4}$," "wt $\ce{CN5}$," "pentagonal planar $\ce{CN5}$," "square pyramidal $\ce{CN5}$," "trigonal bipyramidal $\ce{CN5}$," "wt $\ce{CN6}$," "hexagonal planar $\ce{CN6}$," "octahedral $\ce{CN6}$," "pentagonal pyramidal $\ce{CN6}$," "wt $\ce{CN7}$," "hexagonal pyramidal $\ce{CN7}$," "pentagonal bipyramidal $\ce{CN7}$," "wt $\ce{CN8}$," "body-centered cubic $\ce{CN8}$," "hexagonal bipyramidal $\ce{CN8}$," "wt $\ce{CN9}$," "q2 $\ce{CN9}$," "q4 $\ce{CN9}$," "q6 $\ce{CN9}$," "wt $\ce{CN10}$," "q2 $\ce{CN10}$," "q4 $\ce{CN10}$," "q6 $\ce{CN10}$," "wt $\ce{CN11}$," "q2 $\ce{CN11}$," "q4 $\ce{CN11}$," "q6 $\ce{CN11}$," "wt $\ce{CN12}$," "cuboctahedral $\ce{CN12}$," "q2 $\ce{CN12}$," "q4 $\ce{CN12}$," "q6 $\ce{CN12}$," "wt $\ce{CN13}$," "wt $\ce{CN14}$," "wt $\ce{CN15}$," "wt $\ce{CN16}$," "wt $\ce{CN17}$," "wt $\ce{CN18}$," "wt $\ce{CN19}$," "wt $\ce{CN20}$," "wt $\ce{CN21}$," "wt $\ce{CN22}$," "wt $\ce{CN23}$," and "wt $\ce{CN24}$." Note that $q_{n}$ refers to Steinhardt bond orientational order parameter of order *n*. The resulting site fingerprint is thus defined as: |
There was a problem hiding this comment.
The math in this paragraph doesn't come out right at all when rendered.
|
|
||
| ## Site Fingerprints | ||
| The second step of the structure similarity calculation is the computation of a crystal site fingerprint, $v^{site}$, for each site in the two structures. The fingerprint is a 61-dimensional vector in which each element carries information about the local coordination environment computed with the *site* module of the python package [matminer](https://github.com/hackingmaterials/matminer). For example, the first two elements "wt $\ce{CN1}$" and "single bond $\ce{CN1}$" provide estimates of the likelihood (or weight) of how much the given site should be considered 1-fold coordinated (i.e., *w*$|_{CN=1}$). The third element "wt $\ce{CN2}$" provides a 2-fold coordination likelihood, whereas the fourth element "L-shaped $\ce{CN2}$" holds the resemblance similarity to an L-shaped coordination geometry (also called local structure order parameter) given that we find a coordination configuration with 2 atoms ($q_{L}|_{CN=2}$). The local structure order parameters can assume values between 0, meaning that the observed local environment has no resemblance with the target motif to which it is compared, and 1, which stands for perfect motif match. The remaining elements are: "water-like $\ce{CN2}$," "bent 120 degrees $\ce{CN2}$," "bent 150 degrees $\ce{CN2}$," "linear $\ce{CN2}$," "wt $\ce{CN3}$," "trigonal planar $\ce{CN3}$," "trigonal non-coplanar $\ce{CN3}$," "T-shaped $\ce{CN3}$," "wt $\ce{CN4}$," "square co-planar $\ce{CN4}$," "tetrahedral $\ce{CN4}$," "rectangular see-saw-like $\ce{CN4}$," "see-saw-like $\ce{CN4}$," "trigonal pyramidal $\ce{CN4}$," "wt $\ce{CN5}$," "pentagonal planar $\ce{CN5}$," "square pyramidal $\ce{CN5}$," "trigonal bipyramidal $\ce{CN5}$," "wt $\ce{CN6}$," "hexagonal planar $\ce{CN6}$," "octahedral $\ce{CN6}$," "pentagonal pyramidal $\ce{CN6}$," "wt $\ce{CN7}$," "hexagonal pyramidal $\ce{CN7}$," "pentagonal bipyramidal $\ce{CN7}$," "wt $\ce{CN8}$," "body-centered cubic $\ce{CN8}$," "hexagonal bipyramidal $\ce{CN8}$," "wt $\ce{CN9}$," "q2 $\ce{CN9}$," "q4 $\ce{CN9}$," "q6 $\ce{CN9}$," "wt $\ce{CN10}$," "q2 $\ce{CN10}$," "q4 $\ce{CN10}$," "q6 $\ce{CN10}$," "wt $\ce{CN11}$," "q2 $\ce{CN11}$," "q4 $\ce{CN11}$," "q6 $\ce{CN11}$," "wt $\ce{CN12}$," "cuboctahedral $\ce{CN12}$," "q2 $\ce{CN12}$," "q4 $\ce{CN12}$," "q6 $\ce{CN12}$," "wt $\ce{CN13}$," "wt $\ce{CN14}$," "wt $\ce{CN15}$," "wt $\ce{CN16}$," "wt $\ce{CN17}$," "wt $\ce{CN18}$," "wt $\ce{CN19}$," "wt $\ce{CN20}$," "wt $\ce{CN21}$," "wt $\ce{CN22}$," "wt $\ce{CN23}$," and "wt $\ce{CN24}$." Note that $q_{n}$ refers to Steinhardt bond orientational order parameter of order *n*. The resulting site fingerprint is thus defined as: | ||
| $$ |
There was a problem hiding this comment.
This math doesn't get rendered either
| ## Structure Fingerprints | ||
| The fingerprints from sites in a given structure are subsequently statistically processed to yield the minimum, maximum, mean, and standard deviation of each coordination information element. The resultant ordered vector defines a structure fingerprint, $v^{struct}$: | ||
|
|
||
| $$ |
| ## Structure Distance/Dissimilarity | ||
| Finally, structure similarity is determined by the distance, *d*, between two structure fingerprints $v_{i}^{struct}$ and $v_{j}^{struct}$: | ||
|
|
||
| $$ |
|
|
||
| Below is a python code snippet that allows you to quickly reproduce above results. You will need to install [pymatgen](https://github.com/materialsproject/pymatgen) and [matminer](https://github.com/hackingmaterials/matminer) for this to work. Both are easily accessible via the [Python Package Index](https://pypi.python.org/pypi). | ||
|
|
||
| ```python |
There was a problem hiding this comment.
maybe long lines can be shortened to avoid having to scroll horizontally?
| [^3]: H. Pan, J. Dagdelen, N. E. R. Zimmermann, A. Jain, in preparation (2018) | ||
|
|
||
| ## Authors | ||
| Nils Zimmermann, Donny Winston, Handong Ling, Oxana Andriuc |
There was a problem hiding this comment.
make authors an unnumbered list
Sign up for free
to subscribe to this conversation on GitHub.
Already have an account?
Sign in.
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
@tschaume ready to merge
#4