The utilization of CO via electrochemical reduction constitutes a promising approach toward production of value-added chemicals or fuels using intermittent renewable energy sources. For this purpose, molecular electrocatalysts are frequently studied and the recent progress both in tuning of the catalytic properties and in mechanistic understanding is truly remarkable. While in earlier years research efforts were focused on complexes with rare metal centers such as Re, Ru, and Pd, the focus has recently shifted toward earth-abundant transition metals such as Mn, Fe, Co, and Ni. By application of appropriate ligands, these metals have been rendered more than competitive for CO reduction compared to the heavier homologues. In addition, the important roles of the second and outer coordination spheres in the catalytic processes have become apparent, and metal-ligand cooperativity has recently become a well-established tool for further tuning of the catalytic behavior. Surprising advances have also been made with very simple organocatalysts, although the mechanisms behind their reactivity are not yet entirely understood. Herein, the developments of the last three decades in electrocatalytic CO reduction with homogeneous catalysts are reviewed. A discussion of the underlying mechanistic principles is included along with a treatment of the experimental and computational techniques for mechanistic studies and catalyst benchmarking. Important catalyst families are discussed in detail with regard to mechanistic aspects, and recent advances in the field are highlighted.

One Sentence Summary The central light atom in the iron-molybdenum cofactor of nitrogenase is identified as carbon. Nitrogenase is a complex enzyme that catalyzes the reduction of dinitrogen to ammonia. Despite insight from structural and biochemical studies, its structure and mechanism await full characterization. An iron-molybdenum cofactor (FeMoco) is thought to be the site of dinitrogen reduction, but the identity of a central atom in this cofactor remains unknown. Fe Kß X-ray emission spectroscopy (XES) of intact nitrogenase MoFe protein, isolated FeMoco, and the FeMoco-deficient ∆nifB protein indicates that among the candidate atoms O, N, and C, it is C that best fits the XES data. The experimental XES is supported by computational efforts, which shows that oxidation and spin states do not affect the assignment of the central atom to C4-. Identification of the central atom will drive further studies on its role in catalysis.

A novel restricted-open-shell configuration interaction with singles (ROCIS) approach for the calculation of transition metal L-edge X-ray absorption spectra is introduced. In this method, one first calculates the ground state and a number of excited states of the non-relativistic Hamiltonian. By construction, the total spin is a good quantum number in each of these states. For a ground state with total spin S excited states with spin S' = S, S - 1, and S + 1 are constructed. Using Wigner-Eckart algebra, all magnetic sublevels with MS = S,..., -S for each multiplet of spin S are obtained. The spin-orbit operator is represented by a mean-field approximation to the full Breit-Pauli spin-orbit operator and is diagonalized over this N-particle basis. This is equivalent to a quasi-degenerate treatment of the spin-orbit interaction to all orders. Importantly, the excitation space spans all of the molecular multiplets that arise from the atomic Russell-Saunders terms. Hence, the method represents a rigorous first-principles approach to the complicated low-symmetry molecular multiplet problem met in L-edge X-ray absorption spectroscopy. In order to gain computational efficiency, as well as additional accuracy, the excitation space is restricted to single excitations and the configuration interaction matrix is slightly parameterized in order to account for dynamic correlation effects in an average way. To this end, it is advantageous to employ Kohn-Sham rather than Hartree-Fock orbitals thus defining the density functional theory∕ROCIS method. However, the method can also be used in an entirely non-empirical fashion. Only three global empirical parameters are introduced and have been determined here for future application of the method to any system containing any transition metal. The three parameters were carefully calibrated using the L-edge X-ray absorption spectroscopy spectra of a test set of coordination complexes containing first row transition metals. These parameters are universal and transferable. Hence, there are no adjustable parameters that are used to fit experimental X-ray absorption spectra. Thus, the new approach classifies as a predictive first-principles method rather than an analysis tool. A series of calculations on transition metal compounds containing Cu, Ti, Fe, and Ni in various oxidation and spin states is investigated and a detailed comparison to experimental data is reported. In most cases, the approach yields good to excellent agreement with experiment. In addition, the origin of the observed spectral features is discussed in terms of the electronic structure of the investigated compounds.

A series of manganese coordination compounds has been investigated by X-ray absorption spectroscopy (XAS). The K-pre-edge spectra are interpreted with the aid of time-dependent density functional theory (TD-DFT). This method was calibrated for the prediction of manganese K-pre-edges with different functionals. Moreover the nature of all observed features could be identified and classified according to the corresponding set of acceptor orbitals, either 1s to 3d transitions or metal-to-ligand charge transfer (MLCT) bands. The observable MLCT bands are further divided into features that correspond to transitions into empty π* orbitals of π-donor ligands and those of π-acceptor ligands. The ability to computationally reproduce the observed features at the correct relative transition energy is strongly dependent on the nature of the transition. A detailed analysis of the electronic structure of a series of Mn coordination compounds reveals that the different classes of observable transitions provide added insight into metal-ligand bonding interactions.

A systematic series of high-spin mononuclear Mn(II), Mn(III), and Mn(IV) complexes has been investigated by manganese Kβ X-ray emission spectroscopy (XES). The factors contributing to the Kβ main line and the valence to core region are discussed. The Kβ main lines are dominated by 3p-3d exchange correlation (spin state) effects, shifting to lower energy upon oxidation of Mn(II) to Mn(III) due to the decrease in spin state from S = 5/2 to S = 2, whereas the valence to core region shows greater sensitivity to the chemical environment surrounding the Mn center. A density functional theory (DFT) approach has been used to calculate the valence to core spectra and assess the contributions to the energies and intensities. The valence spectra are dominated by manganese np to 1s electric dipole-allowed transitions and are particularly sensitive to spin state and ligand identity (reflected primarily in the transition energies) as well as oxidation state and metal-ligand bond lengths (reflected primarily in the transition intensities). The ability to use these methods to distinguish different ligand contributions within a heteroleptic coordination sphere is highlighted. The similarities and differences between the current Mn XES study and previous studies of Fe XES investigations are discussed. These findings serve as an important calibration for future applications to manganese active sites in biological and chemical catalysis.

A detailed study of the electronic and geometric structure of V2O5 and its X-ray spectroscopic properties is presented. Cluster models of increasing size were constructed in order to represent the surface and the bulk environment of V2O5. The models were terminated with hydrogen atoms at the edges or embedded in a Madelung field. The structure and interlayer binding energies were studied with dispersion-corrected local, hybrid and double hybrid density functional theory as well as the local pair natural orbital coupled cluster method (LPNO-CCSD). Convergence of the results with respect to cluster size was achieved by extending the model to up to 20 vanadium centers. The O K-edge and the V L2,3-edge NEXAFS spectra of V2O5 were calculated on the basis of the newly developed Restricted Open shell Configuration Interaction with Singles (DFT-ROCIS) method. In this study the applicability of the method is extended to the field of solid-state catalysis. For the first time excellent agreement between theoretically predicted and experimentally measured vanadium L-edge NEXAFS spectra of V2O5 was achieved. At the same time the agreement between experimental and theoretical oxygen K-edge spectra is also excellent. Importantly, the intensity distribution between the oxygen K-edge and vanadium L-edge spectra is correctly reproduced, thus indicating that the covalency of the metal-ligand bonds is correctly described by the calculations. The origin of the spectral features is discussed in terms of the electronic structure using both quasi-atomic jj coupling and molecular LS coupling schemes. The effects of the bulk environment driven by weak interlayer interactions were also studied, demonstrating that large clusters are important in order to correctly calculate core level absorption spectra in solids.

A series of mononuclear V((V)), V((IV)) and V((III)) complexes were investigated by V L-edge near edge X-ray absorption fine structure (NEXAFS) spectroscopy. The spectra show significant sensitivity to the vanadium oxidation state and the coordination environment surrounding the vanadium center. The L-edge spectra are interpreted with the aid of the recently developed Density Functional Theory/Restricted Open Shell Configuration Interaction Singles (DFT/ROCIS) method. This method is calibrated for the prediction of vanadium L-edges with different hybrid density functionals and basis sets. For the B3LYP/def2-TZVP(-f) and BHLYP/def2-TZVP(-f) functional/basis-set combinations, good to excellent agreement between calculated and experimental spectra is obtained. A treatment of the spin-orbit coupling interaction to all orders is achieved by quasi-degenerate perturbation theory (QDPT), in conjunction with DFT/ROCIS for the calculation of the molecular multiplets while accounting for dynamic correlation and anisotropic covalency. The physical origin of the observed spectral features is discussed qualitatively and quantitatively in terms of spin multiplicities, magnetic sublevels and individual 2p to 3d core level excitations. This investigation is an important prerequisite for future applications of the DFT/ROCIS method to vanadium L-edge absorption spectroscopy and vanadium-based heterogeneous catalysts.

The accurate description of magnetic level energetics in oligonuclear exchange-coupled transition-metal complexes remains a formidable challenge for quantum chemistry. The density matrix renormalization group (DMRG) brings such systems for the first time easily within reach of multireference wave function methods by enabling the use of unprecedentedly large active spaces. But does this guarantee systematic improvement in predictive ability and, if so, under which conditions? We identify operational parameters in the use of DMRG using as a test system an experimentally characterized mixed-valence bis-μ-oxo/μ-acetato Mn(III,IV) dimer, a model for the oxygen-evolving complex of photosystem II. A complete active space of all metal 3d and bridge 2p orbitals proved to be the smallest meaningful starting point; this is readily accessible with DMRG and greatly improves on the unrealistic metal-only configuration interaction or complete active space self-consistent field (CASSCF) values. Orbital optimization is critical for stabilizing the antiferromagnetic state, while a state-averaged approach over all spin states involved is required to avoid artificial deviations from isotropic behavior that are associated with state-specific calculations. Selective inclusion of localized orbital subspaces enables probing the relative contributions of different ligands and distinct superexchange pathways. Overall, however, full-valence DMRG-CASSCF calculations fall short of providing a quantitative description of the exchange coupling owing to insufficient recovery of dynamic correlation. Quantitatively accurate results can be achieved through a DMRG implementation of second order N-electron valence perturbation theory (NEVPT2) in conjunction with a full-valence metal and ligand active space. Perspectives for future applications of DMRG-CASSCF/NEVPT2 to exchange coupling in oligonuclear clusters are discussed.