add references for ASI

Author: naik-aakash

README.md

@@ -92,6 +92,10 @@ If you use any of the following Featurizers, also cite the respective papers:
 * `FeaturizeCharges`: R. Nelson, C. Ertural, P. C. Müller, R. Dronskowski, in Comprehensive Inorganic Chemistry III, *Elsevier*, **2023**, pp. 141–201. [https://doi.org/10.1016/B978-0-12-823144-9.00120-5](https://doi.org/10.1016/B978-0-12-823144-9.00120-5)
 * `FeaturizeIcoxxlist`: V. L. Deringer, W. Zhang, M. Lumeij, S. Maintz, M. Wuttig, R. Mazzarello, R. Dronskowski, *Angewandte Chemie International Edition 2014*, *53*, 10817–10820. [https://doi.org/10.1002/anie.201404223](https://doi.org/10.1002/anie.201404223)
 
+Cite the following paper as well if using aysmmetry index:
+
+F. Belli, E. Zurek, I. Errea, 2025 [https://arxiv.org/abs/2501.14420](https://arxiv.org/abs/2501.14420).
+
 Please cite [pymatgen](https://github.com/materialsproject/pymatgen), [Lobster](https://schmeling.ac.rwth-aachen.de/cohp/index.php?menuID=1), and [ChemEnv](https://doi.org/10.1107/S2052520620007994) correctly as well.
 
 

docs/fundamentals/index.ipynb

@@ -281,8 +281,9 @@
    ]
   },
   {
-   "metadata": {},
    "cell_type": "markdown",
+   "id": "a2f623edafa5efc9",
+   "metadata": {},
    "source": [
     "### ICOXX based features (ICOXX: ICOHP / ICOBI / ICOOP)\n",
     "\n",
@@ -292,9 +293,18 @@
     "\n",
     "In the formula above, $\\delta$ is the Dirac delta function, $r$ is the distance between atoms A and B, and $B_{\\mathrm{AB}}$ is the bond strength between atoms A and B. The bond strength can be ICOHPs, ICOBIs, or ICOOPs. The BWDF is thus a histogram of bond strengths as a function of bond length. One can compute this for entire structure, for each unique atom pair in the structure, per site or per bond label.\n",
     "\n",
-    "Here, from the BWDF mainly statistical features like mean, standard deviation, skewness, kurtosis, weighted mean, and weighted standard deviation are computed.\n"
-   ],
-   "id": "a2f623edafa5efc9"
+    "Here, from the BWDF mainly statistical features like mean, standard deviation, skewness, kurtosis, weighted mean, and weighted standard deviation are computed.\n",
+    "\n",
+    "As proposed by [F. Belli, E. Zurek, I. Errea, 2025](https://arxiv.org/abs/2501.14420), one can also generate the asymmetry index (ASI) of the local bonding environment using ICOBI / ICOHP / ICOOP for a site using following formulation\n",
+    "\n",
+    "$$\n",
+    "\\boldsymbol{V}_{x} = \\frac{1}{B_{x}} \\sum_{\\alpha=1}^{B_{x}} \\mathrm{iCOXX}(x, \\alpha) \\, \\boldsymbol{i}_{x \\alpha}\n",
+    "$$\n",
+    "\n",
+    "$V_x$, is computed for each atom $x$ in the structure.  The vector is the sum of the iCOXX values for all of the interactions between an atom and its  neighboring atoms $\\alpha$ (iCOXX(x, $\\alpha$)) weighted by a unit vector, $i_{xα}$, which denotes the direction of  each interaction. This summation is performed over all neighbors for which the iCOXX values fall  above a user-defined threshold, and divided by the number of interactions considered, $B_x$.\n",
+    "\n",
+    "One can then get statistics of ASI from all sites in the structure."
+   ]
   }
  ],
  "metadata": {