Car–Parrinello molecular dynamics in the DFT + U formalism: Structure and energetics of solvated ferrous and ferric ions

We implemented a rotationally-invariant Hubbard U extension to density-functional theory in the Car–Parrinello molecular dynamics framework, with the goal of bringing the accuracy of the DFT + U approach to finite-temperature simulations, especially for liquids or solids containing transition-metal ions. First, we studied the effects on the Hubbard U on the static equilibrium structure of the hexa-aqua ferrous and ferric ions, and the inner-sphere reorganization energy for the electron-transfer reaction between aqueous ferrous and ferric ions. It is found that the reorganization energy is increased, mostly as a result of the Fe–O distance elongation in the hexa-aqua ferrous ion. Second, we performed a first-principles molecular dynamics study of the solvation structure of the two aqueous ferrous and ferric ions. The Hubbard term is found to change the Fe–O radial distribution function for the ferrous ion, while having a negligible effect on the aqueous ferric ion. Moreover, the frequencies of vibrations between Fe and oxygen atoms in the first-solvation shell are shown to be unaffected by the Hubbard corrections for both ferrous and ferric ions.