  A molecular level understanding of the properties of electroactive vanadium
species in aqueous solution is crucial for enhancing the performance of
vanadium redox flow batteries (RFB). Here, we employ Car-Parrinello molecular
dynamics (CPMD) simulations based on density functional theory to investigate
the hydration structures, first hydrolysis reaction and diffusion of aqueous
V$^{2+}$, V$^{3+}$, VO$^{2+}$, and VO$_2^+$ ions at 300 K. The results indicate
that the first hydration shell of both V$^{2+}$ and V$^{3+}$ contains six water
molecules, while VO$^{2+}$ is coordinated to five and VO$_2^+$ to three water
ligands. The first acidity constants (p$K_\mathrm{a}$) estimated using
metadynamics simulations are 2.47, 3.06 and 5.38 for aqueous V$^{3+}$, VO$_2^+$
and VO$^{2+}$, respectively, while V$^{2+}$ is predicted to be a fairly weak
acid in aqueous solution with a p$K_\mathrm{a}$ value of 6.22. We also show
that the presence of chloride ions in the first coordination sphere of the
aqueous VO$_2^+$ ion has a significant impact on water hydrolysis leading to a
much higher p$K_\mathrm{a}$ value of 4.8. This should result in a lower
propensity of aqueous VO$_2^+$ for oxide precipitation reaction in agreement
with experimental observations for chloride-based electrolyte solutions. The
computed diffusion coefficients of vanadium species in water at room
temperature are found to increase as V$^{3+}$ $<$ VO$_2^+$ $<$ VO$^{2+}$ $<$
V$^{2+}$ and thus correlate with the simulated hydrolysis constants, namely,
the higher the p$K_\mathrm{a}$ value, the greater the diffusion coefficient.
