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In mixed-valence (MV) systems essentially identical, more or less electronically coupled, redox centres are brought into formally different oxidation states by removal or addition of an electron. Depending on the strength of electronic coupling, an electron or a hole is either concentrated on one of the redox centres, or it is symmetrically delocalised onto several sites, or the situation is somewhere in between, which leads to the classification system for MV systems introduced by Melvin Robin and Peter Day. These different characteristics are of fundamental importance for the understanding of electron transfer processes. Applications of quantum-chemical methods to aid the classification and to unravel the nature of the electronic structure and spectroscopic data of both organic and transition-metal MV systems, have gained tremendous importance over the last two decades. In this review, we emphasise the prerequisites the quantum-chemical methods need to fulfill to successfully describe MV systems close to the borderline between Robin-Day classes II and III. These are, in particular, a balanced treatment of exchange, dynamical and non-dynamical correlation effects, as well as consideration of the crucial influence of the (solvent or solid-state) environment on the partial localisation of charge. A large variety of applications of quantum-chemical methods to both organic and inorganic MV systems are critically appraised here in view of these prerequisites. Practical protocols based on a combination of suitable density functional methods with continuum or non-continuum solvent models provided good agreement with experimental data for the ground states and the electronic excitations of a large range of MV systems close to the borderline. Recent applications of such methods have highlighted the crucial importance of conformational effects on electronic coupling, all the way to systems where conformational motion may cause a thermal mixing of class II and class III situations in one system.

The charge density and its Laplacian at the Li-C and C-H bond critical points and other features of the electron density distribution of the methyl lithium crystal have been compared by density functional methods for (i) the isolated (LiCH(3))(4) tetramer or larger clusters, (ii) for quantum mechanically treated clusters in polarizable continuum model (PCM) surroundings, (iii) for clusters augmented by the periodic electrostatic embedded cluster model (PEECM), and for (iv) the periodic crystal. Comparisons with identical functional and basis sets indicate that both PCM and PEECM embedding of only a tetramer did not fully account for the environmental effect. In contrast, embedding of a full unit cell gave results that were essentially converged to the periodic crystal data. Effects of basis set and exchange correlation functional on the QTAIM bond descriptors are of a comparable order of magnitude as the crystal environmental effects. In this context, embedded cluster computations provide distinct advantages over explicit solid-state calculations with respect to their freedom of the choice of computational and theoretical level. This is demonstrated by embedded MP2 calculations., (2010 Wiley Periodicals, Inc.)

The DFT B3LYP/SBKJC method has been used to calculate the gas-phase optimized geometries of the glycolate oxoperoxo vanadium(V) complexes [V(2)O(2)(OO)(2)(gly)(2)](2-), [V(2)O(3)(OO)(gly)(2)](2-) and [VO(OO)(gly)(H(2)O)](-). The (51)V, (17)O, (13)C and (1)H chemical shifts have been calculated for the theoretical geometries in all-electron DFT calculations at the UDFT-IGLO-PW91 level and have been subsequently compared with the experimental chemical shifts in solution. In spite of being applied to the isolated molecules, the calculations allowed satisfactory reproduction of the multinuclear NMR solution chemical shifts of the complexes, suggesting that the theoretical structures are probably close to those in solution. The effects of structural changes on the (51)V and (17)O NMR chemical shifts have been analysed using the referred computational methodologies for one of the glycolate complexes and for several small molecules taken as models. These calculations showed that structural modifications far from the metal nucleus do not significantly affect the metal chemical shift. This finding explains why it is possible to establish reference scales that correlate the type of complex (type of metal centre associated with a certain type of ligand) with its typical region of metal chemical shifts. It has also been found that the V[double bond, length as m-dash]O bond length is the dominant geometrical parameter determining both delta(51)V and the oxo delta(17)O in this kind of complex.

Bonds are at the very heart of chemistry. Although the order of carbon–carbon bonds only extends to triple bonds, metal–metal bond orders of up to five are known for stable compounds, particularly between chromium atoms. Carbometallation and especially carboalumination reactions of carbon–carbon double and triple bonds are a well established synthetic protocol in organometallic chemistry and organic synthesis. We now extend these reactions to compounds containing chromium–chromium quintuple bonds. Analogous reactivity patterns indicate that such quintuple bonds are not as exotic as previously assumed. Yet the particularities of these reactions reflect the specific nature of the high metal–metal bond orders.

Various combinations of density functionals and pseudopotentials with associated valence basis-sets are compared for reproducing the known solid-state structure of [V 2O 2(OO) 2 l-lact 2] (2-) cis . Gas-phase optimizations at the B3LYP/SBKJC level have been found to provide a structure that is close to that seen in the solid state by X-ray diffraction. Although this may result in part from error compensation, this optimized structure allowed satisfactory reproduction of solution multinuclear NMR chemical shifts of the complex in all-electron DFT-IGLO calculations (UDFT-IGLO-PW91 level), suggesting that it is probably close to that found in solution. This combination of approaches has subsequently been used to optimize the structures of the vanadium oxoperoxo complexes [V 2O 3(OO) l-lact 2] (2-) cis , [V 2O 3(OO) l-lact 2] (2-) trans , and [VO(OO)( l-lact)(H 2O)] (-) cis . The (1)H, (13)C, (51)V, and (17)O NMR chemical shifts for these complexes have been calculated and compared with the experimental solution chemical shifts. Excellent agreement is seen with the (13)C chemical shifts, while somewhat inferior agreement is found for (1)H shifts. The (51)V and (17)O chemical shifts of the dioxo vanadium centers are well reproduced, with differences between theoretical and experimental shifts ranging from 22.9 to 35.6 ppm and from 25.1 to 43.7 ppm, respectively. Inferior agreement is found for oxoperoxo vanadium centers, with differences varying from 137.3 to 175.0 ppm for (51)V shifts and from 148.7 to 167.0 ppm for (17)O(oxo) shifts. The larger errors are likely to be due to overestimated peroxo O-O distances. The chosen methodology is able to predict and analyze a number of interesting structural features for vanadium(V) oxoperoxocomplexes of alpha-hydroxycarboxylic acids.