Modeling Energy Landscapes of Proton Motion in Nonaqueous, Tethered Proton Wires

We have modeled structures and energetics of anhydrous proton-conducting wires: tethered hydrogen-bonded chains of the form ···HX···HX···HX···, with functional groups HX = imidazole, triazole, and formamidine; formic, sulfonic, and phosphonic acids. We have applied density functional theory (DFT) to model proton wires up to 19 units long, where each proton carrier is linked to an effective backbone to mimic polymer tethering. This approach allows the direct calculation of hydrogen bond strengths. The proton wires were found to be stabilized by strong hydrogen bonds (up to 50 kJ/mol) whose strength correlates with the proton affinity of HX [related to pKb(HX)] and not to pKa(HX) as is often assumed. Geometry optimizations and ab initio molecular dynamics near 400 K on imidazole-based proton wires both predict that adding a proton to the end of such wires causes the excess charge to embed into the interior segments of these wires. Proton translocation energy landscapes for imidazole-based wires are sensitive to the imidazole attachment point (head or feet) and to wire architecture (linear or interdigitated). Linear imidazole wires with head-attachment exhibit low barriers for intrawire proton motion, rivaling proton diffusion in liquid imidazole. Excess charge relaxation from the edge of wires is found to be dominated by long-range Grotthuss shuttling for distances as long as 42 Å, especially for interdigitated wires. For imidazole, we predict that proton translocation is controlled by the energetics of desorption from the proton wire, even for relatively long wires (600 imidazole units). Proton desorption energies show no correlation with functional group properties, suggesting that proton desorption is a collective process in proton wires.