Novel electrochemical route to cleaner fuel dimethyl ether

Methanol, the simplest alcohol, and dimethyl ether, the simplest ether, are central compounds in the search for alternative “green” combustion fuels. In fact, they are generally considered as the cornerstones of the envisaged “Methanol Economy” scenario, as they are able to efficiently produce energy in an environmentally friendly manner. However, despite a massive amount of research in this field, the synthesis of dimethyl ether from liquid methanol has never so far been reported. Here we present a computational study, based on ab initio Molecular Dynamics, which suggests a novel synthesis route to methanol dehydration – leading thus to the dimethyl ether synthesis – through the application of strong electric fields. Besides proving the impressive catalytic effects afforded by the field, our calculations indicate that the obtained dimethyl ether is stable and that it can be progressively accumulated thanks to the peculiar chemical pathways characterising the methanol reaction network under electric field. These results suggest that the experimental synthesis of dimethyl ether from liquid methanol could be achieved, possibly in the proximity of field emitter tips.

With the aim to partially understand the physical reasons behind the observation that DME molecules can be regarded as a sort of "sink" or "chemical well" of the methanol reaction network under electric field, a systematic investigation of the enthalpy of the system has been carried out. In standard ab initio Molecular Dynamics (AIMD) simulations this latter quantity is determined as H = E(KS) + P · V , where E(KS) is the Kohn-Sham total energy of the system, P is the pressure, and V is the volume which holds a fixed value within our NVT simulation. In particular, the total enthalpy of the system has been sampled for each event of formation of a DME molecule (in symbiosis, of course, with the release of a water molecule; i.e., reaction (3) of the main text). Moreover, the same calculation has been performed for the synthesis of formaldehyde (along with methane and water; i.e., reaction (1) of the main text). The sampling process has been conducted for dynamics of the order of 1 ps subsequent to a given formation event. The time-scale, or better the temporal cutoff for the accumulation of data, is clearly dependent on the eventual occurrence of other chemical transformations in the numerical sample and, for the formaldehyde case, it depends also on the occurrence that the simplest aldehyde undergoes to further reactions. In such a way, the variation of the total enthalpy of the system can be entirely ascribed either to the formation of DME or to the formaldehyde synthesis. Therefore, the accumulation of the statistical points has been carried out for three different field strengths: 0.60 V/Å, 0.65 V/Å, and 0.70 V/Å. The results, shown in Fig. S1, indicate that the formation of DME molecules + 3 kcal/mol -22 kcal/mol -28 kcal/mol FIG. 1. Distributions of the total enthalpy of the whole system (i.e., composed by 192 atoms) ascribable to the DME (black curves) and to the formaldehyde (red curves) formation. Although at a field strength of 0.60 V/Å (left) the creation of formaldehyde is very slightly favoured with respect to that of DME (i.e., by 3 kcal/mol), at higher field intensities the average enthalpy of the system associated with the DME synthesis is 22 kcal/mol and 28 kcal/mol, at 0.65 V/Å (center) and at 0.70 V/Å (right), respectively, lower than that characterising the formaldehyde formation.
becomes progressively more favoured with respect to that of the simplest aldehyde as the field intensity is increased. In fact, the difference in the average enthalpy of the system associated either to the formation of DME or to that of formaldehyde gets more pronounced with the field strength. This way, the synthesis of DME will be preferred, from the energetic side, at those regimes. Finally, once formed, DME molecules do not undergo to any further chemical transformations, leading to the progressive accumulation laid out in the main text.
A rough analysis of the energetic contribution carried by the applied electric field has been carried out. In particular, by taking as the reaction coordinate the sequence of molecular configurations characterising the most prominent reaction mechanism leading to the synthesis of DME (see Fig. 3-e-h of the main text), a series of self-consistent field (i.e., single point) calculations in absence of the electrical perturbation has been performed. In Fig. S2 the en- the peculiar recombination process, a DME and a water molecule are synthesised and their respective Wannier centers are rapidly stabilized (Fig. S3-c) As laid out in the main text, the electric field is able to induce a peculiar cooperativeness between the molecules. These effects are particularly colorful when the application of the  electrical perturbation is performed in a highly correlated system such a liquid. This way, at intense field strengths, concerted reaction mechanisms are recorded, as shown in Fig. S4, where an impressive sequence of synthesis processes are highlighted. Here (Fig. S4-a), a newly formed formaldehyde through the standard process -shown also in the upper panels of Fig. 4 of the main text -interacts with a just created methanol cation ( Fig. S4-b) leading to the onset of DME ( Fig. S4-b). This scenario shows again that the local environment plays a major role in assisting the chemical reactions by acting inter alia as a sort of reservoir of proton H + and hydride H − acceptor/donor sites.
In the main text we have shown how the solvent is able to locally screen the field-induced polarization effects that would be strongly manifested in an hypothetical gas phase. To this aim, a Löwdin population analysis [5] has been performed and the coloring of the atomic sites of the main intermediate configuration leading to the synthesis of DME (Fig. 5  in the gas (Gas) and in the liquid (Liq) phases both in presence and in absence of an external electric field. The rows corresponding to oxygen and carbon atoms have been highlighted since, in principle, the eventual field-induced polarization effects are more evident on these atomic sites. H 1,2 sites refer to the "alcoholic" hydrogen atoms of CH 3 OH 2 + whereas H 3,4,5 represent the methyl hydrogen atoms of the latter and of CH 3 O − . same four cases. It turns out that whereas the difference in the centers locations between the "solvated" intermediate states in absence and in presence of the field is in practice negligible (i.e., they are stackable and the result in presence of a field strength of 0.60 V/Å is shown in Fig. S3-a), in the gas phase the field induces a visible shift of the charge as shown in Fig. S5.
Thus, though in the framework of the MLWF an over-localization of the charges is present by construction, the field-induced shift of the charge appears manifest in the gas phase at these strengths.
Because of the lack of traces of formaldehyde at the end of our numerical experiment (i.e., at 0.75 V/Å), the mean lifetime of this species has been evaluated at different electric field strengths, as shown in Table S2. It turns out that do not exist an analytical relationship -at least within the explored range of field intensities -between these two quantities and, from the analysis of the trajectories, it appears clear that at high strengths the local environment (i.e., the "solvent") is much more decisive on the reactivity of a given species than the field intensity.
In addition to these evidences, another aspect that suggests the key role played by the "solvent" is represented by the fact that the transition states shown in the central panel of Fig. 4 of the main text -determined through a committor analysis [6] at our numerical    electrical perturbation, the Noncovalent Interactions (NCI) [7] have been evaluated. As shown in Fig. S6, the intermolecular interactions between the local reactants have been identified by taking into account the reduced density gradient obtained after a single point calculation performed via the PBE [8] exchange and correlation functional. This kind of calculation has been conducted by following the standard procedure [7] and therefore by selecting a correct isosurface in order to map the real space regions where the NCI act. As it is clear in both cases, strong NCI arise when the two counterions are close to each other (as it can be argued also from the previous Löwdin population analysis). This means that a non-negligible force acts in both gas phase systems just in the portion of space which lies in the middle of the two counterions. This neighbouring effect, as confirmed also by some standard electron density calculations (not shown here), perturbs the respective molecular orbitals. This represents the reason that underlies the evidence, emerged both through Car-Parrinello [9] and Born-Oppenheimer molecular dynamics simulations in the gas phase starting from these two atomic configurations, that both reactions proceed spontaneously even without the external electric field. This way, in liquid, the reaction pathways (i.e., the intermediate and transition states) would appear to be dramatically different from any