## 3 Results and Discussions
\begin{table}
\begin{tabular}{c c} \hline
**Deviation Descriptor** & **Description of Core Descriptor** \\ \hline \(\Delta\)(Ms)\({}_{sn}\) & Ms: Mean electrotopological state \\ \(\Delta\)(Dm)\({}_{te}\) & Dm: D total accessibility index, \\  & weighted by mass \\ \(\Delta\)(E1s)\({}_{sn}\) & E1s: 1 st component accessibility directional WHIM index, \\  & weighted by I-state \\ \(\Delta\)(MATS1e)\({}_{te}\) & MATS1e: Moran autocorrelation of lag 1, \\  & weighted by Sanderson electronegativity \\  & De: D total accessibility index, \\ \(\Delta\)(De)\({}_{co}\) & weighted by Sanderson electronegativity \\ \(\Delta\)(XLOGP2)\({}_{sn}\) & XLOGP2: Squared Wang octanol water partition coefficient \\  & GATS3m: Geary autocorrelation of lag 3, \\  & weighted by atomic masses \\  & MATS7v: Moran autocorrelation of lag 7, \\ \(\Delta\)(MATS7v)\({}_{sn}\) & weighted by atomic van der Waals volumes \\  & MATS8v: Moran autocorrelation of lag 8, \\  & weighted by atomic van der Waals volumes \\ \(\Delta\)(CONA)\({}_{co}\) & CONA: C(=O)-[nitrogen, aromatic attach] \\ \hline \end{tabular}
\end{table} 
Table 5: Description of the deviation descriptors in the linear L08 model. the fact that the lipophilicity-based descriptor \(\Delta(\text{XLOGP2})_{sn}\) was found to be positively correlated with the response variable of the model [33]. As depicted in Figure 5, some data points with high values of \(\Delta(\text{XLOGP2})_{sn}\) were indeed found to be toxic, whereas low values for this deviation descriptor were observed in non-toxic PPCPs. However, the mt-QSTR model itself suggests a more complex relationship between structural attributes and toxicity. Even though Ms is simply a constitutional descriptor, the second most significant descriptor of the model, \(\Delta(\text{Dm})_{te}\), is based on the 3D Weighted Holistic Invariant Molecular (WHIM) descriptor D total accessibility index (weighted by mass) [34]. WHIM descriptors represent the entire 3D-molecular structure in terms of size, shape, symmetry, and atom distribution. Previously, WHIM descriptors were recommended for environmental modeling [35]. Generally, the values of 3D WHIM descriptors depend strongly on the 3D conformations of chemical structures [36]. In this work, we relied on the semi-empirical quantum chemical technique for geometrical optimization of the dataset compounds. To check how the 3D conformations influence the quality of the generated model, we generated models with descriptors calculated from dataset compounds optimized using the molecular mechanics force field under OCHEM webserver's 'Rdkit' option. The new model showed significantly low predictivity for both sub-training and test sets (i.e., MCC values of 0.723 and 0.762, respectively). Additionally, the Dm descriptor is heavily dependent on the molecular density (molecular mass/molecular volume) of compounds. Significantly, the presence of heavy atoms (e.g., Cl, I) responsible for higher molecular density may increase the risk of environmental toxicity. This is exemplified in Figure 6, which shows correctly predicted toxic compounds with high values of \(\Delta(\text{Dm})_{te}\) and non-toxic compounds with low values of this descriptor. Conversely, non-toxic compounds lack such atoms. Simultaneously, another descriptor, \(\Delta(\text{De})_{cu}\), also based on a D-type WHIM descriptor, was negatively correlated to toxicity. The De descriptor is weighted by electronegativity, and thus, compounds with an increased number of polar atoms are less likely to induce aquatic toxicity. Figure 5: Examples of data points to explain the contribution of \(\Delta(\text{XLOGP2})_{sn}\) to aquatic toxicity. Interestingly, even though \(\Delta(\text{Ms})_{sn}\) was found to have the maximum influence on the model, it is not the only intrinsic state-weighted descriptor. The \(\Delta(\text{E1s})_{sn}\) is another WHIM descriptor that is weighted by the intrinsic state.