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.
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