Car–Parrinello simulation of hydrogen bond dynamics in sodium hydrogen bissulfate

We studied proton dynamics of a short hydrogen bond of the crystalline sodium hydrogen bissulfate, a hydrogen-bonded ferroelectric system. Our approach was based on the established Car–Parrinello molecular dynamics (CPMD) methodology, followed by an a posteriori quantization of the OH stretching motion. The latter approach is based on snapshot structures taken from CPMD trajectory, calculation of proton potentials, and solving of the vibrational Schrödinger equation for each of the snapshot potentials. The so obtained contour of the OH stretching band has the center of gravity at about $1540cm−1$ and a half width of about $700cm−1$⁠, which is in qualitative agreement with the experimental infrared spectrum. The corresponding values for the deuterated form are 1092 and $600cm−1$⁠, respectively. The hydrogen probability densities obtained by solving the vibrational Schrödinger equation allow for the evaluation of potential of mean force along the proton transfer coordinate. We demonstrate that for the present system the free energy profile is of the single-well type and features a broad and shallow minimum near the center of the hydrogen bond, allowing for frequent and barrierless proton (or deuteron) jumps. All the calculated time-averaged geometric parameters were in reasonable agreement with the experimental neutron diffraction data. As the present methodology for quantization of proton motion is applicable to a variety of hydrogen-bonded systems, it is promising for potential use in computational enzymology.