How Close Are the Slater and Becke–Roussel Potentials in Solids?

The Becke–Roussel (BR) potential [<i>Phys. Rev. A</i> <b>1989</b>, <i>39</i>, 3761] was proposed as an approximation to the Slater potential, which is the Coulomb potential generated by the exact exchange hole. In the present work, a detailed comparison between the Slater and BR potentials in solids is presented. It is shown that the two potentials usually lead to very similar results for the electronic structure; however, in a few cases, e.g., Si, Ge, or strongly correlated systems like NiO, the fundamental band gap or magnetic properties can differ markedly. Such differences should not be neglected when the computationally expensive Slater potential is replaced by the cheap semilocal BR potential in approximations to the exact-exchange Kohn–Sham potential, such as the one proposed by Becke and Johnson [<i>J. Chem. Phys.</i> <b>2006</b>, <i>124</i>, 221101]

Structural, Spectroscopic, and Computational Studies on Tl₄Si₅O₁₂: A Microporous Thallium Silicate

Single crystals of the previously unknown thallium silicate Tl₄Si₅O₁₂ have been prepared from hydrothermal crystallization of a glassy starting material at 500 °C and 1kbar. Structure analysis resulted in the following basic crystallographic data: monoclinic symmetry, space group <i>C</i>2/<i>c</i>, <i>a</i> = 9.2059(5) Å, <i>b</i> = 11.5796(6) Å, <i>c</i> = 13.0963(7) Å, β = 94.534(5)°. From a structural point of view the compound can be classified as an interrupted framework silicate with Q³- and Q⁴-units in the ratio 2:1. Within the framework 4-, 6-, and 12-membered rings can be distinguished. The framework density of 14.4 T-atoms/1000 ų is comparable with the values observed in zeolitic materials like Linde type A, for example. The thallium cations show a pronounced one-sided coordination each occupying the apex of a distorted trigonal TlO₃ pyramid. Obviously, this reflects the presence of a stereochemically active 6s² lone pair electron. The porous structure contains channels running along [110] and [−1 1 0], respectively, where the Tl⁺ cations are located for charge compensation. Structural investigations have been completed by Raman spectroscopy. The interpretation of the spectroscopic data and the allocation of the bands to certain vibrational species have been aided by DFT calculations, which were also employed to study the electronic structure of the compound

Theoretical and Experimental Study on the Optoelectronic Properties of Nb₃O₇(OH) and Nb₂O₅ Photoelectrodes

Nb₃O₇(OH) and Nb₂O₅ nanostructures are promising alternative materials to conventionally used oxides, e.g. TiO₂, in the field of photoelectrodes in dye-sensitized solar cells and photoelectrochemical cells. Despite this important future application, some of their central electronic properties such as the density of states, band gap, and dielectric function are not well understood. In this work, we present combined theoretical and experimental studies on Nb₃O₇(OH) and H–Nb₂O₅ to elucidate their spectroscopic, electronic, and transport properties. The theoretical results were obtained within the framework of density functional theory based on the full potential linearized augmented plane wave method. In particular, we show that the position of the H atom in Nb₃O₇(OH) has an important effect on its electronic properties. To verify theoretical predictions, we measured electron energy-loss spectra (EELS) in the low loss region, as well as, the O–K and Nb–M₃ element-specific edges. These results are compared with corresponding theoretical EELS calculations and are discussed in detail. In addition, our calculations of thermoelectric conductivity show that Nb₃O₇(OH) has more suitable optoelectronic and transport properties for photochemical application than the calcined H–Nb₂O₅ phase

Molecular Structure of Isocyanic Acid, HNCO, the Imide of Carbon Dioxide

Isocyanic acid, HNCO, the imide of carbon dioxide, was prepared by reaction of stearic acid and potassium cyanate (KOCN) at 60 °C in a sealed, thoroughly dried reactor. Interestingly, its crystal structure, solved by X-ray single crystal diffraction at 123(2) K, shows a group–subgroup relation for the NCO^– anion to carbon dioxide: (for CO₂, <i>cP</i>12, <i>Pa</i>3̅, <i>a</i> = 5.624(2) Å, 150 K, C–O 1.151(2) Å; for HNCO, <i>oP</i>16, <i>Pca</i>2₁, <i>a</i> = 5.6176(9), <i>b</i> = 5.6236(8), <i>c</i> = 5.6231(7) Å, 123(2) K). Precise positions of H, N, C, and O were determined by DFT calculations with WIEN2k leading to interatomic distances C–O 1.17, C–N 1.22, N–H 1.03, and −N–H···N 2.14 Å, and the interatomic angle N–C–O 171°

Molecular Structure of Isocyanic Acid, HNCO, the Imide of Carbon Dioxide

Isocyanic acid, HNCO, the imide of carbon dioxide, was prepared by reaction of stearic acid and potassium cyanate (KOCN) at 60 °C in a sealed, thoroughly dried reactor. Interestingly, its crystal structure, solved by X-ray single crystal diffraction at 123(2) K, shows a group–subgroup relation for the NCO^– anion to carbon dioxide: (for CO₂, <i>cP</i>12, <i>Pa</i>3̅, <i>a</i> = 5.624(2) Å, 150 K, C–O 1.151(2) Å; for HNCO, <i>oP</i>16, <i>Pca</i>2₁, <i>a</i> = 5.6176(9), <i>b</i> = 5.6236(8), <i>c</i> = 5.6231(7) Å, 123(2) K). Precise positions of H, N, C, and O were determined by DFT calculations with WIEN2k leading to interatomic distances C–O 1.17, C–N 1.22, N–H 1.03, and −N–H···N 2.14 Å, and the interatomic angle N–C–O 171°

Atomic-Scale Structure of the Hematite α‑Fe₂O₃(11̅02) “R-Cut” Surface

The α-Fe₂O₃(11̅02) surface (also known as the hematite r-cut or (012) surface) was studied using low-energy electron diffraction (LEED), X-ray photoelectron spectroscopy (XPS), ultraviolet photoelectron spectroscopy (UPS), scanning tunneling microscopy (STM), noncontact atomic force microscopy (nc-AFM), and <i>ab initio</i> density functional theory (DFT)+<i>U</i> calculations. Two surface structures are stable under ultrahigh vacuum (UHV) conditions; a stoichiometric (1 × 1) surface can be prepared by annealing at 450 °C in ≈10^–6 mbar O₂, and a reduced (2 × 1) reconstruction is formed by UHV annealing at 540 °C. The (1 × 1) surface is close to an ideal bulk termination, and the undercoordinated surface Fe atoms reduce the surface bandgap by ≈0.2 eV with respect to the bulk. The work function is measured to be 5.7 ± 0.2 eV, and the VBM is located 1.5 ± 0.1 eV below <i>E</i>_F. The images obtained from the (2 × 1) reconstruction cannot be reconciled with previously proposed models, and a new “alternating trench” structure is proposed based on an ordered removal of lattice oxygen atoms. DFT+<i>U</i> calculations show that this surface is favored in reducing conditions and that 4-fold-coordinated Fe²⁺ cations at the surface introduce gap states approximately 1 eV below <i>E</i>_F. The work function on the (2 × 1) termination is 5.4 ± 0.2 eV

Cluster Nucleation and Growth from a Highly Supersaturated Adatom Phase: Silver on Magnetite

The atomic-scale mechanisms underlying the growth of Ag on the (√2×√2)<i>R</i>45°-Fe₃O₄(001) surface were studied using scanning tunneling microscopy and density functional theory based calculations. For coverages up to 0.5 ML, Ag adatoms populate the surface exclusively; agglomeration into nanoparticles occurs only with the lifting of the reconstruction at 720 K. Above 0.5 ML, Ag clusters nucleate spontaneously and grow at the expense of the surrounding material with mild annealing. This unusual behavior results from a kinetic barrier associated with the (√2×√2)<i>R</i>45° reconstruction, which prevents adatoms from transitioning to the thermodynamically favorable 3D phase. The barrier is identified as the large separation between stable adsorption sites, which prevents homogeneous cluster nucleation and the instability of the Ag dimer against decay to two adatoms. Since the system is dominated by kinetics as long as the (√2×√2)<i>R</i>45° reconstruction exists, the growth is not well described by the traditional growth modes. It can be understood, however, as the result of supersaturation within an adsorption template system

Cluster Nucleation and Growth from a Highly Supersaturated Adatom Phase: Silver on Magnetite

The atomic-scale mechanisms underlying the growth of Ag on the (√2×√2)<i>R</i>45°-Fe₃O₄(001) surface were studied using scanning tunneling microscopy and density functional theory based calculations. For coverages up to 0.5 ML, Ag adatoms populate the surface exclusively; agglomeration into nanoparticles occurs only with the lifting of the reconstruction at 720 K. Above 0.5 ML, Ag clusters nucleate spontaneously and grow at the expense of the surrounding material with mild annealing. This unusual behavior results from a kinetic barrier associated with the (√2×√2)<i>R</i>45° reconstruction, which prevents adatoms from transitioning to the thermodynamically favorable 3D phase. The barrier is identified as the large separation between stable adsorption sites, which prevents homogeneous cluster nucleation and the instability of the Ag dimer against decay to two adatoms. Since the system is dominated by kinetics as long as the (√2×√2)<i>R</i>45° reconstruction exists, the growth is not well described by the traditional growth modes. It can be understood, however, as the result of supersaturation within an adsorption template system