Compositions and structures of nanoparticles of pentagonal axial symmetry <Emphasis Type="Italic">D</Emphasis><Subscript>5<Emphasis Type="Italic">d</Emphasis></Subscript>: Nanotubes

The method of determination of the structure and the number of atoms in the shells of nanoparticles as a function of the arrangement of atoms at the symmetry elements of a symmetry group has been developed. The formulas for the calculation of the number of particles with symmetry group D _5d are reported. The number of particles in these shells is determined by three structurally invariant numbers and the “quantum number” of the group order n. The classification of all possible nanostructures with symmetry group D _5d is given: C _θ+10z , z = 0, 1, 2, …, where the basic shells are C _θ = C ₂, C ₁₀, C ₁₂. The sum rule has been obtained for the coordination numbers of shell sites located at symmetry axes. Pentagonal axial nanoparticles are shown to be the initial shells for obtaining (5,5) and (10,10) armchair nanotubes or (5,0) and (10,0) zigzag nanotubes. The general formula of these nanotubes closed with icosahedral and dodecahedral caps is N _20+10p , N _60+10p (p = 1, 2, …). The graphical constructions of all classes of nanoparticles and nanotubes of the pentagonal axial type are reported.     

Compositions and structures of nanoparticles of trigonal symmetry <Emphasis Type="Italic">D</Emphasis><Subscript>3<Emphasis Type="Italic">d</Emphasis></Subscript>: Nanotubes

A method has been developed for the determination of the structure and number of atoms in the shells of nanoparticles as a function of the arrangement of atoms at the symmetry elements of a symmetry group. The formulas for calculation of the number of particles of symmetry D _3d have been reported. It has been shown that the number of atoms in trigonal shells is determined by three structurally invariant numbers and the quantum number of the group order n. All possible nanostructures of symmetry D _3d have been classified: C_{θ + 6z} , z = 0, 1, 2, ..., where the basic shells are C_θ = C₆, C₈, and C₁₄. A sum rule has been obtained for the coordination numbers of the shell sites located on symmetry axes. Trigonal nanoparticles are parent ones for obtaining (3,0), (6,0), and (9,0) nanotubes of trigonal type. The general formulas of these nanotubes with icosahedral, dodecahedral, and cubic caps are N_{8 + 12p} , N_{20 + 24p} , and N_{60 + 36p} (p = 1, 2, ...), respectively. The graphical constructions of all classes of trigonal nanoparticles and nanotubes are reported.     

Preparation and Crystalline Structure of Dihydrate of <Emphasis Type="Italic">hemi</Emphasis>-(Diazonium-18-crown-6) Isocyanurate of Isocyanuric Acid

Crystalline dihydrate of hemi-(diazonium-18-crown-6) isocyanurate of isocyanuric acid, 0.5[H₂DA18K6]²⁺?(C₃H₂N₃O₃)^??C₃H₃N₃O₃?2H₂O, was prepared and investigated by X-ray crystallography. In the given structure the dication DA18K6 is center-symmetric and possesses crown conformation of approximate D_3h symmetry. Molecule of isocyanuric acid and its anion are nearly planer. This molecule possesses approximate D_3h symmetry and its anion possesses approximate C_2v symmetry. With sufficient precision were determined geometrical parameters (bond lengths, bond angles etc.) of ions and molecules and was determined their packing in the given crystalline structure in which there is developed system of intermolecular (interion) hydrogen bonds.     

Quantum-chemical study of ytterbium fluorides and of complex F<Subscript>2</Subscript>YbF<Subscript>2</Subscript>CeF<Subscript>2</Subscript>

The structural parameters of the (²Σ⁺//C_∞v)-YbF, (¹A₁//C_2v)-YbF2, (²A₂^′//D_3h)-YbF₃, (¹Ag//D_2h)-YbF₂Yb, (¹Ag//C_2h)-FYbF₂YbF, (¹A₁//C_2v)-FYbF₂YbF, (¹A₁//C_2v)-YbF₂YbF₂, (³B_3u//D_2h)-F₂YbF₂YbF₂, (²A′//C_s)-FYbF₂YbF₂, and (³B₂//С_2v)-F₂YbF₂CeF₂ molecules have been determined. Disproportionation of ytterbium monofluoride (2YbF → YbF₂ + Yb + 0.46 eV) is less exothermic than dimerization (2YbF → YbF₂Yb + 2.10 eV). The bond energy of the ytterbium difluoride molecules in the trans dimer (2.93 eV) exceeds those in the cis dimer (2.86 eV) and the coaxial dimer (1.66 eV). Ytterbium trifluoride dimerizes exothermically (2.95 eV) without spin pairing. The dipole and quadrupole moments of the molecules as well as the charges and spin populations of the atoms and the valence electron configurations of the lanthanides have been calculated.     

Compositions of nanoparticles of hexagonal symmetry

The formulas for calculation of the number of atoms in nanoparticles with symmetry group D _6h are reported. The numbers of atoms are determined by six structurally invariant numbers and the “quantum number” of the group order n. Eight classes of nanostructures with symmetry group D _6h are revealed: C _{? + 12z} , where z = 0, 1, 2, …, and C _? is C ₂, C ₆, C ₈, or C ₁₄. The sum rule for the coordination numbers of all atoms of subshells related to symmetry elements is established. Two-dimensional nanoparticles are considered.     

Quantum-chemical study of lutetium,ytterbium, and gadolinium phthalocyaninates PcLnCl

Structural parameters and IR spectra of the (¹A₁//C_4v)-PcLuCl, (²B₂//C_4v)-PcYbCl, and (⁸A₂//C_4v)-PcGdCl molecules, (²A₂//C_4v)-Pc⁺LuCl, (3B₁//C_4v)-Pc⁺YbCl, and (⁹A₁//C_4v)-Pc⁺GdCl cations, (¹A_g//D_2h)-PcLuCl₂LuPc dimer, and PcLuCl···PcLuCl coaxial molecular pair have been simulated using the DFT (U) PBE0/SDD method. The PcLnCl (Ln = Lu, Yb, Gd) molecules have exhibited the equilibrium Ln–N bond length of 222, 223, and 230 pm, the Ln–Cl bond length of 245, 246, and 253 pm, the dipole moment of 4.73, 4.57, and 4.84 D directed from Cl to Ln, and ionization potential of 6.6 eV. β-Decay (¹A₁//C_4v)-Pc¹⁷⁷LuCl → (¹A₁//C_4v)-(Pc^177mHfCl)⁺ occurs with no significant change of the charge on the metal atom.     

Calculation of the thermodynamic characteristics of ions in vapor over sodium fluoride

The geometric parameters, normal vibration frequencies, and thermochemical characteristics of the ions present in vapor over sodium fluoride, Na₂F⁺, Na₃F ₂ ⁺ , NaF ₂ ^? , and Na₂F ₃ ^? , were calculated ab initio by the Hartree-Fock method and taking into account electron correlation. The main equilibrium configuration of all ions was found to be the linear configuration of D _∞h symmetry. Pentaatomic ions could also exist as two isomers, planar cyclic of C _2v symmetry and bipyramidal of D _3h symmetry. Their energies were higher than that of the D _∞h isomers, and their contents in vapor were negligibly low. The energies and enthalpies of dissociation of the ions with the elimination of the NaF molecule were calculated. The enthalpies of formation of the ions were obtained.     

A quantum chemical study of the Fe@<Emphasis Type="Italic">C</Emphasis><Subscript>60</Subscript> endocomplex

At the DFT (U)PBE0/cc-pVDZ level the structural parameters of a hypothetical Fe@C ₆₀ endocomplex are determined. The (A ₁//C _3v )–Fe@C ₆₀ state characterized by the electron spin square of 3.07 au, the free valence of 4.15, the dipole moment of 1.15 D, and the 172 pm Fe nuclear shift relative to the center of inertia of С₆₀ corresponds to the energy minimum. The Stone–Wales rearrangement in the quasi-triplet state increases the endocomplex energy by 1.56 eV and by 0.79 eV in the quasi-quintet state.     

The equilibrium structures of the Li[C<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>]<Subscript>1</Subscript> (<Emphasis Type="Italic">n</Emphasis> = 7–12) complexes and their alternation depending on <Emphasis Type="Italic">n</Emphasis>

The equilibrium geometric configurations of the Li[C _n ]₁ (n = 7–12) complexes, where [C _n ]₁ is a cylindrical hydrocarbon containing the simplest zigzag nanotube fragment, were determined by the density functional theory method with the PBE0 exchange-correlation functional. Analytic molecular orbital (MO) estimates were obtained for isolated [C _n ]₁ hydrocarbons in the Hückel approximation. The appearance of nonbonding MOs for hydrocarbons with even n was demonstrated. Equilibrium structure types were found to alternate as n increased. This alternation correlated with the behavior of the frontier orbitals of the [C _n ]₁ hydrocarbon. At odd n, the Li atom was situated near the boundary of the π electron density of the bracelet, and the complex had C _s symmetry. Complexes with even n had the C _2v point group, and lithium was situated in the inner cylinder cavity above the center of one of benzene rings.     

Aromaticity of Bare Iridium Trimers and Ir3M0/+ and $$\rm{Ir}_3M_2^{+/3+}$$ (M = Li,Na, K,and Be,Ca) Bimetallic Clusters

The structural stabilities, bonding nature, electronic properties, and aromaticity of bare iridium trimers \(\rm{Ir}_3^{+/-}\) with different geometries and spin multiplicities are studied at the DFT/B3LYP level of theory. The ground state of the \(\rm{Ir}_3^{+}\) cation is found to be the ³A₂ (C_2v) triplet state and the ground state of the \(\rm{Ir}_3^{-}\) anion the ⁵A₂ (C_2v) quintet state. A detailed molecular orbital (MO) analysis indicates that the ground-state \(\rm{Ir}_3^{+}\) ion (C_2v, ³A₂) possesses double (σ and partial δ) aromaticity as well as the ground-state \(\rm{Ir}_3^{-}\) ion (C_2v, ⁵A₂). The multiple d-orbital aromaticity is responsible for the totally delocalized three-center metal-metal bond of the triangular Ir₃ framework. \(\rm{Ir}_3^{-}\) (C_2v, ¹A₁) structure motif is perfectly preserved in pyramidal Ir₃M^0/+ (C_s, ¹A′) and bipyramidal \(\rm{Ir}_3M_2^{+/3+}\) (C_2v, ¹A₁) (M = Li, Na, K and Be, Ca) bimetallic clusters which also possess the corresponding d-orbital aromatic characters.     

Maximum filling principle and sublattices of lanthanide atoms in crystal structures

The most important characteristics of the Voronoi-Dirichlet polyhedra (VDP) were determined for 20526 Ln atoms (Ln = La?Lu) in sublattices containing chemically identical lanthanide atoms in the crystal structures of 14659 inorganic, coordination, and organoelement compounds. The number of lanthanide VDP faces in the sublattice can vary from 4 to 36 and, irrespective of the lanthanide nature, the VDP have most often 14 faces. The Fedorov cuboctahedron is the most abundant type of VDP. In the crystal structures, Ln atoms were found to have, most often, C ₁ site symmetry (～49% of cases) and also C _s (16), C _2v (7%), or C ₂ (6%) site symmetries.     

Determination of molar extinction coefficients for endohedral metallofullerene Dy@C<Subscript>82</Subscript>(C<Subscript>2v</Subscript>)

Isomerically pure endohedral metallofullerene Dy@C₈₂(C _2v) was synthesized by the electric arc method, extracted from the soot with o-dichlorobenzene, isolated from the extract by HPLC, and characterized by mass spectrometry and spectrophotometry. The spectrophotometric titration of a solution of endohedral metallofullerene Dy@C₈₂(C _2v) was conducted with potassium perchlorotriphenylmethide. The concentration of Dy@C82(C _2v) in o-dichlorobenzene was determined, and the molar absorption coefficients for its neutral and anionic forms were calculated (3.0?10³ (at 927 nm) and 4.0?10³ mol^–1 L cm^–1 (at 884 nm), respectively.     

Photolysis of <Emphasis Type="Italic">ortho</Emphasis>-azidophenol in various solvents

The photolysis of ortho-azidophenol in water, ethanol, acetonitrile, chloroform, and benzene was studied by IR and electronic spectroscopy and thin-layer chromatography. It was found that an equilibrium between ortho-azidophenol and its quinonoid form occurred in benzene. In the photolysis of ortho-azidophenol in benzene, intramolecular hydrogen bonding facilitates the degradation of the azido group through the mechanism of formation of intermediate triazene structures. In the other solvents, which exclude intramolecular hydrogen bonding, the nitrene mechanism of photolysis yielding ortho-aminophenol, ortho-iminoquinone, and an azo compound is operative. The rate of formation of photolysis products depends on the nature of the solvent.     

Structural systematics and conformational analyses of an isomer grid of nine tolyl-<Emphasis Type="Italic">N</Emphasis>-pyridinylcarbamates

A 3 × 3 isomer grid of nine Methylphenyl-N-pyridinylcarbamates (CxxM) is reported with seven CxxM crystal structures at 294 K (xx = pp, pm, po, mp, op, om, oo; x = para-, meta-, ortho), where Cx = pyridinyl ring (as C₅NH₄NH-) and xM is representative of –C(=O)OC₆H₄CH₃. All seven carbamate crystal structures aggregate via N–H…N intermolecular interactions with the three CpxM carbamates having C(6) zigzag chains, CmpM with C(5) zigzag chains and three ortho-pyridine CoxM structures as hydrogen-bonded dimers with graph set \(R_{2}^{2}\) (8) and augmented by flanking C–H…O contacts. The CpoM crystal structure crystallises with 0.25 CHCl₃ per carbamate molecule and solvent channels aligning along the a-axis direction. Conformational analyses of the nine minimised CxxM structures in gas phase are detailed for comparisons with the solid-state structures and demonstrate similarities between both structural methods. The modelling results also demonstrate the problems associated with pendant ortho-groups sterically clashing in the CmoM and CooM structures and methods to find a reasonable estimate of the CxxM conformational landscape.     

Sterically oriented synthesis and structure of new perphosphorylated resorcinarenes

Tetraarylresorcinarenes in a chair conformation of C_2h symmetry were synthesized by sterically oriented condensation of aromatic aldehydes with resorcinol and 2-methylresorcinol. By further phosphorylation of resorcinarenes with phosphorous amides perphosphorylated derivatives were obtained with rctt configuration of substituents at internuclear methylidene bridges. Structure of these compounds was proved using NMR spectroscopy and X-ray diffraction analysis.     

The thermodynamic properties of the [(Me<Subscript>3</Subscript>Si)<Subscript>7</Subscript>C<Subscript>60</Subscript>]<Subscript>2</Subscript> fullerene complex

The temperature dependence of the heat capacity C _p ^o of the [(Me₃Si)₇C₆₀]₂ fullerene complex was measured for the first time using precision adiabatic vacuum calorimetry over the temperature range 6.7–340 K and high-accuracy differential scanning calorimetry at 320–635 K. For the most part, the error in the C _p ^o values was about ±0.5%. An irreversible endothermic effect caused by the splitting of the dimeric bond between fullerene fragments and the thermal decomposition of the complex was observed at 448–570 K. The thermodynamic characteristics of this transformation were calculated and analyzed. Multifractal analysis of the low-temperature (T < 50 K) heat capacity was performed, and conclusions were drawn concerning the character of the heterodynamicity of the structure. The experimental data obtained were used to calculate the standard thermodynamic functions C _p ^o (T), H ^o (T) ? H ^o (0), S ^o (T) ? S ^o (0), and G ^o (T) ? H ^o (0) over the temperature range from T → 0 to 445 K and estimate the standard entropy of formation of the compound from simple substances at 298.15 K. The standard thermodynamic properties of [(Me₃Si)₇C₆₀]₂ are compared with those of the (C₆₀)₂ dimer, the [(η⁶-Ph₂)₂Cr]⁺[C₆₀]^?? fulleride, and the initial C₆₀ fullerene.     

Synthesis and complexation of novel dibenzo[<Emphasis Type="Italic">c.e</Emphasis>][1,2]oxaphosphorine-based P-ligands

The reaction of chloro-dibenzo[c.e][1,2]-oxaphosphorine with (L)-methyl prolinate gave the corresponding phosphorous ester-amide, while the interaction of the same starting material with half an equivalent of 2-methylaminothanol and (1S,2R)-(+)-ephedrine led to the corresponding bis(dibenzooxaphosphorine) derivatives that are bidentate P-ligands. The new P-ligands prepared were characterized as the corresponding P-borane and P-oxide derivatives. The P-ligands were utilized in the synthesis of novel Pt-complexes, which gave a species of PtCl₂P₂ type, while two others were seven-membered chelate ring complexes. Structures of the Pt-complexes were elucidated on the basis of stereospecific J _Pt–P couplings and quantum chemical calculations.     

Crystal structure of glycine phosphite C<Subscript>2</Subscript>H<Subscript>5</Subscript>NO<Subscript>2</Subscript>·H<Subscript>3</Subscript>PO<Subscript>3</Subscript>

Single crystal X-ray diffraction study of glycine phosphite C₂H₅NO₂·H₃PO₃ was performed (monoclinic, space group P2₁/c, a = 7.401(3) Å, b = 8.465(3) Å, c = 9.737(3) Å; β = 100.73(5)°, Z = 4). It has been found that one of hydrogen atoms is located at the centre of symmetry forming two strong hydrogen bonds to yield H₄P₂O ₆ ^?2 dimers, while another hydrogen atom is statistically disordered over two positions and organizes the dimers into an infinite corrugated chain. The ordering of this hydrogen atom position and/or displacement of the other one from the centre of symmetry will lead to the loss of symmetry centre and lowering of the point group symmetry from C_2h to piezo-active group C₂ or C _s .     

Crystal structures of two one-dimensional coordination polymers constructed from Mn<Superscript>2+</Superscript> ions,chelating hexafluoro-acetylacetonate anions,and flexible bipyridyl bridging ligands

The syntheses and crystal structures of two one-dimensional coordination polymers, [Mn(C₅HO₂F₆)₂(C₁₆H₂₀N₂)] _n (1) and [Mn(C₅HO₂F₆)₂(C₂₀H₂₀N₂)] _n (2), are described, where C₅HO₂F₆ ^? is the hexafluoro acetylacetonate anion, C₁₆H₂₀N₂ is 1,6-bis(4-pyridyl)-hexane, and C₂₀H₂₀N₂ is 1,4-bis[2-(3-pyridyl)ethyl]-benzene. In both phases, the metal ion lies on a crystallographic twofold axis and is coordinated by two chelating C₅HO₂F₆ ^? anions and two bridging bipyridyl ligands to generate a cis-MnN₂O₄ octahedron. The bridging ligands, which are completed by crystallographic inversion symmetry in both compounds, connect the metal nodes into zigzag [20 1 ] chains in 1 and contorted [001] chains in 2. Intrachain C–H???O interactions occur in 1 but not in 2, which may be correlated with the relative orientations of the ligands. Crystal data: 1, C₂₆H₂₂F₁₂MnN₂O₄, M _r = 709.40, monoclinic, C2/c (No. 15), a = 9.3475(2) Å, b = 16.6547(3) Å, c = 18.3649(4) Å, β = 91.1135(8)°, V = 2858.50(10) ų, Z = 4, R(F) = 0.030, w R(F ²) = 0.075. 2, C₃₀H₂₂F₁₂MnN₂O₄, M _r = 757.44, monoclinic, C2/c (No. 15), a = 19.9198(2) Å, b = 10.6459(2) Å, c = 16.8185(3) Å, β = 119.8344(8)°, V = 3093.91(9) Å3, Z = 4, R(F) = 0.032, w R(F ²) = 0.078.     

Pseudo Jahn-Teller effect in oxepin,azepin, and their halogen substituted derivatives

Oxepin and azepin are heterocyclic compounds with a seven-membered ring, which are present in the main skeleton of many anti-depressive drugs. Planar configuration instability due to the pseudo Jahn-Teller effect (PJTE) in oxepin, azepin and six their halogen substituted derivatives were investigated as an original PJTE study. Optimization and the following frequency calculations in these two series illuminated that all of these eight compounds were unstable in high-symmetry planar (with C _2v symmetry) configuration and their structures were puckered to lower C _s symmetry stable geometry. Moreover, the vibronic coupling interaction between ¹ A ₁ ground and the first ¹ B ₁ excited states via (¹ A ₁ + ¹ A ₁ ^’ + ¹ B ₁) ? b ₁ and (¹ A ₁ + ¹ B ₁ + ¹ A ₁ ^’ ) ? b ₁ PJTE problems were the reasons for the symmetry breaking phenomenon and non-planarity of the seven-member ring in those series. Finally, numerical fitting of the adiabatic potential energy surface (APES) cross-sections along the b ₁ puckering coordination was employed to estimate the vibronic coupling constants of PJTE problems for all the considered compounds.