We calculate the lattice properties and electronic structure of graphite and LiC 6 within the most widely used density-functional theory implementation, the local density approximation ͑LDA͒. Improvements to the LDA in the form of a generalized gradient approximation ͑GGA͒ are explored. Structural parameters predicted by the LDA, as expected, underestimate experiment within a 1%-2% margin of accuracy. The GGA does not give a good account in the prediction of lattice parameter c, especially in graphite, although it does give a reliable description of LiC 6 . The effect on intercalating lithium into graphite, where charge transfer from lithium to carbon layers ͑graphenes͒ is expected, is discussed from the valence charge density, partial density of states, and energy band structure plots. The latter plot is also compared with inelastic neutron scattering results and low-energy electron diffraction results. We extend this work by calculating the elastic constants and bulk modulus for both graphite and LiC 6 structures. These results are in excellent agreement with the available experimental data. The calculated hydrostatic pressure dependence of the crystal structures is also found to be in good agreement with the results of high-resolution x-ray structural studies and with other experimental data as well as with other calculations. The analysis of electronic structure at 0 GPa ͑ambient pressure͒ is used to resolve inconsistencies between previous LDA calculations.

Static-lattice calculations have been employed to model the phases of VO 2 and V 1-δ W δ O 2 . Interatomic potentials were empirically fitted to reproduce the low-and high-temperature phases (monoclinic and tetragonal, respectively) of vanadium dioxide as well as the monoclinic phase of tungsten dioxide. For pure VO 2 , we located the soft modes of the high-temperature phase, which characterize the initial atomic displacements that lead to the displacive phase transition to the low-temperature phase. The T ) 0 structure of the saddle point, where only half of the one-dimensional chains have undergone Peierls distortions, and the ionic motion along the lowest-energy path for the phase transition are described. For V 1-δ W δ O 2 , we found that doping significantly stabilizes the high-temperature phase relative to the low-temperature phase, which explains the observed depression in the transition temperature as δ increases. For the highand low-temperature phases, the local structures about the dopant, which were obtained by employing a Mott-Littleton approach, resembled those of the low-and high-temperature phases, respectively.

The electron structure, magnetic, structural, and elastic properties of ilmenite ͑FeTiO 3 ͒ are computed within a hybrid density functional formalism. The computed properties are found to be very sensitive to the treatment of electronic exchange and correlation; Hartree-Fock and generalized gradient approximation calculations are performed for comparison. Within the hybrid formalism a qualitatively correct description of the ground-state electronic structure is obtained. Predicted geometric and elastic parameters are in close agreement with experiment as is the charge transfer excitation energy. The essential features of this functional are its treatment of the electronic self interaction and its reasonable estimate of the pair correlation energy of the doubly occupied Fe-d orbital.

Nanoporous beta-MnO2 can act as a host lattice for the insertion and deinsertion of Li with application in rechargeable lithium batteries. We predict that, to maximize its electrochemical properties, the beta-MnO2 host should be symmetrically porous and heavily twinned. In addition, we predict that there exists a "critical (wall) thickness" for MnO2 nanomaterials above which the strain associated with Li insertion is accommodated via a plastic, rather than elastic, deformation of the host lattice leading to property fading upon cycling. We predict that this critical thickness lies between 10 and 100 nm for beta-MnO2 and is greater than 100 nm for alpha-MnO2: the latter accommodates 2 x 2 tunnels compared with the smaller 1 x 1 tunnels found in beta-MnO2. This prediction may help explain why certain (nano)forms of MnO2 are electrochemically active, while others are not. Our predictions are based upon atomistic models of beta-MnO2 nanomaterials. In particular, a systematic strategy, analogous to methods widely and routinely used to model crystal structure, was used to generate the nanostructures. Specifically, the (space) symmetry associated with the nanostructure coupled with basis nanoparticles was used to prescribe full atomistic models of nanoparticles (0D), nanorods (1D), nanosheets (2D), and nanoporous (3D) architectures. For the latter, under MD simulation, the amorphous nanoparticles agglomerate together with their periodic neighbors to formulate the walls of the nanomaterial; the particular polymorphic structure was evolved using simulated amorphization and crystallization. We show that our atomistic models are in accord with experiment. Our models reveal that the periodic framework architecture, together with microtwinning, enables insertion of Li anywhere on the (internal) surface and facilitates Li transport in all three spatial directions within the host lattice. Accordingly, the symmetrically porous MnO2 can expand and contract linearly and crucially elastically under charge/discharge. We also suggest tentatively that our predictions for MnO2 are more general in that similar arguments may apply to other nanomaterials, which might expand and contract elastically upon charging/discharging.

Models of MnO2 nanoparticles, with full atomistic detail, have been generated using a simulated amorphization and recrystallization strategy. In particular, a 25,000-atom "cube" of MnO2 was amorphized (tension-induced) under molecular dynamics (MD). Long-duration MD, applied to this system, results in the sudden evolution of a small crystalline region of pyrolusite-structured MnO2, which acts as a nucleating "seed" and facilitates the recrystallization of all the surrounding (amorphous) MnO2. The resulting MnO2 nanoparticle is about 8 nm in diameter, conforms to the pyrolusite structure (isostructural with rutile TiO2, comprising 1 x 1 octahedra) is heavily twinned and comprises a wealth of isolated and clustered point defects such as cation vacancies. In addition, we suggest the presence of ramsdellite (2 x 1 octahedra) intergrowths. Molecular graphical snapshots of the crystallization process are presented.

The adsorption and co-adsorption of lithium and oxygen at the surface of rutile-like manganese dioxide (b-MnO 2 ), which are important in the context of Li-air batteries, are investigated using density functional theory. In the absence of lithium, the most stable surface of b-MnO 2 , the (110), adsorbs oxygen in the form of peroxo groups bridging between two manganese cations. Conversely, in the absence of excess oxygen, lithium atoms adsorb on the (110) surface at two different sites, which are both tricoordinated to surface oxygen anions, and the adsorption always involves the transfer of one electron from the adatom to one of the five-coordinated manganese cations at the surface, creating (formally) Li + and Mn 3+ species. The co-adsorption of lithium and oxygen leads to the formation of a surface oxide, involving the dissociation of the O 2 molecule, where the O adatoms saturate the coordination of surface Mn cations and also bind to the Li adatoms. This process is energetically more favourable than the formation of gas-phase lithium peroxide (Li 2 O 2 ) monomers, but less favourable than the formation of Li 2 O 2 bulk. These results suggest that the presence of b-MnO 2 in the cathode of a nonaqueous Li-O 2 battery lowers the energy for the initial reduction of oxygen during cell discharge.

Atomistic simulation techniques are used to investigate the surface structure, stability and reactivity of pyrite. We introduce a potential model for FeS2 which reproduces experimental structural parameters, elastic constants and hydration energies of pyrite. We modeled the {100}, {110}, and {111} surfaces of pyrite and calculated the {100} surface to be the most stable and to show little surface relaxation, in agreement with experiment. The surfaces were hydrated by associative adsorption of water molecules which stabilized all three surfaces, especially the unstable {111} surface. The calculated adsorption energy of −47 kJ mol-1 for water on the {100} surface agrees well with an adsorption energy of −42 kJ mol-1, determined for the stoichiometric (100) surface by temperature-programmed desorption. Adsorption of water molecules at surface sites of lower coordination (four- or three- coordinated) showed increased reactivity of these sites. We calculated an increase in adsorption energy of 50−60 kJ mol-1 per loss of bond. We next created stepped {100} planes in order to model a more realistic {100} surface with one-dimensional defects. Four different steps were investigated in two orthogonal directions. Because of the asymmetry of the sulfur dimers, the geometry of the dimers on the edge showed the dimers either leaning forward (F-steps) or backward (B-steps) with respect to the {100} terrace. We used water molecules as a probe of the reactivity of the different surface sites. Corresponding adsorption sites (terrace, edge or below the step) on the F- and B-steps were found to have different reactivities toward water due to the different adsorption modes of the probe molecule. On the B-steps the increased reactivity of the low-coordinated edge iron atom toward water (approximately −70 kJ mol-1) was outweighed by the network of interactions of the water molecule to atoms on terrace and step wall in the position below the step (−91 kJ mol-1). On the F-steps the four-coordinated edge site was calculated to be the most reactive adsorption site.

The structural and dynamic properties of the mineral Cooperite ͑PtS͒ are investigated using densityfunctional theory. The results show that a competition with the less symmetric but more compact PdS structure leads to a phase transition when the pressure is increased. However, before the phase transition, PtS displays a rare anomalous elastic behavior by expanding along its long axis under hydrostatic pressure. We report the elastic constants of PtS and interpret this negative linear compressibility in the context of a displacive phase transition. We also show that the real structure of PtS is less symmetric than originally determined by experiment.