D2d Symmetry Research Articles

Ab Initio Molecular Orbital Studies of the Structure and Stability of the BeAl2F8 Complex

Ab initio molecular orbital calculations have been carried out on the 1:2 metal halide complex BeAl2F8 using a minimal basis set. Seven possible structures with different fluorine bridging combinations were considered. The most stable structure has D2d symmetry with a tetracoordinated beryllium in a tetrahedral configuration. Generally, structures with high coordination numbers for beryllium were more stable than those with low coordination numbers. A ring structure with beryllium in a trigonal configuration was also among the more favorable structures.

Polytype Selection and Structural Disorder Mediated by Intercalated Sulfate Ions Among the Layered Double Hydroxides of Zn with Al and Cr

The stacking of metal hydroxide layers is mediated by intercalated anions. Thereby, anions of different molecular symmetries select for different polytypes. The sulfate ion (molecular symmetry Td) intercalates with one of its axes of rotation parallel to the c-crystallographic axis, also the stacking direction. When the C3 axis of the sulfate is parallel to the c-axis (coordination symmetry C3v), the resulting solid crystallizes in the structure of the 1H or the 3R1 polytype. The coordination symmetry of the SO42− ion (C3v) is a subset of both Oh and D3h, which are respectively the local symmetries of interlayer sites in the 1H and 3R1 polytypes. When the sulfate ion intercalates with one of its C2-axes parallel to the c-axis (coordination symmetry D2d), the resulting solid has a faulted structure, and the local structure of the stacking faults resembles a crystal of monoclinic symmetry. When the sulfate retains the Td symmetry in the interlayer, the LDH crystallizes with turbostratic disorder, which is a...

Nobel‐Metal Centered Polycations [Au@Bi10]5+ or [Pd@Bi10]4+ Embedded in Halogenido‐Bismuthate(III)‐Stannate(II) Frameworks

AbstractThe metal‐rich halogenides AuBi14–δSn2+δX21–δ (δ ≈ 0.4) and PdBi15–δSn1+δX21–δ (δ ≈ 0.6) with X = Cl, Br were crystallized from melts of the metals and BiX3. In the rhombohedral structures (space group R; a ≈ 1050 pm; α ≈ 94°), noble‐metal centered pentagonal antiprisms [Au@Bi10]5+ resp. [Pd@Bi10]4+ are embedded in halogenidometallate frameworks ∞3[Bi4–δSn2+δX21–δ]5– resp. ∞3[Bi5–δSn1+δX21–δ]4–. Mixed BiIII/SnII site occupation allows the framework to adopt different charges. Further exchange of BiIIIX3 against SnIIX2 results in vacancies (δ) on the position of an isolated halide ion. In quantum chemical calculations the naked metal‐clusters are found to be stable in D5d symmetry with interatomic distances close to the observed ones. The significance of interactions between the Wade‐type host cluster Bi104+ and the closed‐subshell guest atoms Au+ or Pd0 is reflected in the molecular orbital diagram, the population analyses and the ELI‐D.

Bis(η5-pentamethylcyclopentadienyl)cobalt(II)

The crystal structure of the title compound, deca­methyl­cobaltocene, [Co(C10H15)2], has been determined. High-quality single crystals were grown from a cold saturated hexa­methyl­disiloxane solution. The structure is related to the manganese and iron analogs. The molecule has D 5d symmetry, with the Co atom in a crystallographic 2/m position. The cobalt–centroid(C5) distance is 1.71Å and the centroid(C5)–Co–centroid(C5) angle is 180°, by symmetry.

Synthesis and Reactivity of a Tetragallium Macrocycle

The reaction of GaCl3 with 1,8-bis(trimethylstannyl)biphenylene produces the tetragallium macrocycle (C12H6)4Ga4Cl4 (1) in high yield. Compound 1 contains a cyclic array of four Ga(biphenylene) units that form a 20-membered ring. The Ga atoms are bridged by μ2-Cl atoms so that the Ga atoms are four-coordinate. The structure adopts a saddle-shaped conformation with approximate D2d symmetry. 1 reacts with Lewis bases (CH3CN and THF) and halide ions (Cl− and Br−) to form (C12H6)2Ga2Cl2L and (C12H6)2Ga2Cl2X− species.

Structure and Heats of Formation of Iodine Fluorides and the Respective Closed-Shell Ions from CCSD(T) Electronic Structure Calculations and Reliable Prediction of the Steric Activity of the Free-Valence Electron Pair in ClF6−, BrF6−, and IF6−

Atomization energies at 0 K and heats of formation at 0 and 298 K are predicted for IF, IF2-, IF2+, IF3, IF4-, IF4+, IF5, IF6-, IF6+, IF7, IF8-, BrF6-, and ClF6- from coupled cluster theory [CCSD(T)] calculations with effective-core potential correlation-consistent basis sets for I. In order to achieve near chemical accuracy (+/-1 kcal/mol), three corrections were added to the complete basis set binding energies based on frozen-core coupled-cluster theory energies: a correction for core-valence effects, a correction for scalar relativistic effects, and a correction for first-order atomic spin-orbit effects. Vibrational zero-point energies were computed at the coupled-cluster level of theory except for IF6-, IF7, and IF8-. The calculated heats of formation for the neutral and ionic IFn fluorides were used to predict fluoride affinities. It is shown that high-level calculations are required to predict correctly the steric activity of the free-valence electron pair on the central atoms in IF6- (C3v), BrF6- (Oh), and ClF6- (Oh ). The vibrational spectrum of IF8- was reanalyzed, and complete mode descriptions for square-antiprismatic XF8 species of D4d symmetry are given.

Optical Excitation and Absorption Spectra of C2v and D2d Isomers of CO4

Recently the CO4 isomer with C 2vsymmetry has been detected in an experiment [C. S. Jamieson et al., Chem. Phys. Lett. 440, 105 (2007)]. To further characterize this isomer, we report its optical excitation and absorption spectra calculated by the time-dependent density functional theory. Its rich spectral features are compared with those of another stable isomer having D 2d symmetry. Their spectral difference can be an evidence to distinguish the isomers in experiments.

Homoleptic, Four-Coordinate Azadipyrromethene Complexes of d10Zinc and Mercury

Tetraarylazadipyrromethenes, and especially their boron chelates, are a growing class of chromophores that are photoactive toward red light. The coordination chemistry of these ligands remains to be explored. Reported here are four-coordinate zinc(II) and mercury(II) complexes of tetraarylazadipyrromethene ligands. The new complexes contain two azadipyrromethenes bound per d(10) metal center and are characterized by (1)H NMR, optical absorption spectroscopy, X-ray diffraction crystallography, and elemental analysis. Solid-state structures show that these bis-chelate complexes distort significantly from idealized D2d symmetry. AM1 geometry optimizations indicate relaxation energies in the range of 6.8-15.2 kcal mol(-1); interligand pi-stacking provides an added energetic impetus for distortion. The absorption spectra show a marked increase in the absorption intensity in the red region and, in the case of the zinc(II) complexes, the development of a second distinct absorption band in this region, which is red-shifted by ca. 40-50 nm relative to the free ligand. Semiempirical INDO/S computations indicate that these low-energy optical absorptions derive from allowed excitations among ligand-based orbitals that derive from the highest occupied molecular orbital and lowest unoccupied molecular orbital of the free azadipyrromethene.

CHEMICAL BONDS AND ELECTRONIC STRUCTURES OF THE METHONIUM CATIONS ${\rm CH}_{6}^{2+}$ AND ${\rm CH}_{7}^{3+}$

Six isomers with C2v, D3h, C5v, D2d, Oh, and C4vsymmetries of [Formula: see text] and two isomers with C3vand C2vsymmetries of [Formula: see text] are investigated at the high ab initio level combined with the natural bond orbital and the atoms-in-molecules theorems. The hyperconjugative interaction and the electron topological analyses indicate that the multiple three-center two-electron (3c-2e) hyperbond is the common chemical-bonding basis for [Formula: see text] and [Formula: see text] species. In contrast to the planar 3c-2e (triangle structure) and planar four-center four-electron (4c-4e) hyperbonds in [Formula: see text] isomeric species, the 3c-2e hyperbond in [Formula: see text] (C4v) is linear while the 4c-4e hyperbonds in [Formula: see text] (C5v, D2d, Oh) are unplanar. [Formula: see text] (C2v) and [Formula: see text] (C3v) as the global minima have many resonance structures predicted by the natural bond resonance theory, indicating the high possibility of the hydrogen scrambling which is similar to the scenario of [Formula: see text].

Synthesis and crystal structure of triaqua[0.25(bromo)1.75(nitrato-O)]copper(II) 18-crown-6 hydrate (solvate)

A complex triaqua[0.25(bromo)1.75(nitrato-O)]copper(II) 18-crown-6 hydrate (solvate), [CuBr0.25(NO3)1.75(H2O)3] · 18-crown-6 · 5H2O, is synthesized, and its crystal structure is studied by X-ray diffraction analysis (space group Cmc21, a = 13.705, b = 14.583, c = 13.174 A, Z = 4; direct method, full-matrix least-squares refinement in the anisotropic approximation to R = 0.069 for 2547 independent reflections; CAD-4 automated diffractometer, λMoKα radiation). The mixed complex molecule is a randomly disordered mixture of [Cu(NO3)2(H2O)3] and [CuBr(NO3)(H2O)3] molecules with site occupancies of 0.875 and 0.125, respectively. The mixed complex molecule and 18-crown-6 molecule lie on the m plane. In the main complex molecule [Cu(NO3)2(H2O)3], the coordination polyhedron of the Cu2+ cation is a slightly distorted square pyramid. The 18-crown-6 molecule has the conformation of a crown with the approximate symmetry D3d.

Magnetic-dependent structure in eight-atom gold clusters

We have performed ab initio calculations on the lowest energy structure of eight-atom gold clusters, a tetracapped square with D4h symmetry, locking it to several total magnetic moments. We have found that for nonzero values of the total magnetic moment, the D4h symmetry is not stable. We have also found that for a fixed nonzero total magnetic moment, the stable structure is a distortion of the tetracapped square, along the square’s diagonals. This structure has a D2h symmetry. The rest of possible structures for this cluster have been calculated as well, and no magnetism-dependent deformation was found, except for the tetracapped tetrahedron with symmetry Td, which is unstable for nonzero total magnetic moment. In this case, the favored structure is a bicapped octahedron with symmetry D2d. The structural change due to magnetic constraints is relevant since the surface of gold clusters has shown a catalytic behavior highly dependent on the structure.

Stabilizing the silicon fullerene Si24 by La and Gd encapsulation

Using gradient-corrected spinpolarized density-functional theory (DFT) for electronic structure calculations，we study the fullerene of silicon Si24 with Th and D2d symmetries in the neutral state stabilized by lanthanum and gadolinium encapsulation. The electronic and magnetic properties of La@Si24 and Gd@Si24 are calculated using spin unrestricted DFT. The higher spin magnetic moment is achieved for Gd@Si24 and the magnetic moment of La@Si24 is completely quenched. These results could possibly lead to new phases and derivatives of silicon.

Local Lattice Structure Study of the Octahedral (CrO6)9- Clusters for Cr3+ Ion Doping in a Variety of Oxide Crystals by Simulating the Corresponding EPR and Optical Spectra

On the basis of the 120 x 120 complete energy matrix, the local lattice structures of the octahedral (CrO6)9- clusters for Cr3+ ions doping in a variety of oxide crystals with D3d or C3v site symmetry have been studied by employing two distorted parameters, respectively. By simulating the calculated EPR and optical spectra data to the experimental results, the local lattice structure parameters are determined unambiguously. It is shown, by means of a series of calculations, that although the local lattice structures around the M (M = Al3+, Ga3+, Li+, Sc3+, etc.) ions in host crystals are obviously different, the local lattice structures of the octahedral (CrO6)9- clusters in a variety of oxide crystals doped with Cr3+ ions are similar and fluctuant in the vicinity of that of the Cr2O3. This may be ascribed to the fact that there is the similarly octahedral (CrO6)9- clusters in a variety of oxide crystals doped with Cr3+ and the Cr2O3 crystal. Our viewpoint is consistent with that of Gaudry et al. [Phys. Rev. B 2003, 67, 094108].

Halogen Exchange and Scrambling between C−X and M−X‘ Bonds in Copper, Nickel, and Cobalt Complexes of 6,6‘-bis(bromo/ chloromethyl)-2,2‘-bipyridine. Structural, Electrochemical, and Photochemical Studies

The synthesis, reactivities, spectroscopic, electrochemical, and structural studies of copper(I), copper(II), nickel(II), and cobalt(II) complexes of 6,6'-bis(bromomethyl)-2,2'-bipyridine (bpy-Br2) and 6,6'-bis(chloromethyl)-2,2'-bipyridine (bpy-Cl2) have been reported. The copper(I) complex [CuI(bpy-Br2)2](ClO4) (1) has been obtained in two crystallographic modifications, in which the coordination geometry of the metal center has the D2d symmetry. The reaction between CuCl2.2H2O and bpy-Br2 has been followed spectrophotometrically at 45 degrees C over a period of 7 h, and a mechanism for the intramolecular halogen exchange and scrambling in the initially formed compound [CuII(bpy-Br2)Cl2] (5) has been proposed. Depending upon the reaction conditions, several halogen-exchanged products, namely [CuII(bpy-Br1.86Cl0.14)(Cl1.89Br0.11)] (2), [CuII(bpy-Br1.81Cl0.19)(Cl1.70Br0.30)(H2O)] (3), and [CuII(bpy-Br0.63Cl1.37)(Cl0.54Br1.46)] (4), have been isolated in crystalline form. The reaction between bpy-Cl2 and CuCl2.2H2O provides [CuII(bpy-Cl2)Cl2] (7) and [CuII(bpy-Cl2)Cl2(H2O)] (8), whereas CoCl2.6H2O and NiCl2.6H20 on reaction with bpy-Br2 under boiling condition produce [CoII(bpy-Br0.5Cl1.5)(ClBr)] (11) and [NiII(bpy-Br0.46Cl1.54)(Cl0.73Br1.27)(H2O)] (12), respectively. The X-ray structures determined for the 4-coordinate compounds 2, 4, and 7 show flattened tetrahedral geometry for the metal center with the D2 symmetry. Both 5-coordinate compounds 3 and 12 have square pyramidal geometry, and whereas the nickel(II) complex 12 has near-perfect geometry (tau = 0.015), considerable distortion is observed for the copper(II) complex 3 (tau = 0.25). Complexes [CuII(bpy-Cl2)Br2] (6) and [CuII(bpy-Br2)Br2] under boiling condition undergo photoreduction to produce the dimeric copper(I) complexes [{CuI(bpy-Cl1.30Br0.70)(mu-Br)}2](9) and [{CuI(bpy-Br2)(mu-Br)}2] (10), respectively. The fact that the photoreduction of [CuII(bpy-Cl2)Br2] (6) and [CuII(bpy-Br2)Br2] do not take place in absence of light has been established by spectrophotometric measurements. The crystal structures of 9 and 10 have been determined. The electrochemical behavior of all the copper complexes 1-10 has been studied in acetonitrile and dichloromethane. The E1/2 values for the CuI/CuII redox couples show strong solvent dependence and for a given system the E1/2 value is more positive in dichloromethane relative to that in acetonitrile. For the compounds [CuII(bpy-Br2-xClx)(Cl2-yBry)] (x = 0-2, y = 0-2), the E1/2 values become more positive with the increase of y value.

Solid-phase synthesis and characterization of rare-earth chromates

Simple chromates(V) MCrO4 (M = Sc, Y, Gd, Er, or Yb) and chromate(V) vanadates Gd(CrO4)x(VO4)1 − x have been synthesized by a solid-phase method. All compounds crystallize in the xenotime-type structure, space group I41/amd, Z = 4. The unit cell parameters have been calculated as follows: for GdCrO4, a = 7.209(5) A, c = 6.318(4) A; for ErCrO4, a = 7.088(2) A, c = 6.231(1) A; for YbCrO4, a = 7.034(1) A, c = 6.205(2) A; for YCrO4, a = 7.108(3) A, c = 6.254(3) A; and for ScCrO4, a = 7.012(2) A, c = 6.188(2) A. Symmetry D2d, established for the CrO4 tetrahedron during the Rietveld structure refinement, is verified by IR spectroscopy. The MCrO4 simple chromates are paramagnets; their magnetic moments range from 1.7 to 8.1 μB.

Examining the structural changes in Fe2(CO)9 under high external pressures by Raman spectroscopy

Pressure-induced structural changes in di-iron nonacarbonyl [Fe2(CO)9] were examined by in situ Raman spectroscopy with the aid of a diamond anvil cell. Our results indicate that Fe2(CO)9 undergoes a pressure-induced phase transformation at about 0.9 GPa. Upon further compression, another structural transformation is identified at 7 GPa. In the low-pressure phase below 0.9 GPa, the π back-bonding between metal and carbonyl increases with increasing pressure. In the high-pressure phase above 7 GPa, the combination of high-pressure and laser irradiation induces a change in structure from Fe2(CO)9 to Fe2(CO)8. Fe2(CO)8 appears to adopt a structure with C2v rather than D3d or D2h symmetry. The metal–metal bond is gradually weakened under high pressures, and Fe2(CO)8 eventually decomposes by breaking the Fe–Fe bond when compressed up to 17.7 GPa.Key words: metal carbonyl, Raman spectroscopy, high pressure, diamond anvil cell.

Is This a Chemical Bond? A Theoretical Study of Ng2@C60(Ng=He, Ne, Ar, Kr, Xe)

Quantum-chemical calculations using DFT (BP86) and ab initio methods (MP2, SCS-MP2) have been carried out for the endohedral fullerenes Ng2@C60 (Ng=He-Xe). The nature of the interactions has been analyzed with charge- and energy-partitioning methods and with the topological analysis of the electron density (Atoms-in-Molecules (AIM)). The calculations predict that the equilibrium geometries of Ng2@C60 have D3d symmetry when Ng=Ne, Ar, Kr, while the energy-minimum structure of Xe2@C60 has D5d symmetry. The precession movement of He2 in He2@C60 has practically no barrier. The Ng--Ng distances in Ng2@C60 are much shorter than in free Ng2. All compounds Ng2@C60 are thermodynamically unstable towards loss of the noble gas atoms. The heavier species Ar2@C60, Kr2@C60, and Xe2@C60 are high energy compounds which are at the BSSE corrected SCS-MP2/TZVPP level in the range 96.7-305.5 kcal mol(-1) less stable than free C60+2 Ng. The AIM method reveals that there is always an Ng--Ng bond path in Ng2@C60. There are six Ng--C bond paths in (D3d) Ar2@C60, Kr2@C60, and Xe2@C60, whereas the lighter D3d homologues He2@C60 and Ne2@C60 have only three Ng--C2 paths. The calculated charge distribution and the orbital analysis clearly show that the bonding situation in Xe2@C60 significantly differs from those of the lighter homologues. The atomic partial charge of the [Xe2] moiety is +1.06, whereas the charges of the lighter dimers [Ng2] are close to zero. The a2u HOMO of (D3d) Xe2@C60 in the 1A1g state shows a large mixing of the highest lying occupied sigma* orbital of [Xe2] and the orbitals of the C60 cage. There is only a small gap between the a2u HOMO of Xe2@C60 and the eu LUMO and the a2u LUMO+1. The calculations show that there are several triplet states which are close in energy to each other and to the 1A1g state. The bonding analysis suggests that the interacting species in Xe2@C60 are the charged species Xe2q+ and C60q-, where 1<q<2. The calculated Xe--Xe distance in the endohedral fullerene (2.494 A) is even shorter than the calculated value for free Xe2(2+) (2.746 A). Thus, the Xe--C and Xe--Xe interactions in Xe2@C60 should be considered as genuine chemical bonds which are enforced by the compression energy. The Ng--Ng and Ng--C interactions in the lighter homologues Ar2@C60 and Kr2@C60 may also be considered as chemical bonds because the theoretically predicted properties of the endohedral fullerenes are significantly different from the free C60 and noble gas atoms. According to the bonding analysis, He2@C60 and Ne2@C60 are weakly bonded van der Waals complexes.

Optical studies of structural and magnetic anisotropies in epitaxial CdSe/ZnSe quantum dots

AbstractWe summarize experimental studies on the optical polarization properties of MBE‐grown shape‐asymmetric self‐assembled CdSe/ZnSe quantum dots (QDs). The zero magnetic field fine structure splitting of excitonic transitions in structurally anisotropic QDs gives rise to an effective linear‐to‐circular and circular‐to‐linear optical polarization conversion upon resonant excitation of the QD ensemble. The effect is qualitatively modelled in terms of a pseudospin formalism. Furthermore, we show how an in‐plane magnetic field leads to a complex rotation behavior of the axis of the optical polarization. Our analysis based on the exciton pseudospin Hamiltonian unambiguously displays that these effects are induced by isotropic and anisotropic contributions to the heavy hole Zeeman term. Likewise we show that the latter mechanism can be used to tune the optical respone of shape‐anisotropic QDs such that the optical polarization properties are equal to QDs of perfect D2d symmetry. (© 2007 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Synthesis and crystal structure of hexaaquamagnesium 18-crown-6 dibromide dihydrate

A new complex compound [Mg(H2O)6]Br2 · 18-crown-6 · 2H2O(I) is synthesized, and its structure is studied by X-ray diffraction analysis. The crystals are monoclinic: space group P21/c, a = 7.128 A, b = 18.584 A, c = 9.598 A, A = 103.01°, Z = 2; R = 0.039 for 2180 independent reflections (CAD-4 automated diffractometer, λMoKα radiation). The coordination polyhedron of the Mg2+ cation is a slightly distorted octahedron. The 18-crown-6 molecule has the conformation of a distorted crown with the approximate D3d symmetry. The crystal contains a branched three-dimensional network of intermolecular (interionic) hydrogen bonds.

Sodium barium hexahydrogenhexamolybdoaluminate(III) decahydrate

The title compound, NaBa[AlMo6(OH)6O18]·10H2O, contains a B-type Anderson polyanion [AlMo6(OH)6O18]3− having an inversion center with approximate D3d symmetry. There are two uncoordinated water mol­ecules per formula unit, the remaining eight being coordinated to the Na+ and Ba2+ cations, which link the polyanions to form the three-dimensional structure. Hydrogen-bonding inter­actions exist to stabilize the structure.