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Time dependent density functional theory (TDDFT) calculations have been performed on a series of symmetry-preserving excited states of the uranyl dication, UO 2 2+ . The simulated excited state electronic structures are compared to that of the ground state at both ground and excited state-optimised geometries. For the first time, the Quantum Theory of Atoms in Molecules (QTAIM) has been applied to the excited states electronic structures of uranyl in order to quantify the variation in bond covalency upon electronic excitation. QTAIM analysis of vertical excitations at the ground state geometry demonstrated an inverse relationship between the orbital mixing coefficient, λ , and the excitation energy. Furthermore, it was found that, for MOs with U 5f character, λ was more dependent on the metal-ligand Hamiltonian matrix element H ML , whereas for those with U 6d character, λ became increasingly dependent on the difference in fragment orbital energy levels, Δ E ML . Charge transfer from O to U reduced as the excitation energy increased, as did the degree of electron sharing between the centres. When considering the relaxed excited state geometries, a relationship between excitation energy and bond elongation was established, commensurate with the large magnitude of λ and its dependence on H ML for MOs with U 5f character, and enhanced charge transfer otherwise.

Ab initio molecular dynamics (AIMD) simulations of the Mg2+, Ca2+, Sr2+ and UO22+ ions in either a pure aqueous environment or an environment containing two hydroxide ions have been carried out at the density functional level of theory, employing the generalised gradient approximation via the PBE exchange-correlation functional. Calculated mean M-O bond lengths in the first solvation shell of the aquo systems compared very well to existing experimental and computational literature, with bond lengths well within values measured previously and coordination numbers in line with previously calculated values. When applied to systems containing additional hydroxide ions, the methodology revealed increased bond lengths in all systems. Proton transfer events (PTEs) were recorded and were found to be most prevalent in the strontium hydroxide systems, likely due to the low charge density of the ion and the consequent lack of hydroxide coordination. For all alkaline earths, intrashell PTEs which occurred outside of the first solvation shell were most prevalent. Only three PTEs were identified in the entire simulation data of the uranium dihydroxide system, indicating the clear impact of the increased charge density of the hexavalent uranium ion on the strength of metal-oxygen bonds in aqueous solution. Broadly, systems containing more charge dense ions were found to exhibit fewer PTEs than those containing ions of lower charge density.

The inverse trans influence (ITI) is investigated in uranyl, UO22+, and its isoelectronic imido (U(NH)22+) and carbene (U(CH2)22+) analogues at the density functional and complete active space self consistent field levels of theory. The quantum theory of atoms in molecules is employed to quantify, for the first time, the effect of the ITI on covalent bond character and its relationship to bond lengths and complex stability.

Solubility is a fundamental property of widespread significance. Despite its importance, its efficient and accurate prediction from first principles remains a major challenge. Here we propose a novel method to predict the solubility of molecules using a density of states (DOS) approach from classical molecular simulation. The method offers a potential route to solubility prediction for large (including drug-like) molecules over a range of temperatures and pressures, all from a modest number of simulations. The method was employed to predict the solubility of sodium chloride in water at ambient conditions, yielding a value of 3.77(5) mol kg-1. This is in close agreement with other approaches based on molecular simulation, the consensus literature value being 3.71(25) mol kg-1. The predicted solubility is about half of the experimental value, the disparity being attributed to the known limitation of the Joung-Cheatham force field model employed for NaCl. The proposed method also accurately predicted the NaCl model's solubility over the temperature range 298-373 K directly from the density of states data used to predict the ambient solubility.