# Predicting Melting Points of Biofriendly Choline-Based Ionic Liquids with Molecular Dynamics
## 3 Results
### Annealing Temperature Rate Effect  
To be assured that the hysteresis effect does not affect our determined melting \"onset\" temperatures, we carried out annealing simulations with different temperature rates for those solid phases that yielded the predicted melting points. If the delayed phase transition, that we observe as non-linearity in \(D\)-\(T\) dependencies, is accompanied by superheating, then the predicted melting point should strongly depend on the simulation temperature increase regime.  
As can be seen in Figure 5, the annealing temperature rate indeed influences the evaluated melting point values. For most ILs, these values seem to converge, but for Choline Acesulfamate and Choline 2-Methylbutanoate the resulting dependence was unclear. Within subgroups shown in Figure 5A-D, except for these two ILs, the order of predicted \(T_{\text{M}}\) agrees with the experimental one. In case of superheating due to hysteresis, faster temperature rates should systematically produce higher melting point estimates which is not the case for our systems. Hence, it is possible that there is a hysteresis effect, but it does not severely affect our obtained results.  
Interestingly, in most cases faster temperature rates tended to yield underestimated predictions rather overestimated predictions, while the latter would be the expected if superheating effect occurred. We can speculate that rapid heating either causes local overheating or the velocity rescaling temperature coupling algorithm misbehaves at such extreme conditions. In any case it is concluded, that the temperature rate of \(10\text{ K}\cdot\text{ns}^{-1}\) used in this work is sufficient to provide accurate results.  
A linear regression line was added to Figure 5 to indicate trend in predicted melting point when the rate of melting is slowed. The most straightforward albeit expensive way to minimize the effect of hysteresis is to conduct longer simulations. Another way is to conduct simulations with different and not necessarily slower duration and extrapolate the results. We added a regression line to simulations with different time rates in Figure 5 to enable the estimation of extrapolated melting point by their intercept values at \(0\text{ K}\cdot\text{ns}^{-1}\).  
The root-mean-squared error of the extrapolated melting points prediction was 19-23 K, which is almost identical to the error of the regular predictions (18-24 K). It appears that most regression lines in Figure 5 tend to steer close to the experimental values than predictions at \(10\text{ K}\cdot\text{ns}^{-1}\), but there is a severe outlier--choline 2-methylbutanoate. With the exclusion of choline 2-methylbutanoate the root-mean-squared error of the extrapolated predictions is 12-18K (17-22 K for regular predictions). Individual melting points predicted from the extrapolated results are found in Table S1 in the Supplementary Materials.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Cation: Choline** & **Experimental** & **Predicted** & \(\Delta T_{\text{M}}\) \\
**Anion** & \(T_{\text{M}}\) (K) & \(T_{\text{M}}\) (K) & (K) \\ \hline Acesulfamate & 298 [23] & 341 & 43 \\ Acetate & 353 [11], 324 [14], 345 [15], 354\({}^{a}\) & 330 & \(-23,6,-15,-24\) \\ Benzoate & 320 [14] & 335 & 15 \\ Citrate & 345 [16], 376 [17], 378 \({}^{a}\) & 348 & \(3,-28,-30\) \\ Glutamate & 312 [38] & 328 & 16 \\ Ibuprofen & 342 [39] & 330 & \(-12\) \\ Isobutanoate & 308 [11], 341 \({}^{a}\) & 344 & \(36,3\) \\ Isovalerate & 334 \({}^{a}\) & 335 & 1 \\
2-Methylbutanoate & 363 \({}^{a}\) & 335 & \(-28\) \\ Saccharinate & 342 [23] & 347 & 5 \\ Salicylate & 323 [40] & 343 & 20 \\ TFSI & 306 [24] & 321 & 15 \\ \hline Acetylsalicylate & n/a & 341 & n/a \\ Lactate & n/a & 331 & n/a \\ Malonate & n/a & 329 & n/a \\ \hline \hline \end{tabular} \({}^{a}\)—measured in this work; n/a—data not available.  
\end{table}
Table 2: The experimental and predicted melting points (\(T_{\text{M}}\)) of choline cation-based ionic liquids and their difference (\(\Delta T_{\text{M}}\)).