I've been working on amorphous structures derived from a crystalline one (using MD) containing $N$ atoms. I want to prove that these structures are different and to quantify their "differentness". One could think of simply displaying the structures, but:
- I actually have 20 of them and I don't want to show them 2 by 2 (poor information density)
- This does not quantify these differences (the "differentness" metric)
I thought about calculating the RMS of the corresponding atom pairs distances using two different structures, but:
- I have to associate pairs so that the RMS is minimized
- A single atom cannot form two pairs
- A rotation and a shift (of unknown magnitude) should be allowed due to the periodic and symmetric nature of the reference cell to help minimizing the RMS
I've been working on this for a week with mitigated success: the algorithm is slow and incomplete, the execution time is too slow but it kinda works. But the algorithm(/method?) is too sensitive to outliers: when I compare 3 structures, 2 close from each other (visually) and one more different, I get almost the same RMS (due to outliers).
I think now that the RMS might not be a good idea after all, what figure/graph would you use to quantify the differences between these structures?