Crystal Orbitals Research Articles

Tuning the near-gap electronic structure of tin-halide and lead-halide perovskites via changes in atomic layering

Using density functional theory (DFT)-based calculations, we explore the extent to which achievable modes of atomic layering can tune the near-gap electronic structure of tin- and lead-halide perovskites with applications in dye-sensitized solar cells. We show that regardless of how atomic layering is achieved---whether by the growth of layered inorganic phases such as the Ruddlesden-Popper series, hybrid perovskites connected by organic linker molecules, or layered perovskite heterostructures---their band gaps can similarly be widened by several tenths of an eV or more. Because these classes of compounds are known to have band gaps spanning much of the visible region of the solar spectrum, the ability to controllably tune their near-gap electronic structure could further optimize their performance in solar energy conversion applications. Throughout this work, trends in band gap are explained based on the effects of atomic layering and quantum confinement on the character and energy of band-edge crystal orbitals.

Band-gap energy as a descriptor of catalytic activity for propene oxidation over mixed metal oxide catalysts.

The development of a descriptor or descriptors that can relate the activity of catalysts to their physical properties is a major objective of catalysis research. In this study, we have found that the apparent activation energy for propene oxidation to acrolein over scheelite-structured, multicomponent, mixed metal oxides (Bi3FeMo2O12, Bi2Mo2.5W0.5O12, and Bi1-x/3V1-xMoxO4, where 0 ≤ x ≤ 1) correlates with the band gap of the catalyst measured at reaction temperature. We show through theoretical analysis of the energy components comprising the activation energy why the band-gap energy is the primary component dependent on catalyst composition and, hence, why one should expect the activation energy for propene oxidation to correlate with the band-gap energy. We also demonstrate that the change in band-gap energy with composition arises from the interplay between the sizes and energies of the V 3d, Fe 3d, Mo 4d, and W 5d orbitals, which give rise to the lowest unoccupied crystal orbitals. Both the utility of the band-gap energy as a descriptor for catalytic activity and the role of orbital overlap in determining the band gap are likely to be general features in mixed metal oxide oxidation catalysts, enabling the rational design of catalysts with greater activity for oxidation reactions.

Theoretical investigation on carrier mobilities of armchair graphene nanoribbons with substituted edges

Armchair graphene nanoribbons with several substituent groups (–OH, –NH2, –NO2, –CN and –Cl) present on the edges are investigated by using crystal orbital method based on density functional theory. It is indicated that substituting half of the edge hydrogen atoms does not significantly change the frontier band structures of the graphene nanoribbons. However, the carrier mobilities obtained from deformation potential theory are significantly modified. Activating groups especially for hydroxyl groups can greatly increase the major carrier mobilities, while deactivating groups decrease them. These can be explained by the modified frontier crystal orbitals caused by the substituent groups.

Polyfurans: A Computational Study

AbstractPolyfurans and furan‐based polymers have recently emerged as a new class of conjugated materials. We undertook the first comprehensive computational study of polyfurans, especially doped polyfurans, and systematically compared their properties with those of the corresponding polythiophenes. Parent polyfuran has higher highest occupied crystal orbit and lowest unoccupied crystal orbit energies (by 0.25 and 0.61 eV, respectively), as well as a higher band gap (by 0.36 eV) and significantly larger twisting energy than that of polythiophenes. Doping of polyfuran and polythiophene was less exothermic than polyselenophene in all cases. For thermodynamic reasons, polyfurans should be easier to dope lightly than polythiophenes, whereas at heavy doping levels polyfurans and polythiophenes should be doped with similar ease.

Isolobal Analogies in Intermetallics: The Reversed Approximation MO Approach and Applications to CrGa4- and Ir3Ge7-Type Phases

Intermetallic phases offer a wealth of unique and unexplained structural features, which pose exciting challenges for the development of new bonding concepts. In this article, we present a straightforward approach to rapidly building bonding descriptions of such compounds: the reversed approximation Molecular Orbital (raMO) method. In this approach, we reverse the usual technique of using linear combinations of simple functions to approximate true wave functions and employ the fully occupied crystal orbitals of a compound as a basis set for the determination of the eigenfunctions of a simple, chemically transparent model Hamiltonian. The solutions fall into two sets: (1) a series of functions representing the best-possible approximations to the model system's eigenstates constructible from the occupied crystal orbitals and (2) a second series of functions that are orthogonal to the bonding picture represented by the model Hamiltonian. The electronic structure of a compound is thus quickly resolved into a series of orthogonal bonding subsystems. We first demonstrate the raMO analysis on a familiar molecule, 1,3-butadiene, and then move to illustrating its use in discovering new bonding phenomena through applications to three intermetallic phases: the PtHg4-type CrGa4 and the Ir3Ge7-type compounds Os3Sn7 and Ir3Sn7. For CrGa4, a density of states (DOS) minimum coinciding with its Fermi energy is traced to 18-electron configurations on the Cr atoms. For Os3Sn7 and Ir3Sn7, 18-electron configurations also underlie DOS pseudogaps. This time, however, the 18-electron counts involve multicenter interactions isolobal with classical Ir-Ir or Os-Os covalent bonds, as well as Sn-Sn single bonds serving as electron reservoirs. Our results are based on DFT-calibrated Hückel calculations, but in principle the raMO analysis can be implemented in any method employing one-electron wave functions.

Electronic Structure of Ternary Rhodium Hydrides with Lithium and Magnesium

Chemical bonding in and electronic structure of lithium and magnesium rhodium hydrides are studied theoretically using DFT methods. For Li3RhH4 with planar complex RhH4 structural units, Crystal Orbital Hamilton Populations reveal significant Rh−Rh interactions within infinite one-dimensional ∞ 1 [RhH4] stacks in addition to strong rhodium−hydrogen bonding. These metal−metal interactions are considerably weaker in the hypothetical, heavier homologue Na3RhH4. Both compounds are small-band gap semiconductors. The electronic structures of Li3RhH6 and Na3RhH6 with rhodium surrounded octahedrally by hydrogen, on the other hand, are compatible with a classical complex hydride model according to the limiting ionic formula (M+)3[RhH6]3− without any metal−metal interaction between the 18-electron hydridorhodate complexes. In MgRhH, building blocks of the composition (RhH2)4 are formed with strong rhodium−hydrogen and significant rhodium−rhodium bonding (bond lengths of 298 pm within Rh4 squares). These units are linked together to infinite two-dimensional layers ∞ 2 [(RhH2/2)4] via common hydrogen atoms. Li3RhH4 and MgRhH are accordingly examples for border cases of chemical bonding where the classical picture of hydridometalate complexes in complex hydrides is not sufficient to properly describe the chemical bonding situation.

The role of equilibrium volume and magnetism on the stability of iron phases at high pressures

The present study provides new insights into the pressure dependence of magnetism by tracking the hybridization between crystal orbitals for pressures up to 600 GPa in the known hcp, bcc and fcc iron. The Birch–Murnaghan equation of state parameters are; bcc: V0 = 11.759 A3/atom, K0 = 177.72 GPa; hcp: V0 = 10.525 A3/atom, K0 = 295.16 GPa; and fcc: V0 = 10.682 A3/atom, K0 = 274.57 GPa. These parameters compare favorably with previous studies. Consistent with previous studies we find that the close-packed hcp and fcc phases are non-magnetic at pressures above 50 GPa and 60 GPa, respectively. The principal features of magnetism in iron are predicted to be invariant, at least up to ∼6% overextension of the equilibrium volume. Our results predict that magnetism for overextended fcc iron disappears via an intermediate spin state. This feature suggests that overextended lattices can be used to stabilize particular magnetic states. The analysis of the orbital hybridization shows that the magnetic bcc structure at high pressures is stabilized by splitting the majority and minority spin bands. The bcc phase is found to be magnetic at least up to 600 GPa; however, magnetism is insufficient to stabilize the bcc phase itself, at least at low temperatures. Finally, the analysis of the orbital contributions to the total energy provides evidence that non-magnetic hcp and fcc phases are likely more stable than bcc at core earth pressures.

Do silicene nanoribbons have high carrier mobilities?

Armchair silicene nanoribbons with width of 9–39 silicon atoms are investigated by using the self-consistent field crystal orbital method based on density functional theory. The carrier mobilities obtained from deformation potential theory oscillate with respect to the width and the values are comparable with those the graphene nanoribbons have. The buckled structure, hydrogen saturation, edge reconstruction as well as edge roughness decrease the carrier mobilities which are explained with the aid of crystal orbitals.

The effect of the phase transition on the elasticity of cubic platinum carbide

A study of the high-pressure elastic properties of ideal stoichiometric platinum carbide (PtC) in the rock-salt (RS) and zinc-blende (ZB) structures was conducted using first-principles calculations based on density functional theory, in which we employ the generalized gradient approximation of the Perdew–Burke–Eruzerhof form together with plane-wave basis sets for expanding the crystal orbitals and periodic electron density. Our calculation shows that the recently synthesized compound PtC possess a high-bulk modulus value in the RS phase and the ZB phase is more stable. The investigation of the elastic stability under pressure indicated that the transition pressure from ZB to RS structure of PtC is about 30 GPa and the high-pressure RS phase is stable up to 100 GPa. Our conclusions are consistent with the other theoretical predictions but are reversed with the diamond anvil cell experimental results. Therefore, the experimental observation of the RS structure in PtC remains a puzzle and our study indicates that more experimental and theoretical works need to be performed to ascertain the true nature of the newly discovered PtC material. In addition, the pressure dependence of the bulk modulus K, the shear modulus G, the Young’s modulus E, the Poisson’s ratio υ, the Debye temperature Θ D, the compressional wave velocity V p, the shear wave velocity V s, and the elastic anisotropy factor A for the ZB and RS structures of PtC are all successfully obtained. Moreover, the pressure dependence of the longitudinal and the shear wave velocities in three directions [100], [110], and [111] for cubic PtC are also predicted for the first time.

Magnetic Ordering in Porous Graphenes

Magnetic ordering in porous graphenes is analyzed by crystal orbital methods. While in triangle- and parallelogram-pored graphenes, the frontier bands have wide band widths, and in hexagon-pored graphenes, the HOCOs (highest occupied crystal orbitals) and LUCOs (lowest unoccupied crystal orbitals) are completely flat at the Huckel approximation. The flat bands in the resultant honeycomb systems are disjoint/nondisjoint composite types, and ferromagnetic interactions in the cationic and anionic states are predicted by quantum-chemical calculations including electronic correlations. Possible isoelectronic systems with nitrogen and boron atoms are also investigated as spin doped materials. The origin of spin alignment and pore size effects on magnetism are clarified by Wannier analysis. These systems are promising candidates for two-dimensional organic ferromagnets.

The Prolific {ZR6}X12R and {ZR6}X10 Structure Types with Isolated Endohedrally Stabilized (Z) Rare‐Earth Metal (R) Cluster Halide (X) Complexes

AbstractComproportionation reactions of rare‐earth metal trihalides, RX3, with the respective R metal in the presence of a transition metal Z, preferably from group 8 through 10, yielded single crystals of 31 {ZR6}X12R and 22 {ZR6}X10 type compounds, in most cases for the first time, especially with R = Tb, Dy, Ho, and Er. These are compared with literature entries. The crystal structures are discussed for the equal‐atom pair {IrEr6}I12Er and {IrEr6}I10. In both cases, {IrEr6}Ii12Ia6 cluster complexes are connected via i‐i and i‐a/a‐i bridges, respectively, the {IrEr6} clusters are isolated. Band structure calculations were carried out on the LMTO‐ASA level for a number of {ZY6}X10 examples; the density of states (DOS) and Crystal Orbital Hamiltonian Populations (COHP) derived therefrom exhibit strong Z–Y and Y–X bonding interactions. Most profitable are X = I and endohedral elements of sixth period atoms, especially Z = Os, Ir.

Intermolecular Interaction Energies in Molecular Crystals: Comparison and Agreement of Localized Møller–Plesset 2, Dispersion-Corrected Density Functional, and Classical Empirical Two-Body Calculations

A comparative analysis of the intermolecular energy for a data set including 60 molecular crystals with a large variety of functional groups has been carried out using three different computational approaches: (i) a method based on a physically meaningful empirical partition of the interaction energy (PIXEL), (ii) density functional methods with a posteriori empirical correction for the dispersion interactions (DFT-D), and (iii) a full periodic ab initio quantum mechanical method based on Møller-Plesset perturbation theory for the electron correlation using localized crystal orbitals (LMP2). Due to the large computational cost, LMP2 calculations have been restricted to a subset of seven molecular crystal comprising benzene, formic acid, formamide, succinic anhydride, urea, oxalic acid, and nitroguanidine, and the results compared with PIXEL and DFT-D data as well as with the experimental data show excellent agreement among all adopted methods. This shows that both DFT-D and PIXEL approaches are robust predictive tools for studying molecular crystals. A detailed analysis shows a very similar dispersion contribution of the two methods across the 60 considered molecular crystals. The study also confirms that pure DFT shows serious deficiencies in properly handling molecular crystals in which the dispersive contribution is large. Due to the negligible requested computational resources, PIXEL is the method of choice in screening of a large number of molecular crystals, an essential step to predict crystal polymorphism or to study crystal growth processes. DFT-D can then be used to refine the ranking emerged from PIXEL calculations due to its general applicability and robustness in properly handling short-range interactions.

Copper(I)d10···d10Interactions and Diselenide(1–) Radical Anions in Mixed Valent Selenides Cu4–δBiSe4I

AbstractMelting reactions of copper, CuI, selenium, and Bi2Se3yielded black, shiny needles of Cu4BiSe4I = Cu4BiSe2(Se2)I. The compound decomposes peritectically above 635(5) K and crystallizes in the orthorhombic space groupPnmawitha =960.1(1) pm,b= 413.16(3) pm, andc= 2274.7(2) pm (T= 293(2) K). In the crystal structure, strands${1}\atop{{\infty}}$[BiSeSe2/2(Se2)2/2]3–run along [010]. Therein, the bismuth(III) cation is coordinated by five selenium atoms, which form a square pyramid. The copper(I) cations are coordinated tetrahedrally by selenide, diselenide and iodide ions. Edge‐sharing of these tetrahedra results in zigzag chains of copper cations with short distances of 262.7(4) pm. Enhanced dispersion of the 3dbands, the Crystal Orbital Hamilton Populations (COHP), and disynaptic ELI‐D basins indicate weakly attractived10···d10interactions between the copper cations. The semiconducting properties and the calculated electronic band structure suggest an electron‐precise compound. In copper‐deficient Cu3.824(8)BiSe4I, the Cu···Cu distances are 5 pm shorter, and Raman spectroscopy indicates the presence of diselenide(1–) radical anions besides the diselenide(2–) groups. As a result, in Cu3.824(8)BiSe4I, selenium coexists in the oxidations states –II, –I, and –0.5.

Crystal Orbital Hamilton Population (COHP) Analysis As Projected from Plane-Wave Basis Sets

Simple, yet predictive bonding models are essential achievements of chemistry. In the solid state, in particular, they often appear in the form of visual bonding indicators. Because the latter require the crystal orbitals to be constructed from local basis sets, the application of the most popular density-functional theory codes (namely, those based on plane waves and pseudopotentials) appears as being ill-fitted to retrieve the chemical bonding information. In this paper, we describe a way to re-extract Hamilton-weighted populations from plane-wave electronic-structure calculations to develop a tool analogous to the familiar crystal orbital Hamilton population (COHP) method. We derive the new technique, dubbed "projected COHP" (pCOHP), and demonstrate its viability using examples of covalent, ionic, and metallic crystals (diamond, GaAs, CsCl, and Na). For the first time, this chemical bonding information is directly extracted from the results of plane-wave calculations.

A density‐functional study of the phase diagram of cementite‐type (Fe,Mn)3C at absolute zero temperature

The phase diagram of (Fe(1-x) Mn(x))(3)C has been investigated by means of density-functional theory (DFT) calculations at absolute zero temperature. The atomic distributions of the metal atoms are not random-like as previously proposed but we find three different, ordered regions within the phase range. The key role is played by the 8d metal site which forms, as a function of the composition, differing magnetic layers, and these dominate the physical properties. We calculated the magnetic moments, the volumes, the enthalpies of mixing and formation of 13 different compositions and explain the changes of the macroscopic properties with changes in the electronic and magnetic structures by means of bonding analyses using the Crystal Orbital Hamilton Population (COHP) technique.

Molecular designing of novel ternary copolymers of donor–acceptor polymers using genetic algorithm

An efficient designing route to novel ternary copolymers consisting of polypyrrole (PPy), polythiophene (PTh) and polyfuran (PFu) is developed with the help of genetic algorithm. Using the band structure results obtained from ab initio crystal orbital (CO) calculations, the electronic structures and conduction properties of real ternary copolymers based on donor acceptor type polymers are investigated. The electron rich heterocyclic rings in the backbone chain of the copolymer are joined together by electron withdrawing groups Y, carbonyl group (>C O) and difluoromethylene group (>C CF 2) in an attempt to design the conducting polymer with lowest band gap. A comparative study of various electronic properties is presented. The effects of substitution on the behaviour and properties of the copolymers as well as on the density of states (DOS) are discussed. Band gap decreases as a result of substitution on the polymer backbone chain due to decrease in ionization potential and increase in electron affinity values. This is expected to enhance the intrinsic conductivity of the resulting copolymer. Use of alternate donor acceptor moieties within the repeat units should maximize the extended π conjugation.

Topological analysis of real space properties for the solid-state full-potential APW DFT method

For the solid-state density functional program Elk a module was developed that enables to interface the crystal orbitals data into the DGrid package. Within DGrid the real-space electronic properties, like the electron density and its gradient or Laplacian, kinetic energy density, electron localizability indicator, etc., are computed. The properties can be searched for critical points as well as for the interconnection lines between them. Additionally, the basins can be evaluated and the property integrals can be calculated. The results of topological analysis for fcc Al, MgB 2, CaTiO 3, and urea molecular crystal are discussed and compared with the experimental data. The role of certain computation parameters of (L)APW method is also analyzed.

Wannier analysis of magnetic graphenes

The spin alignment in graphenes with methylene edges is deduced using the crystal orbital method. The ferromagnetic interactions result from exchange integrals between Wannier functions of nonbonding crystal orbitals, in which the amplitudes are localized at the edges. The exchange integral per unit cell decreases as the number of ladders increases.

Orbital ordering inCa2RuO4investigated byR99uperturbed angular correlation

The $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ perturbed angular correlation technique (PAC) using $^{99}\text{R}\text{u}$ was applied to investigate the orbital ordering of $\text{Ru}\text{ }4d$ electrons in ${\text{Ca}}_{2}{\text{RuO}}_{4}$. It was confirmed that the ferro-orbital ordering characterized by the double occupation of ${d}_{xy}$ orbitals at every Ru ion is realized in the stoichiometric ${\text{Ca}}_{2}{\text{RuO}}_{4}$. A strong temperature dependence of the quadrupole interaction below the metal-insulator transition around 360 K reflects variation in the occupation of crystal field orbitals enhanced by very pronounced change in the lattice parameters. Temperature dependence of the hyperfine magnetic field ${H}_{\text{hf}}$ at the Ru site shows very steep increase just below the ordering temperature, which could suggest a two-dimensional character of the magnetic ordering in ${\text{Ca}}_{2}{\text{RuO}}_{4}$.

Orthonormalization and symmetry adaptation of crystal orbitals

Out of a set of localized basis functions we construct completely orthonormalized functions which are symmetry-adapted in the sense that they transform according to the irreducible representations of a space group.