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The chemistry of actinides in aqueous solution is important, and it is essential to build adequate conceptual models and develop methods applicable for actinide systems. The complex electronic structure makes benchmarking necessary. In the thesis a prototype reaction of the water exchange reaction for uranyl(VI), for both ground and luminescent states, described with a six-water model, was used to study the applicability of density functional methods on actinides and different solvation models. An excellent agreement between the wave function methods CCSD(T) and MP2 was obtained in the ground state, implying that near-minimal CASPT2 can be used with confidence for the reaction in the luminescent state of uranyl(VI), while density functionals are not suited to describe energetics for this type of reaction. There was an ambiguity concerning the position of the waters in the second hydration sphere. This issue was resolved by investigating a larger model, and prop- erly used the six-water model was found to adequately describe the water exchange reaction. The effect of solvation was investigated by comparing the results from conductor-like polarizable continuum models using two cavity models. Scattered numbers made it difficult to determine which solvation model to use. The final conclusion was that the water exchange reaction in the luminescent state of uranyl(VI) should be addressed with near-minimal CASPT2 and a solvation model without explicit cavities for hydrogens. Finally it was shown that no new chemistry appears in the luminescent state for this reaction. The thesis includes a methodological investigation of a multi-reference density functional method based on a range separation of the two-electron interaction. The method depends on a universal parameter, which has been determined for lighter elements. It is shown here that the same parameter could be used for actinides, a prerequisite for further development of the method. The results are in that sense promising.