Diffusion of ferrocene through vanadyl phosphate by density functional theory

Here, we employed the nudged elastic band (NEB) method to simulate the diffusion of ferrocene through vanadyl phosphate (VOPO₄), with a focus on understanding the diffusion pathways arising from the complex structure of ferrocene. We systematically evaluated a total of 36 potential diffusion paths, categorizing them into three groups based on their directional orientation: 15 paths between V sites along the [110] direction, 15 paths from V to P sites along the [100] direction, and 6 paths between P sites also along the [110] direction. Our analysis revealed that the energy barriers for diffusion along the [110] direction typically ranged between 0.25 and 0.35 eV, which are notably higher than those observed for pathways along the [100] direction, where the energy barriers ranged from 0.11 to 0.20 eV. To further elucidate the complex deformation of ferrocene during diffusion, we established four key measures to characterize the structural conformation: the angle of the axis of the ferrocene molecule relative to the [010] direction within the (001) plane, the dihedral angle between the two cyclopentadienyl rings, the orientation angle of the -CH bonds with respect to the [001] direction, and the angle between two -CH bonds from the two cyclopentadienyl rings.