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 hexaaqua ferrous and ferric ions, and the inner-sphere reorganization energy for the elect ron-tran sfer 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.