  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.

Materials Science;Soft Condensed Matter