A quantum description of the proton movement in an idealized NHN+ bridge

Abstract

A series of model calculations was done to analyze the delocalization of the proton in the linking hydrogen bond of the (Dih)₂H⁺ cation (Dih: 4,5-dihydro-1H-imidazole). Standard quantum chemical calculations (B3LYP/D95+(d,p)) predict a low barrier hydrogen bond (LBHB) and thereby a delocalized proton in the NHN⁺ hydrogen bridge. Explicit quantum calculations on the proton indicate that the delocalization of the proton does not provide enough energy to stabilize a permanent LBHB. Additional Born–Oppenheimer Molecular Dynamics (BOMD) simulations indicate further that the proton is localized at either side of the NHN⁺ bridge and that a central proton position is the result of temporal averaging. The possibility of the proton to tunnel from one side to the other side of the NHN⁺ bridge increases with the temperature as the trajectory of the (Dih)₂H⁺ cation runs through regions where the thermal excitation of Dih ring vibrations creates equal bonding opportunities for the proton on both sides of the bridge (vibrationally assisted proton tunneling). The quantum calculations for the proton in (Dih)₂H⁺ suggest further a broad peak for the 1 ← 0 transition with a maximum at 938 cm⁻¹ similar to that observed for LBHBs. Moreover, the asymmetric NHN⁺ bridge in a thermally fluctuating environment is strong enough to create a significant peak at 1828 cm⁻¹ for the 2 ← 0 transition, while contributions from the 2 ← 1 are expected to be weak for the same reason.