Interstitial Lithium Diffusion Pathways in γ‑LiAlO₂: A Computational Study

Although the Li diffusion in single crystalline γ-LiAlO₂ was studied with temperature-dependent Li-7 NMR spectroscopy and conductivity measurements recently, the exact diffusion pathways are not yet clearly identified. Therefore, the present study aims at elucidating the diffusion pathways in γ-LiAlO₂ theoretically from first principles. Competing pathways for Li diffusion are investigated using the climbing-image nudged-elastic-band approach with periodic quantum-chemical density functional theory (DFT) method. Li can migrate between two regular LiO₄ tetrahedral sites via Li point defect (V_Li) and via a Li Frenkel defect (V_Li + Li_<i>i</i>). On the basis of calculated activation energies for Li diffusion pathways, it is concluded that Li conductivity is strongly dependent on the distribution of Li vacancies and interstitial Li in the lattice. For Frenkel defects where Li_<i>i</i> is far away from the migrating Li atom, the calculated activation energies for jumps to nearest-neighbor vacant sites agree with experimental values

Lithium Diffusion Pathways in β‑Li₂TiO₃: A Theoretical Study

In recent experimental studies based on NMR techniques, the ion dynamics in β-Li₂TiO₃ has been discussed controversially. In order to shed light on this discussion, Li ion diffusion processes in β-Li₂TiO₃ are investigated theoretically using periodic quantum–chemical DFT methods. It is observed that Li⁺ migrates along the <i>ab</i> plane as well as in the direction perpendicular to the LiTi₂ layers with the activation energies ranging between 0.44 and 0.54 eV, suggesting a slow ion dynamics. In addition, the structural, electronic, and defect properties and the electric field gradient (EFG) parameters at Li positions of β-Li₂TiO₃ are calculated. According to our results, β-Li₂TiO₃ is a wide gap insulator with an indirect band gap at Γ–C. The calculated defect formation energy values as well as the EFG parameters show that there are three different Li sites in the structure, namely, Li(1), Li(2), and Li(3), which are in well accord with the experiment

Mixed Pentele-Chalcogen Cationic Chains from Aluminum and Gallium Halide Melts

The reactions of tellurium or selenium with bismuth or antimony in chloridogallate and iodidoaluminate melts in the presence of group 15 trihalides as weak oxidants yielded the compounds (Sb₂Te₂)­[GaCl₄] (<b>1</b>), (Sb₂Te₂)­I­[AlI₄] (<b>2</b>), (Bi₂Te₂)­Cl­[GaCl₄] (<b>3a</b>), (Bi₂Se₂)­Cl­[GaCl₄] (<b>3b</b>), (Sb₃Te₄)­[GaCl₄] (<b>4</b>), and (SbTe₄)­[Ga₂Cl₇] (<b>5</b>). In the crystal structures one-dimensional polymeric cations (Sb₂Te₂⁺)_<i>n</i> (<b>1</b>), (Sb₂Te₂²⁺)<i>_n</i> (<b>2</b>), (Bi₂Te₂²⁺)<i>_n</i> (<b>3a</b>), (Bi₂Se₂²⁺)_<i>n</i> (<b>3b</b>), (Sb₃Te₄⁺)_<i>n</i> (<b>4</b>), and (SbTe₄⁺)_<i>n</i> (<b>5</b>) are present. The polymeric cationic strands in <b>2</b>, <b>3a</b>, <b>3b</b>, and <b>4</b> consist of pentele/chalcogen dumbbells, which are connected to ladder-shaped bands. The strands in <b>1</b> and <b>5</b> consist of condensed rings that involve four-membered Sb₂Te₂ rings for <b>1</b>, and five-membered SbTe₄ rings for <b>5</b>. The counteranions are the weakly coordinating [GaCl₄]⁻, [AlI₄]⁻, and [Ga₂Cl₇]⁻ in addition to Cl^– and I^– anions, which are coordinated to the atoms of the cations. The crystal structures of <b>1</b>–<b>4</b> are characterized by a statistical disorder in the anions with alternatively occupied positions for the Al and Ga atoms. For <b>4</b> superstructure reflections appear in the diffractions patterns, indicating a partial order. A correct assignment of the Sb and Te positions in the cation of <b>5</b> was achieved by periodic quantum-chemical calculations, which were performed via a Hartree–Fock density functional theory hybrid method. A clear preference of the 4-fold coordinated site was obtained for Sb

Analysis of the Vibronic Spectra of Perylene-3,4,9,10-tetracarboxylic Dianhydride Adsorbed on NaCl and KCl

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

The Electronic States of U⁴⁺ in U(PO₄)Cl: An Example for Angular Overlap Modeling of 5f^<i>n</i> Systems

Detailed experimental data on UPO₄Cl comprising single-crystal UV/vis/NIR spectra and temperature-dependent magnetic susceptibilities form the basis for the investigation of the electronic structure of the U⁴⁺ cation in UPO₄Cl. For modeling of the observed physical properties the <i>angular overlap model</i> (AOM) was successfully employed. The computations were performed using the newly developed computer program BonnMag. The calculations show that all electronic transitions and the magnetic susceptibility as well as its temperature dependence are well-reproduced within the AOM framework. Using Judd–Ofelt theory BonnMag allows estimation of the relative absorption coefficients of the electronic transitions with reasonable accuracy. Ligand field splitting for states originating from f-electron configurations are determined. Slater–Condon–Shortley parameters and the spin–orbit coupling constant for U⁴⁺ were taken from literature. The good transferability of AOM parameters for U⁴⁺ is confirmed by calculations of the absorption spectra of UP₂O₇ and (U₂O)­(PO₄)₂. The effect of variation of the fit parameters is investigated. AOM parameters for U⁴⁺ (5f) are compared to those of the rare-earth elements (4f) and transition metals (3d)

Polytellurides of Mn, Fe, and Zn from Mild Solvothermal Reactions in Liquid Ammonia

The reaction of elemental Mn, Fe, and Zn with Te in liquid ammonia at 50 °C leads to the polytellurides [Mn­(NH₃)₆]­Te₄ (<b>1</b>), [Fe­(NH₃)₆]­Te₄·NH₃ (<b>2</b>), and [Zn­(NH₃)₄]₂Te₁₅ (<b>3</b>) in quantitative yield for <b>1</b> and <b>3</b>, and in 30–50% yield for <b>2</b>. The compounds form black crystals, which are air sensitive and easily lose ammonia without a protective atmosphere of NH₃. Compound <b>3</b> is semiconducting with a thermal activation energy of 1.2 eV. In the crystal structures of <b>1</b> and <b>2</b>, tetratelluride anions Te₄^2‑ in gauche conformation with dihedral angles around 90° are present, which are linked to form infinite spiral chains. Compound <b>3</b> contains an unusual Te₁₅^4‑ polyanion in the form of a bent chain Te₇–Te–Te₇. The connection between the Te₄ groups in <b>1</b> and <b>2</b> and the two Te₇ groups in <b>3</b> is achieved via linear Te₃ entities, which are strongly asymmetric in <b>1</b>, almost symmetric in <b>2</b>, and symmetric in <b>3</b> (for <b>1</b>, Te–Te···Te 174.0°, <i>d</i>₁ = 2.87, <i>d</i>₂ = 3.25 Å; for <b>2</b>, Te–Te–Te 178.8°, <i>d</i>₁ = 3.01, <i>d</i>₂ = 3.09 Å; for <b>3</b>, Te–Te–Te 180°, <i>d</i>₁ = <i>d</i>₂ = 3.06 Å). Periodic DFT calculations show that interaction between the Te₄^2‑ units is negligible in <b>1</b> and weak but undoubtedly present in <b>2</b>. The overlap population amounts to 0.09 in the linear Te₃ group of <b>3</b>. The band structure calculation of <b>3</b> gives semiconducting behavior with a band gap of 1.5 eV in fair agreement with experimental data

Low-Cost Quantum Chemical Methods for Noncovalent Interactions

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

Analytical Gradients for the MSINDO-sCIS and MSINDO-UCIS Method: Theory, Implementation, Benchmarks, and Examples

Analytical expressions for the sCIS (scaled configuration interaction singles) and UCIS (unrestricted CIS) energy gradients are presented for the semiempirical method MSINDO. The theoretical background of the derivation of the analytical gradients is presented, and the implementation into the MSINDO program package is described. The computational efficiency of the underlying <i>Z</i>-vector method is greatly enhanced by making use of the transpose-free quasiminimal residual (TFQMR) algorithm. Benchmark timing tests are compared to the widely used TD-B3LYP approach. For a statistical evaluation of the accuracy of MSINDO-sCIS, geometry optimizations are performed for a small set of organic molecules in selected excited states. The obtained results are compared to CASPT2 and TD-B3LYP/TZVP. In order to demonstrate the applicability of the present approach to periodic systems within the cyclic cluster model, we present first calculations of the excited state structure of ethyne adsorbed on the NaCl (100) surface

Identification of Intermediates during the Hydration of Na₈[AlSiO₄]₆(BH₄)₂: A Combined Theoretical and Experimental Approach

Tetrahydroborate sodalites have been discussed as possible materials for reversible hydrogen storage. In order to access the suitability of Na₈[AlSiO₄]₆(BH₄)₂, its reaction with water was investigated theoretically and experimentally. Density functional theory (DFT) calculations at the generalized gradient approximation (GGA) level were performed to identify the reaction intermediates. We compared experimental IR spectra and ¹¹B NMR chemical shifts with theoretical results for selected molecules in the sodalite cage. Furthermore, the free energies of reaction of the intermediates with respect to Na₈[AlSiO₄]₆(BH₄)₂, gaseous water, and molecular hydrogen at different temperatures were also calculated

Theoretical and Experimental Study of Anatase Nanotube Formation via Sodium Titanate Intermediates

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