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Metal fluorides/oxides (MF(x)/M(x)O(y)) are promising electrodes for lithium-ion batteries that operate through conversion reactions. These reactions are associated with much higher energy densities than intercalation reactions. The fluorides/oxides also exhibit additional reversible capacity beyond their theoretical capacity through mechanisms that are still poorly understood, in part owing to the difficulty in characterizing structure at the nanoscale, particularly at buried interfaces. This study employs high-resolution multinuclear/multidimensional solid-state NMR techniques, with in situ synchrotron-based techniques, to study the prototype conversion material RuO2. The experiments, together with theoretical calculations, show that a major contribution to the extra capacity in this system is due to the generation of LiOH and its subsequent reversible reaction with Li to form Li2O and LiH. The research demonstrates a protocol for studying the structure and spatial proximities of nanostructures formed in this system, including the amorphous solid electrolyte interphase that grows on battery electrodes.

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The density functional theory based molecular dynamics (DFTMD) method for the computation of redox free energies presented in previous publications and the more recent modification for computation of acidity constants are reviewed. The method uses a half reaction scheme based on reversible insertion/removal of electrons and protons. The proton insertion is assisted by restraining potentials acting as chaperones. The procedure for relating the calculated deprotonation free energies to Brønsted acidities (pK(a)) and the oxidation free energies to electrode potentials with respect to the normal hydrogen electrode is discussed in some detail. The method is validated in an application to the reduction of aqueous 1,4-benzoquinone. The conversion of hydroquinone to quinone can take place via a number of alternative pathways consisting of combinations of acid dissociations, oxidations, or dehydrogenations. The free energy changes of all elementary steps (ten in total) are computed. The accuracy of the calculations is assessed by comparing the energies of different pathways for the same reaction (Hess's law) and by comparison to experiment. This two-sided test enables us to separate the errors related with the restrictions on length and time scales accessible to DFTMD from the errors introduced by the DFT approximation. It is found that the DFT approximation is the main source of error for oxidation free energies.

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The position of electronic energy levels in a phase depends on the surface potentials at its boundaries. Bringing two phases in contact at an interface will alter the surface potentials shifting the energy levels relative to each other. Calculating such shifts for electrochemical interfaces requires a combination of methods from computational surface science and physical chemistry. The problem is closely related to the computation of potentials of electrochemically inactive electrodes. These so-called ideally polarizable interfaces are impossible to cross for electrons. In this perspective we review two density functional theory based methods that have been developed for this purpose, the workfunction method and the hydrogen insertion method. The key expressions of the two methods are derived from the formal theory of absolute electrode potentials. As an illustration of the workfunction method we review the computation of the potential of zero charge of the Pt(111)-water interface as recently published by a number of groups. The example of the hydrogen insertion method is from our own work on the rutile TiO(2)(110)-water interface at the point of zero proton charge. The calculations are summarized in level diagrams aligning the electronic energy levels of the solid electrode (Fermi level of the metal, valence band maximum and conduction band minimum of the semiconductor) to the band edges of liquid water and the standard potential for the reduction of the hydroxyl radical. All potentials are calculated at the same level of density functional theory using the standard hydrogen electrode as common energy reference. Comparison to experiment identifies the treatment of the valence band of water as a potentially dangerous source of error for application to electrocatalysis and photocatalysis.

CONSPECTUS: All-atom methods treat solute and solvent at the same level of electronic structure theory and statistical mechanics. All-atom computation of acidity constants (pKa) and redox potentials is still a challenge. In this Account, we review such a method combining density functional theory based molecular dynamics (DFTMD) and free energy perturbation (FEP) methods. The key computational tool is a FEP based method for reversible insertion of a proton or electron in a periodic DFTMD model system. The free energy of insertion (work function) is computed by thermodynamic integration of vertical energy gaps obtained from total energy differences. The problem of the loss of a physical reference for ionization energies under periodic boundary conditions is solved by comparing with the proton work function computed for the same supercell. The scheme acts as a computational hydrogen electrode, and the DFTMD redox energies can be directly compared with experimental redox potentials. Consistent with the closed shell nature of acid dissociation, pKa estimates computed using the proton insertion/removal scheme are found to be significantly more accurate than the redox potential calculations. This enables us to separate the DFT error from other sources of uncertainty such as finite system size and sampling errors. Drawing an analogy with charged defects in solids, we trace the error in redox potentials back to underestimation of the energy gap of the extended states of the solvent. Accordingly the improvement in the redox potential as calculated by hybrid functionals is explained as a consequence of the opening up of the bandgap by the Hartree-Fock exchange component in hybrids. Test calculations for a number of small inorganic and organic molecules show that the hybrid functional implementation of our method can reproduce acidity constants with an uncertainty of 1-2 pKa units (0.1 eV). The error for redox potentials is in the order of 0.2 V.

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