# Electric Field and Temperature Effects on the Ab Initio Spectroscopy of Liquid Methanol
## 3 Results and Discussion
This latter is defined as \(\delta=dOH-dO^{\prime}H\), where \(dOH\) is the OH covalent bond length of a reference molecule, whereas \(dO^{\prime}H\) represents the length of the H-bond(s) that the reference molecule donates, as depicted in the inset of Figure 5b. When the proton is transiently closer to the acceptor than to the donor oxygen, then \(\delta>0\). Figure 5 shows the probability distributions of \(\delta\) in bulk liquid methanol simulated by means of AIMD as a function of the field strength. For the sake of clarity, such a proton transfer coordinate has been restricted, during the post-processing analysis, in the region where the probability of finding a proton on a H-bond is maximum (i.e., \(\delta\geq-0.8\)). Moreover, since we are interested in evaluating eventual (partial) proton transfer events, the behavior of the distributions for \(\delta\to 0\) is highlighted by its logarithmic plot (Figure 5b). The range of field strengths here explored is not capable of dissociating statistically significant amounts of methanol molecules, as shown by the tails of the curves in Figure 5b and as also indicated elsewhere [50]. However, the application of intense static electric fields induces a sizable increase in the \"proton excursion\" events along the H-bonds, in that OH covalent bonds appear weakened by the field and hydrogen atoms get closer to the oxygen atom of the neighboring H-bonded methanol molecule when the field is increased, as shown in Figure 5a,b. Such evidence is sufficient to give a rationale to the observed field-induced red-shift of the OH-stretching band of the IR spectrum of Figure 1.3  
Similarly to the OH bond, the CO covalent bond is also elongated by the field, as shown in Figure 6a. In particular, the maximum of the distribution of this intramolecular length shifts toward larger values as the field intensity is increased, indicating that \begin{table}
\begin{tabular}{c c} \hline
**E Field (V/Å)** & **\textless{\(\mathbf{n_{HB}}\)\textgreater{}}** \\ \hline
0.00 & 2.04 \\
0.05 & 1.72 \\
0.10 & 1.43 \\
0.15 & 1.49 \\
0.20 & 1.50 \\
0.25 & 1.57 \\
0.30 & 1.63 \\ \hline \end{tabular}
\end{table} 
Table 1: Average number of H-bonds per molecule at different field strengths. Figure 5: Probability distributions of the proton-sharing coordinate \(\delta\) between methanol molecules under linear (**a**) and logarithmic (**b**) plots at different electric field strengths as detailed in the legends. In the inset of (**b**), the definition of the coordinate, which is determined for every hydrogen atom in the system involved in a tight H-bond, is shown. methanol molecules are stretched by the application of the field. Thus, the field not only re-orients progressively larger portions of molecules toward its direction [49], but also sizably stretches methanol covalent bonds, a circumstance dramatically enhancing the chemical reactivity of the sample. It is worth noting that such an effect is not affordable with the mere variation in the external temperature, as shown in Figure 6b, where the CO bond length distributions at different temperatures and in the absence of the field are plotted. Such qualitative behavior of the CO bond length distributions, determined either under the field action or under different temperatures, is quantitatively examined in Figure 7. In particular, Figure 7a shows the average CO bond length as a function of the field strength and, in the inset, the same quantity is plotted against the temperature. Whereas the application of the field--along with its polarization effects--progressively stretches the CO bond of the methanol molecules, this latter length is somehow insensitive to the increase/decrease in the temperature of the sample. Such evidence clearly explains not only the observed field-induced red-shift of the CO-stretching band of the IR spectrum shown in Figure 2, but also the independence (at least in the range of the explored temperatures) of the same band upon varying the temperature of the liquid (Figure 3).