•For the unreconstructed surfaces the armchair conformation is more stable than the zig-zag conformation•Reconstructed surfaces are much more stable than unreconstructed surfaces and do not decompose into stable allotropes•Reconstruction involving C-C bond formation competes with stabilization involving C-O and C-H bond formations•The Wulff shape of single graphite crystals was constructed based on the calculated surface energiesThe low-index graphite surfaces (101-0), (101-1), (112-0) and (112-1) have been studied by density functional theory (DFT) including van-der-Waals (vdW) corrections. Different from the (0001) surface which has been extensively investigated both experimentally and theoretically, there is no comprehensive study on the (101-0)- (101-1)-, (112-0)- and (112-1)-surfaces available, although they are of relevance for Li insertion processes, e.g. in Li-ion batteries. In this study the structure and stability of all non-(0001) low-index surfaces were calculated with RPBE-D3 and converged slab models. In all cases reconstruction involving bond formation between unsaturated carbon atoms of two neighboring graphene sheets reduces the surface energy dramatically. Two possible reconstruction patterns have been considered. The first possibility leads to formation of oblong nanotubes. Alternatively, the graphene sheets form bonds to different neighboring sheets at the upper and lower sides and sinusoidal structures are formed. Both structure types have similar stabilities. Based on the calculated surface energies the Gibbs–Wulff theorem was applied to construct the macroscopic shape of graphite single crystals.Dispersion corrected density functional theory applied to graphite low-index reconstructed surfaces results in an enormous reduction of the surface energy. Upon this the Wulff shape of the crystal has been constructed.

The vibrational fine structure of the fluorescence spectra of isolated perylene-3,4,9,10-tetracarboxylic dianhydride (PTCDA) molecules adsorbed on (100) surfaces of sodium chloride and potassium chloride has been studied theoretically and experimentally. In order to analyze the experimentally observed differences in the vibronic spectra of PTCDA adsorbed on the two surfaces, we simulated the spectra by calculating the Franck–Condon factors. The calculated spectra are in excellent agreement with the experiment and indicate that the difference between the two surfaces is the result of a stronger distortion of the molecular geometry on NaCl.

Density functional theory (DFT) calculations at generalized gradient approximation (GGA) level were performed to interpret experimental IR and Raman vibrational spectra, to assign 11B-NMR chemical shifts, and to calculate the structure of the tetrahydroxyborate sodalite Na8[AlSiO4]6(B(OH)4)2. Full optimization of the intercalated compound gave the following structural parameters of B(OH)4–: B–O–B (105.3–115.3°) and B–O–H (111.5–115.4°) angles, B–O (1.476 Å, 1.491 Å) and O–H (0.98 Å) distances. The calculated normal modes were assigned to experimental IR and Raman spectra. In general, close agreement between theory and experiment was obtained. The mean absolute deviation (MAD) is below 11 cm–1. We also calculate the thermodynamical stability of Na8[AlSiO4]6(B(OH)4)2 with respect to Na8[AlSiO4]6(BH4)2 in the context of the tetrahydroborate hydration reaction.

The initial stages of the formation of anatase nanotubes starting from TiO2 microparticles are studied theoretically at density-functional theory (DFT) level. Several formation mechanisms proposed in the literature are discussed. In the present study a mechanism is adapted that starts with NaOH adsorption on the anatase (101) surface. A phase transition from NaOH:anatase to sodium titanate is thermodynamically favorable but does not lead to the formation of sodium titanate nanotubes. Instead it is shown that anatase nanotubes with NaOH adsorbed on the inner surface are stabilized with respect to the unmodified 2D-periodic anatase surface structure. The structure and stability of selected intermediates of the nanotube formation process are investigated. In the experimental part we investigated the initial step of the nanotube formation and characterized the crystal structure of the as prepared titanate nanotubes.

The structure and IR vibrational spectra of tetrahydroborate sodalite (Na8[AlSiO4]6(BH4)2) were calculated using density functional theory (DFT) methods. The calculations, performed at the GGA hybrid DFT level yield a close agreement with XRD refinements of the structure and allow interpretation of observed bands of the enclosed BH4– and the framework and, in particular, a verification of hydrogen positions (Buhl, J.-C., Gesing, T. M., and Rüscher, C. H. Microporous Mesoporous Mater. 2005, 80, 57−63). In a first step, different basis sets and functionals were tested on NaBH4 and Na8[AlSiO4]6Cl2. We show that accurate treatment of B–H stretching modes requires anharmonic corrections, while lattice vibrations are well described within the harmonic approximation.

The efficient and reasonably accurate description of noncovalent interactions is important for various areas of chemistry, ranging from supramolecular host–guest complexes and biomolecular applications to the challenging task of crystal structure prediction. While London dispersion inclusive density functional theory (DFT-D) can be applied, faster “low-cost” methods are required for large-scale applications. In this Perspective, we present the state-of-the-art of minimal basis set, semiempirical molecular-orbital-based methods. Various levels of approximations are discussed based either on canonical Hartree–Fock or on semilocal density functionals. The performance for intermolecular interactions is examined on various small to large molecular complexes and organic solids covering many different chemical groups and interaction types. We put the accuracy of low-cost methods into perspective by comparing with first-principle density functional theory results. The mean unsigned deviations of binding energies from reference data are typically 10–30%, which is only two times larger than those of DFT-D. In particular, for neutral or moderately polar systems, many of the tested methods perform very well, while at the same time, computational savings of up to 2 orders of magnitude can be achieved.

Recently, a metastable bixbyite-type polymorph of vanadium sesquioxide V2O3 has been synthesized from vanadium trifluoride. During the preparation, a very low oxygen partial pressure was necessary to prevent oxidation to higher valent vanadium oxides. In order to provide a quantitative description of the oxidation process, periodic quantum-chemical calculations at density-functional theory level were performed to study the thermodynamics of oxygen incorporation into bixbyite-type V2O3. Different defect structures for nonstoichiometric phases with the general composition V2O3+x are discussed, obtained either by removing single atoms from their respective lattice positions or by introducing additional atoms into empty lattice sites. We show that the stoichiometric phase is likely to incorporate excess oxygen into the empty 16c Wyckoff position under ambient pressure. Taking into account the equilibrium of nonstoichiometric phases with the gas phase, we arrive at an estimate of 10–17 bar for the oxygen partial pressure as the upper limit for stabilizing the stoichiometric phase under reaction conditions.

Magnetic, structural, and defect properties of lithium vanadium hexafluoride (α-Li3VF6) are investigated theoretically with periodic quantum chemical methods. It is found that the ferromagnetic phase is more stable than the antiferromagnetic phase. The crystal structure contains three inequivalent Li sites (Li(1), Li(2), and Li(3)), where Li(1) occupies the middle position of the triplet Li(2)–Li(1)–Li(3). The calculated Li vacancy formation energies show that vacancy formation is preferred for the Li(1) and Li(3) sites compared to the Li(2) position. The Li exchange processes between Li(1) ↔ Li(3), Li(1) ↔ Li(2), and Li(2) ↔ Li(3) are studied by calculating the Li+ migration between these sites using the climbing-image nudged elastic band approach. It is observed that Li exchange in α-Li3VF6 may take place in the following order: Li(1) ↔ Li(3) > (Li(1) ↔ Li(2) > Li(2) ↔ Li(3). This is in agreement with recently published results obtained from 1D and 2D 6Li exchange nuclear magnetic resonance spectroscopy.Keywords: activation energy; Li diffusion; lithium vanadium fluoride; migration pathway; point defects; relaxation;

Crystalline solids have become a subject of growing interest for both experimentalists and theorists. In particular their defect properties are of fundamental importance in modern and future technical applications. The efficiency of fuel cells and batteries strongly depends on the mobility of ions in the lattice which is affected by various kinds of point defects and the local crystal structure. Fundamental understanding of processes involved in ion migration at atomic scale can be achieved by combined spectroscopical and theoretical investigation. During the last decades theoretical methods have become an indispensable tool for studying solid state materials. A broad variety of methods and models are available, all of them with peculiar benefits. In this review article an overview of some state-of-the-art methods and model types is given with a focus on their applicability to studies of defects and ion mobility.

The effect of Mn doping on optical properties of zinc oxide ZnO has been studied theoretically. The dependence of the Mn concentration and distribution on the optical band gap was investigated at density-functional level applying a hybrid functional. Supercells of varying size were used to model different Mn concentrations. Possible point defects such as oxygen vacancies and zinc interstitials were taken into account. The thermodynamic stability of defect clustering in ZnO was studied. The magnetic coupling between the Mn ions was studied in dependence of the Mn–Mn distance and the distance to lattice defects. As a main result, we find that Mn clustering in the ZnO host lattice is energetically preferred, and leads to pronounced changes in the electronic structure. In agreement with previous theoretical studies we obtain antiferromagnetic ground states in the absence of point defects. The energy difference between ferromagnetic and antiferromagnetic coupling decreases if electron donating defects such as interstitial Zn are close to Mn ions. The strong dependence of the optical band gap from the Mn–Mn and Mn-defect distances is in line with earlier experiments.

Incorporation of nitrogen into the bulk material is the key step in the preparation of N-doped transition metal oxides. As a first attempt to understand the basic reaction mechanisms involved in the surface process, molecular and dissociative adsorption of nitrogen (N2) and ammonia (NH3) at the perfect and oxygen-deficient (1 1 1) surface of cubic zirconia has been studied theoretically at hybrid density functional level. Coverages θ=12 and θ=14 were considered. In agreement with experimental observation nitrogen does not interact with the nondefective surface. Anionic adsorbed species, mainly N2-, are observed in the presence of oxygen vacancies in the topmost layer independent of coverage. NH3 adsorbs molecularly also on the defect-free surface whereas at the defective surface both molecular and dissociative adsorption is found. After dissociation the anions NH2- and NH−, accompanied by surface bound OH− and H−, are formed.

Structural, energetic and electronic properties of the low-index B2O3 surfaces (1 0 1), (11¯1), (1 0 0) and (0 0 1) were studied theoretically at density-functional level. A composition scheme was developed for slab models of the surfaces. It was found that the surface stability decreases in the order (101)>(11¯1)>(100)>(001), in line with the number of unsaturated bonds per surface area. All surfaces reconstruct in order to increase the average coordination number of atoms in the upper layers. For the (11¯1) surface, a first step toward a phase transition was observed. Occupied surface states were found 0.1 eV above the valence band for the most stable (1 0 1) surface.

The effect of Mn doping on optical properties of zinc oxide ZnO has been studied theoretically. The dependence of the Mn concentration and distribution on the optical band gap was investigated at density-functional level applying a hybrid functional. Supercells of varying size were used to model different Mn concentrations. Possible point defects such as oxygen vacancies and zinc interstitials were taken into account. The thermodynamic stability of defect clustering in ZnO was studied. The magnetic coupling between the Mn ions was studied in dependence of the Mn–Mn distance and the distance to lattice defects. As a main result, we find that Mn clustering in the ZnO host lattice is energetically preferred, and leads to pronounced changes in the electronic structure. In agreement with previous theoretical studies we obtain antiferromagnetic ground states in the absence of point defects. The energy difference between ferromagnetic and antiferromagnetic coupling decreases if electron donating defects such as interstitial Zn are close to Mn ions. The strong dependence of the optical band gap from the Mn–Mn and Mn-defect distances is in line with earlier experiments.