3.3. lnη (T ,P ,I )-QSPR model

The lnη (T ,P ,I )-QSPR model was built to predict η as Eq. (16). The Detailed parameter values are shown in Table C2 of Supporting Information (atomic-distribution-matrix.docx).

n = 9238, R ²= 0.9100,Q ² _LOCO = 0.8863,Q ² _LOAO = 0.8866;

n _training = 7352; ​R ²_training = 0.9091; MAE_training =0.3276 Pas;

n _testing = 1886; ​R ²_testing = 0.9108; MAE_testing =0.3232 Pas;

where, I _IL, I _C andI _A represent the norm index of ILs, cation and anion, respectively. n _C andn _A are the number of cations and anions.

The results of statistical parameters showed that this η model has high R ² and low MAE, which demonstrated the advanced accuracy of the model in predicting η . The experimental and calculated η values from the model expressed in Eq. (16) are shown in Table S2 of Supporting Information (exp-cal-values.xlsx).

3.4.1. Model validation

Internal validation. The distribution of cations and anions as shown in Figures 5a-b. The distribution of cations in theη dataset is more varied and more even than anions. The common anion, [N(SO2CF3)2], accounts for 34.49% of the η dataset, and it is worth noting that 255 different cations are combined with [N(SO2CF3)2]. So, the MAE (0.2034 Pas) of LOAO-CV is relatively lower for [N(SO2CF3)2]. In addition, it can be seen that all five cations with a relatively large data points have a low MAE. Figures 6a-b show the experimental versus calculated values scatter plots of LOCO-CV and LOAO-CV. Obviously, the satisfactory results of theQ ²_LOCO (0.8863) andQ ²_LOAO (0.8866) indicate that the η model has high stability and good prediction performance for ILs containing new cations and anions. The detailed results for internal validation of the η model are given in Table 5. It is clear that the Q ² for the LOO method (Q ²_LOILO = 0.8908 andQ ²_LODPO = 0.9076) are much higher than the Q ² for LOIO (Q ²_LOCO = 0.8863 andQ ²_LOAO = 0.8866), and the MAE for the LOO method (MAE_LOILO = 0.3558 Pas and MAE_LODPO = 0.3300 Pas) are lower than the MAE for LOIO (MAE_LOCO = 0.3654 Pas and MAE_LOAO = 0.3677 Pas). This in turn suggests that the stability of the model validated by LOO-CV is limited to predicting ILs with known ionic types, while the model passed by the LOIO is more stable when faced with ILs containing unknown ionic types. In addition, the AE distributions of the lnη (T ,P ,I )-QSPR model, LOCO-CV and LOAO-CV are shown in Figure 6d. Here, the AE ranges for the both internal validations are roughly the same as the lnη (T ,P ,I )-QSPR model, and the errors of most data points are concentrated in 0 ~ 0.2 Pas, further demonstrating the outstanding stability of the lnη (T ,P ,I )-QSPR model.