NO Reduction Over Noble Metal Ionic Catalysts

In last 40 years, catalysis for NO _x removal from exhaust gas has received much attention to achieve pollution free environment. CeO₂ has been found to play a major role in the area of exhaust catalysis due to its unique redox properties. In last several years, we have been exploring an entirely new approach of dispersing noble metal ions in CeO₂ and TiO₂ for redox catalysis. We have extensively studied Ce_1−x M _x O_2−δ (M = Pd, Pt, Rh), Ce_1−x−y A _x M _y O_2−δ (A = Ti, Zr, Sn, Fe; M = Pd, Pt) and Ti_1−x M _x O_2−δ (M = Pd, Pt, Rh, Ru) catalysts for exhaust catalysis especially NO reduction and CO oxidation, structure–property relation and mechanism of catalytic reactions. In these catalysts, lower valent noble metal ion substitution in CeO₂ and TiO₂ creates noble metal ionic sites and oxide ion vacancy. NO gets molecularly adsorbed on noble metal ion site and dissociatively adsorbed on oxide ion vacancy site. Dissociative chemisorption of NO on oxide ion vacancy leads to preferential conversion of NO to N₂ instead of N₂O over these catalysts. It has been demonstrated that these new generation noble metal ionic catalysts (NMIC) are much more catalytically active than conventional nano crystalline noble metal catalysts especially for NO reduction.     

Syntheses,crystal structures,and properties of two molecular double-supporting polyoxotungstates

Two molecular double-supporting polyoxotungstates [SiW₁₂O₄₀{M(phen)₂H₂O}₂] · nH₂O (phen = 1,10′-phenanthroline, M = Mn 1, n = 2; M = Co 2, n = 3) were synthesized hydrothermally and characterized by elemental analyses, IR, TG, and X-ray single-crystal diffraction. The variable-temperature magnetic susceptibilities were measured at 2–300 K. The double-supporting polyoxotungstate molecule consists of a Keggin-type dodecatungstosilicate anion and a pair of transition metal complex fragments which are covalently linked to opposite sides of the Keggin anion. The transition metal ion locates in the center of a distorted octahedron. Multiple H-bonding interactions are observed between the coordinated waters of the transition metal complex fragments and terminal oxygen atoms of Keggin units and also between the bridging oxygen atoms of Keggin units and the lattice waters, which creates one-dimensional chains or two-dimensional layers. Between the layers or chains there are weak CH···O hydrogen bonding interactions and van der Waals forces. The molecular double-supporting polyoxotungstosilicate begins to decompose at ca. 500 °C. The variable-temperature magnetic behavior of 1 shows weak antiferromagnetic characteristics with a small value of θ = −0.289 K.     

Hydrothermal synthesis,crystal structure and magnetic properties of a new one-dimensional polymer [{Cu(4,4′- bipy)(CH<Subscript>3</Subscript>COO)<Subscript>2</Subscript>}·3H<Subscript>2</Subscript>O]<Subscript>n</Subscript>

One new metal – organic coordination framework formulated as [{Cu(4,4′-bipy)(CH₃COO)₂}·3H₂O]_n (1) (where 4,4′-bipy=4,4′-bipyridine) has been hydrothermally synthesised and characterised by elemental analysis, IR and electronic spectroscopy, variable temperature magnetic moment measurement and single crystal X-ray diffraction study. Single crystal X-ray analysis reveals that 1 is one dimensional polymeric compound in which acetate ligand shows both mono- and bidentate bonding mode, and 4,4′-bipy acts as bridging ligand which supports the formation of infinite chains. The global feature of the χ _M T vs. T curve in 1 is characteristic of moderate antiferromagnetic interaction and the best fit parameters from 300 down to 2 K are found as J = −78.7 cm⁻¹.     

Synthesis of Hexadentate Hexahydro-1,3,5-triazine-Based Ligands and their Copper(I) Complexes

Summary.  Hexadentate ligands were formed by the reaction of primary dimethylaminoethyl- or methoxyethylamines with formaldehyde. The resulting N, N′, N″-functionalized hexahydro-1,3,5-triazines contain pending amino or ether functionalities which are able to coordinate to metals in addition to the ring nitrogen atoms. Both ligands were reacted with CuBr, and novel tricopper clusters were isolated and characterized by X-ray structure analysis. In these compounds a ring nitrogen atom, the pending amino or ether functionality, and two bridging bromine atoms coordinate each of the copper atoms. Received January 22, 2002; accepted (revised) March 22, 2002     

Calorimetric investigation of interactions in the LaNi4.75Al0.25−H2 and LaNi4.8Sn0.2−H2 systems

The interaction of hydrogen with intermetalic compounds LaNi_4.75Al_0.25 and LaNi_4.8Sn_0.2 has been studied in the temperature range 308–353 K by the calorimetry titration method. The mechanism of hydrogenation was investigated. It was shown that, as the temperature increases, the initial concentration of hydrogen in the metal lattice needed for β-hydride formation decreases. It was assumed that this effect is related to the concentration of H^δ+ atoms, which “oxidize” the metallic matrix according to the scheme H^δ++M⁰→H^δ−+M⁺. The enthalpy and entropy of hydrogenation for the LaNi_4.75Al_0.25−H₂ system were calculated from thep-C-T curves and the calorimetry results. The thermodynamic parameters of the LaNi_4.8Sn_0.2−H₂ system were obtained for the first time. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1841–1844, October, 1999.     

Fullerene complexes with divalent metal dithiocarbamates: structures,magnetic properties,and photoconductivity

A series of complexes of fullerenes C₆₀ and C₇₀ with metal dithiocarbamates {M^II(R₂dtc)₂}·C_m (m = 60 or 70) and metal dithiocarbamates coordinated to nitrogen-containing ligands (L), {M^II(R₂dtc)₂)_x·L}·C₆₀ (x = 1 or 2), where M = Cu, Zn, Cd, Hg, Mn, or Fe, R = Me, Et, Prⁿ, Prⁱ, or Buⁿ, L is 1,4-diazabicyclo[2.2.2]octane (DABCO), N,N′-dimethylpiperazine, or hexamethylenetetramine, were synthesized. The shape of dithiocarbamate molecules is sterically compatible with the spherical shape of C₆₀, resulting in an efficient interaction between their π systems. The resulting compounds are characterized by a layered or three-dimensional packing of the fullerene molecules. In the C₆₀ complexes, iron(II) and manganese(II) dithiocarbamates exist in the high-spin states (S = 2 and 5/2). The magnetic susceptibility of {M^II(Et₂dtc)₂}₂·C_m (M = Fe or Mn, m = 60 or 70) in the temperature range of 200–300 K is described by the Curie-Weiss law with Θ = −250 and −96 K and with maxima at 110 and 46 K, respectively, which is indicative of a strong antiferromagnetic spin coupling between M^II. The Weiss constants for the [{M^II(Et₂dtc)₂}₂·DABCO]·C₆₀·(DABCO)₂ complexes (M = Fe or Mn) are 1.7 and 0.3 K, respectively. The magnetic moments of the complexes containing Fe and Mn dithiocarbamates slightly increase at temperatures below 50 and 35 K, respectively, which is evidence of the ferromagnetic spin coupling between M^II in {M^II(Et₂dtc)₂}₂·DABCO. Single crystals of the complexes exhibit low dark conductivity (10⁻¹⁰–10⁻¹¹ S cm⁻¹). The visible light irradiation of these crystals leads to an increase in the photocurrent by two–three orders of magnitude. The photogeneration of free charge carriers in the complexes occurs both due to the photoexcitation of metal dithiocarbamate (Cu^II(Et₂dtc)₂) and through the charge transfer from metal dithiocarbamate (M^II(Et₂dtc)₂, M = Zn or Cd) to C₆₀. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2072–2087, November, 2007.     

Natural monoclinic AgPb(Bi2Sb)3S6, an Sb‐rich gustavite

The crystal structure of the Sb‐rich variety of the mineral gustavite, silver lead tris(dibismuth/antimony) hexasulfide, AgPb(Bi₂Sb)₃S₆, consists of blocks of diagonal chains of four octahedra, viz. M1a (Bi), M2a (Sb/Bi), M2b (Bi/Sb) and M1b (Ag), separated by Pb atoms in a trigonal prismatic coordination. Two marginal octahedral sites, M1a and M1b, where the gustavite substitution Ag⁺ + Bi³⁺ = 2Pb²⁺ takes place, are formed by Bi and Ag, respectively. Two central octahedra, M2a and M2b, where the Bi³⁺ = Sb³⁺ substitution takes place, are formed by two mixed Bi/Sb sites with different occupancies of Bi and Sb. The alternating occupation of the M1 site by Bi and Ag atoms (which thus creates two distinct sites M1a and M1b) results in the monoclinic space group P2₁/c. A statistical distribution of Ag/Bi in the M1 position (one mixed Ag/Bi site) was reported for synthetic gustavite, resulting in the orthorhombic space group Cmcm.     

Divalent transition metal complexes of 3,5-pyrazoledicarboxylate

New divalent transition metal 3,5-pyrazoledicarboxylate hydrates of empirical formula Mpz(COO)₂(H₂O)₂, where M=Mn, Co, Ni, Cu, Zn and Cd (pz(COO)₂=3,5-pyrazoledicarboxylate), metal hydrazine complexes of the type Mpz(COO)₂N₂H₄ where M=Co, Zn or Cd and Mpz(COO)₂nN₂H₄·H₂O, where n=1 for M=Ni and n=0.5 for M=Cu have been prepared and characterized by physico-chemical methods. Electronic spectroscopic data suggest that Co and Ni complexes adopt an octahedral geometry. The IR spectra confirm the presence of unidentate carboxylate anion (Δν=ν_asy(COO^–)–ν_sym(COO^–)>215 cm^–1) in all the complexes and bidentate bridging hydrazine (ν_N–N=985–950 cm^–1) in the metal hydrazine complexes. Both metal carboxylate and metal hydrazine carboxylate complexes undergo endothermic dehydration and/or dehydrazination followed by exothermic decomposition of organic moiety to give the respective metal oxides as the end products except manganese pyrazoledicarboxylate hydrate, which leaves manganese carbonate. X-ray powder diffraction patterns reveal that the metal carboxylate hydrates are isomorphous as are those of metal hydrazine complexes of cobalt, zinc and cadmium.     

Synthesis and Reactivity of Stannyloligosilanes IV [1]: From Hydrido Substituted Stannasilanes Towards Stannasiloxanes

Summary.  Hydrido substituted stannasilanes of the type or (Z = H, Me, Ph; R, R′ = alkyl, Ph) are accessible by reaction of either alkali metal stannides (MSn(Z)R ₂; M = Li, Na) with halogen substituted silanes (; X = F, Cl) or chlorostannanes (R ₂SnCl₂, Ph₃SnCl) and fluorosilanes in the presence of magnesium. Stannasilanes with halogen substituents at the silicon as well as the tin atom are formed by treatment of the hydrido substituted stannasilanes with CHCl₃ or CCl₄. The hydrido substituted stannasilanes decompose in contact with air to distannanes and siloxanes or to the linear ( ^t Bu₂Sn(–O– ^t Bu₂Si–OH)₂) and cyclic ((– ^t Bu₂Sn–O– ⁱ Pr₂Si–O–)₂) stannasiloxanes. Received November 29, 2001. Accepted (revised) January 16, 2002     

Studies On Some Transition Metal Mixed Ligands Complexes Glycinyldithiocarbamate and 8-hydroxyquinoline moiety

This paper reports the isolation and characterisation of mixed ligand complexes of the types Ba[M(Ox)₂glydtc], [M₂′(Ox)₄glydtc], [M₂(QA)₂glydtc] and [M₂′(QA)₄glydtc] (where glydtc=glycinyldithiocarbamate; HOx=8-hydroxyqinoline;HQA=p-methyl-5-phenylazo-8-hydroxyquinoline and M=Co(II),Ni(II) or Cu(II); M′=Fe(III) or Cr(III). The structures for the complexes have been elucidated on the basis of elemental analysis, electronic, IR and mass spectroscopy. Electronic spectral data for the complexes were in accordance with an octahedral environment around the central metal ions in all metal chelates except for [Co₂(QA)₂glydtc] and [Ni₂(QA)₂glydtc] where the structure around Co(II) and Ni(II) may be tetrahedral. The complexes were proposed to be dimeric except those of Ba[M(Ox)₂glydtc]. A study of the thermal decomposition of the complexes has also been carried out. For Ba[M(Ox)₂glydtc], elimination of carbon dioxide was observed. However, evolution of nitrogen and formation of tolyl radicals occur for [M₂(QA)₂glydtc] and [M₂′(QA)₄glydtc]. Kinetic parameters for the various decomposition stages were calculated using the Coats–Redfern and Horowitz–Metzgerequations. This revised version was published online in August 2006 with corrections to the Cover Date.     

Thermal Behaviour Studies on Some Heterotrinuclearpolyacids

An improved method for the synthesis of four heterotrinuclearpolyacids of the type: H_x[EM′_yM″_zO₄₀⋅nH₂O (E=P, Si; M′=Mo, W; M″=V, W) was elaborated. The studied compounds were characterized by elemental analysis, IR spectra and thermal behaviour over 20–800°C temperature range. This revised version was published online in August 2006 with corrections to the Cover Date.     

Synthesis and characterization of trichlorogermyl dioic acids: crystal structures and complementary hydrogen bonding motifs in 3-(trichlorogermyl) pentanedioic acid and 2-[(trichlorogermyl)methyl]butanedioic acid

A series of trichlorogermyl-substituted dicarboxylic acids of general formula HOOC–R′–COOH where R′=–CH₂CH(GeCl₃)CH₂– 1, –CH(CH₂GeCl₃)CH₂– 2, –CH(GeCl₃)CH₂– 3 and –CH(CH₃)CH(GeCl₃)– 4 were synthesized by the hydrogermylation reaction of unsaturated acids, such as trans-glutaconic (2-pentenedioic acid), itaconic (methylenebutanedioic acid), fumaric (2-butenedioic acid), and citraconic (2-methyl-2-butenedioic acid) acids with HGeCl₃, which was produced in situ by the reaction of GeO₂ with 37% HCl in presence of NaH₂PO₂ · H₂O. All these compounds were characterized by melting point, CHN analysis, FTIR, and multinuclear NMR (¹H; ¹³C; H,H-COSY). X-Ray crystal structures of 1 and 2 were analyzed to show supramolecular structures in which central Ge atom in each of these structures is four-coordinated with a slightly distorted tetrahedral geometry. Structurally, both compounds adopt supramolecular forms via strong intermolecular O–H–O interactions through 8-membered and 22-membered hydrogen bonded rings. Supplementary material to this paper is available in electronic form at Correspondence: Muhammad Mazhar, Department of Chemistry, Quaid-i-Azam University, Islamabad 45320, Pakistan.     

Thermal Expansion in the Zr and 1-, 2-valent Complex Phosphates of NaZr2(PO4)3 (NZP) Structure

A_5–4xZr_xZr(PO₄)₃ (A=Na, K;0≤x≤1.25), Na_1-xCd_0.5xZr₂(PO₄)₃ (0≤x≤1), Na_5–xCd_0.5xZr(PO₄)₃ (0≤x≤4) compositions which belong to the NZP structural family were synthesized using the sol-gel method. The lattice thermal expansion of members of these rows were determined up to 600°C by high-temperature X-ray diffractometry. The axial thermal expansion coefficients change from -5.8·10^-6to 7.5·10^-6 °C^-1 (α_a) and from 2.6·10^–6 to 22·10^–6 °C^-1 (α_c). These results, in addition to those for other NZP compounds allow us to explain their low thermal expansion. The mechanism can be attributed to strongly bonded three-dimensional network structure, the existence of structural holes capable to damp some of the thermal vibrations and anisotropyin the thermal expansion of the lattice. This revised version was published online in August 2006 with corrections to the Cover Date.     

Theoretical study of group 11 metal–silonyl complexes: M–SiO and M–(SiO)2 (M = Cu, Ag, or Au)

 The spectroscopic properties of M–SiO and M–(SiO)₂ (1–1 and 1–2 complexes with M = Cu, Ag, or Au) have been theoretically studied. It has been shown that both M–SiO and M–(SiO)₂ compounds in their ground state are bent with a metal–Si bonded structure. The calculated M(ns) spin density agrees well with the electron spin resonance experimental data. From a topological analysis, it has been shown that a rather large charge transfer occurs from the metal towards the SiO moiety, and that the M–Si bond energy correlates with the electron density located at the M–Si bond path (bond critical point). Received: 6 July 2000 / Accepted: 11 October 2000 / Published online: 19 January 2001     

Structural and conductivity studies in LiFeP2O7, LiScP2O7, and NaScP2O7

Structural studies of LiScP₂O₇ by Rietveld refinement confirm that this material is isostructural with LiFeP₂O₇ studied previously. However, NaScP₂O₇ shows a structure different from the structural types of the basic group of Na^IM^IIIP₂O₇ known thus far. Systematic ranges for the six structural types of A^IM^IIIP₂O₇ are presented in terms of ion radii sums and ratios. The framework of LiMP₂O₇ (M=Sc, Fe) has rather wide tunnels running along the crystallographic c-axis. This feature has determined our interest to check the ion conductivity in A^IM^IIIP₂O₇ (A=Li, Na; M=Sc, Fe). The bulk conductivity, however, is low in these compounds, 10⁻⁶–10⁻⁷ S/cm at 300 °C, as determined by impedance spectroscopy. In order to facilitate the conductivity via normal lithium sites, heterovalent substitution is used. Received: 30 April 1999 / Accepted: 15 June 1999     

On the sol–gel preparation of different tungstates and molybdates

The preparation and characterization of the M′–M′′–O nitrate–tartrate (M′ = Ca, Ba, Gd and M′ = W, Mo) precursor gels synthesized by simple, inexpensive, and environmentally benign aqueous sol–gel method is reported. The obtained gels were studied by thermal (TG/DSC) analysis. TG/DSC measurements revealed the possible decomposition pathway of synthesized M′–M′′–O nitrate–tartrate gels. For the synthesis of different metal tungstates and molybdates, the precursor gels were calcined at different temperatures (650, 800, and 900 °C). According to the X-ray diffraction (XRD) analysis data, the crystalline compounds CaMo_1-x W _x O₄ doped with Ce³⁺ ions, BaMo_1-x W _x O₄ doped with Eu³⁺ ions and Gd₂Mo₃O₁₂ were obtained from nitrate–tartrate gels annealed at 650–900 °C temperatures. The XRD data confirmed that the fully crystalline single-phase powellite, scheelite, or Gd₂(MoO₄)₃ structures were formed already at 650 °C. Therefore, the suggested sol–gel method based on the complexation of metal ions with tartaric acid is suitable for the preparation of mixed tungstates–molybdates at relatively low temperature in comparison with solid-state synthesis.     

Structural investigation of cellulose Iα and Iβ by 2D RFDR NMR spectroscopy: determination of sequence of magnetically inequivalent d-glucose units along cellulose chain

In our previous studies of the crystal structure of native cellulose (cellulose I) by solid-state two-dimensional (2D) ¹³C–¹³C INADEQUATE, it was revealed that cellulose I_α contains two kinds of β-d-glucose residues (A and A′) in the unit cell and that cellulose I_β contains another two kinds of residues (B and B′). In the present study, the sequence of residues A and A′ along the same chains in cellulose I_α and that of residues B and B′ in I_β were investigated by 2D ¹³C–¹³C rotor-synchronized radiofrequency-driven recoupling (RFDR) experiments using, respectively, uniformly ¹³C₆-labeled (U−¹³C₆) bacterial cellulose and the same [U−¹³C₆] cellulose sample after thermal treatment at 260 °C. The RFDR spectra recorded with a short mixing time (1.0 ms) showed dipolar-coupled ¹³C spin pairs of only the neighboring carbon of the both phases, while those recorded with a longer mixing time (3.0–15 ms) provided correlations between weakly coupled ¹³C spin pairs as well as strongly coupled ¹³C spin pairs such as neighboring carbon nuclei. In the RFDR spectrum of the [U−¹³C₆] cellulose recorded with a mixing time of 15 ms, the inter-residue ¹³C–¹³C correlation between C4 of residue A and C2 of residue A′ and that between C3 of residue A and C4 of residue A′ were clearly observed. In the case of cellulose I_β, however, inter-residue ¹³C–¹³C correlations between residues B and B′ could not be detected in the series of RFDR spectra recorded with different mixing times of annealed [U−¹³C₆] cellulose. From these findings, that cellulose I_α was revealed to have the –A–A′– repeating units along the cellulose chain. For cellulose I_β, it was revealed that the respective residues B and B′ are composed of independent chains (–B–B– and –B′–B′– repeating units) and that there are no –B–B′– repeating units in the chain.     

Partial ordering in the section Hf5Ge4–Zr5Ge4: Crystallographic investigation and modeling based on ab initio calculations

The section Hf₅Ge₄–Zr₅Ge₄ shows the existence of extended ternary solid solutions based on the binary compounds Hf₅Ge₄ (Pearson symbol: oP36) and Zr₅Ge₄ (Pearson symbol: tP36). The corresponding homogeneity ranges have been determined experimentally at 1350 °C. Partial ordering of the metal atoms at the three crystallographically independent metal sites of the structures was investigated by means of powder X-ray diffraction (XRD) followed by Rietveld refinement as well as by single crystal XRD. The two metals Hf and Zr exhibit site preferences throughout their respective homogeneity ranges.Using a simple thermodynamic model (“compound energy model”) and employing ground state energies of hypothetical ordered compounds calculated from ab initio density functional theory, the experimentally observed site fraction data were reproduced with high accuracy. The obtained Gibbs energies were furthermore used to calculate the stability ranges of the two different phases at 1350 °C. The possible benefit of this approach for the prediction of phase stability and for the Calphad-type modeling of higher-order systems is discussed.     

Noncovalent Interaction of Uridine 5′-Monophosphate with Adenosine, Cytidine, and Thymidine, as well as Adenosine 5′-Monophosphate and Cytidine 5′-Monophosphate in Aqueous Solution

Adduct formation has been studied in the systems of uridine 5′-monophosphate (UMP) with adenosine (Ado), cytidine (Cyd), thymidine (Thd), adenosine 5′-monophosphate (AMP), and cytidine 5′-monophosphate (CMP) by the potentiometric method with computer analysis of the data and ¹³C and ³¹P NMR spectroscopic measurements. It has been established that in the complexes identified, ion–dipole and dipole–dipole interactions occur with the positive reaction centers being protonated nitrogen atoms N(3) of UMP or Thd, and at low pH values, endocyclic nitrogen atoms of the other nucleosides and nucleotides, as e.g., in (UMP)H₂(Ado). The negative reaction centers are the high-electron density atoms N(1) and N(7) from Ado or AMP and N(3) from Cyd or CMP, and the phosphate group of the nucleotides studied, which already undergo partial deprotonation at low pH values. The NMR results have established the presence of noncovalent stacking-type interactions in certain molecular complexes, e.g., (UMP)H₂(AMP). The sites of ion–dipole or dipole–dipole interactions are generated as a result of deprotonation of the nucleosides and nucleotides in the pH range of formation of molecular complexes. Analysis of the equilibrium constants of the reaction allowed a determination of the effectiveness of the phosphate groups and donor atoms of heterocyclic rings in the process of molecular complex formation.     

Theoretical study of the structure and stability of cage-substituted icosahedral closo-boranes, alanes, and gallanes MiM′12 ? iH 122? (M, M′ = B, Al, and Ga; i = 0–12)

The equilibrium geometric parameters and energetic and spectroscopic characteristics of low-lying conformers for several series of model cage-substituted (mixed) borane, alane, and gallane closo-dianions M _i M′_{12 − i} H₁₂²⁻(M, M′ = B, Al, Ga), as well as of “bare” gallium-aluminum anions Ga _i Al_12−i ⁻ with i = 0–12, were calculated within the B3LYP approximation of the density functional theory using 6–31G* and 6–311+G** basis sets. Differences in structure and stability between alanoborane clusters of similar composition are revealed. In clusters where the M and M’ heteroatoms are close in size and electronegativity (in gallonoalanes and gallium-aluminum anions), successive substitutions of M′ for M are accompanied by small energy changes and occur quasi-stochastically in different positions of the cage. When the substituents are significantly different (in alanoboranes), mixed clusters are unstable against disproportionation into homonuclear “predecessors” M₁₂H₁₂²⁻ and M′₁₂H₁₂²⁻, and the most favorable M _i M′_{12 − i} H₁₂²⁻ structures among them are those in which M _i M′_{12 − i} the cages are subdivided into homonuclear “subclusters” M _i and M′t′_12−i with a maximal number of homonuclear bonds (M-M and M′-M′) and a minimal number of heteronuclear bonds (M-M′).