Fig. 5
From: Transparent proton transport through a two-dimensional nanomesh material

Trans-membrane (TM) proton transport driven by electric field. a Typical quantum configuration of TM H5O2+ complex in path-integral molecular dynamics (PIMD) simulations. b The free energy profile of the excess proton during proton transport processes from classical and quantum nuclei simulations under electric field, respectively. The profiles are symmetrized for a more accurate quantification of the barrier. The thermal energy kBT at 300 K is denoted by the horizontal dashed line