# Machine-Learning Model Prediction of Ionic Liquids Melting Points
## 3 Results
### The Important Molecular Descriptors  
To further examine which variables or molecular features influence the model's performance, the top ranking molecular features for the DL- model were computed based on the permutation importance as implemented in the EL15 (EL15 0.11.0) library [51]. Here, it is important to note that although the influence and correlation of the different molecular descriptors or features on the melting points of ILs is not directly obvious, their contributive effects are nonetheless comprehensible by conducting a feature importance analysis. Based on the DL-model (Table 1) and features filtering and ranking scores (Figure S2), important molecular descriptors that have a significant impact on the target property (i.e., \(T_{m}\)) can be obtained. Table 2 shows the top 10 most important molecular features or descriptors that have large impacts on the melting points of ILs obtained from three complementary correlation models, i.e., Pearson, Spearman and Kendall. The top 20 most influential molecular descriptors based on these correlation models can be found in Figure S2 and Table S2. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Reference** & **N** & **Features** & **Model** & **RMSE** & \(R^{2}\) \\ \hline
[42] & 799 & 80 & GC & 24.86 & 0.82 \\
[43] & 799 & 40 & ANN & 33.33 & 0.54 \\
[44] & 808 & 12 & QSPR & 26.85 & 0.72 \\
[45] & 2212 & 226 & RF & 45.00 & 0.66 \\
[46] & 2212 & 5 & KRR & 38.54 & 0.76 \\ This work & 1253 & 137 & DL & 32.88 & 0.90 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The performance metrics for predictions of the ILs melting temperature obtained in this work compared with that of the literature. N refers to the size of the entire dataset, which is the total number of ILs. GC refers to group contribution; ANN is artificial neural network; QSPR is quantitative structure-property relationship; RF is random forest; KRR is kernel ridge regression. For the RMSE, the unit is in Kelvin (K). As shown in Table 2 and Table S2, a consistent finding regarding the topmost influential molecular descriptors can be found using three different correlation methods. To highlight the complementary molecular features, the molecular descriptors listed are colored based on descriptor types or models defined in the literature [23; 24; 35]. From these top 10 descriptors (Table 2), the important contributions from both cations and anions in ILs are captured and found to be closely related to geometrical structures, shapes, the size of the IL molecules, partial charges of IL cations or anions and the hydrogen bonds that influences intermolecular interactions. As shown in Table 2, the key molecular features found in the wide varieties of IL families in the datasets are the molecular descriptors related to the geometrical structures, branching and shapes or topological characters described by topological indices (e.g., DELS, MAXDP, S1K, S2K, etc.) and constitutional molecular weights and size (e.g., MW). For instance, the DELS is the topological indices is a representation of the measure of molecular electrotopological variation [52], which is related to the sum of overall atoms of the intrinsic state differences and could be interpreted as a measure of total charge transfer in ILs molecules. The S1K and S2K are the shape indices [53] which are a measure of the relative cyclicity of IL molecules, and are particularly relevant to cyclic compounds commonly found in IL cationic scaffolds (e.g., imidazolium, pyridinium, etc.). As another leading molecular descriptors, the P-VSA based molecular descriptors in Table 2 and Table S2 is based on atomic contributions to the van der Waals surface area, octanol-water partition coefficient (logP), molar refractivity and atomic partial charge-based [54] descriptors which encode the factors that could possibly influence the melting points of ILs, with a strong correlation to intermolecular hydrogen bonds and the hydrophobic and hydrophilic, polarizability, and electrostatic interaction of the ILs.