Self-assembly and crystal structures of coordination polymers constructed by 4′-hydroxyisoflavone-3′-sulfonates with Cs(I) and Rb(I)

Four coordination polymers, [CsL1(H₂O)₂]·H₂O (1), [CsL2(H₂O)₂]·H₂O (2), [Rb₂(L2)₂(H₂O)₂]·2H₂O (3) and [RbL3(H₂O)] (4), were synthesized by Cs(I), Rb(I) and 4′-hydroxyisoflavone-3′-sulfonates L1–L3 [L1 = 7-methoxy-4′-hydroxyisoflavone-3′-sulfonate, L2 = 7-ethoxy-4′-hydroxyisoflavone-3′-sulfonate, L3 = 7-ethoxy-4′,5-dihydroxyisoflavone-3′-sulfonate]. The crystal structures of 1–4 were determined by single-crystal X-ray diffraction. The influences of 4′-hydroxyisoflavone-3′-sulfonate ligands and Cs⁺, Rb⁺ on their structural features and self-assembly were investigated. The sulfonates of L1–L3 not only coordinate with Cs⁺ or Rb⁺ directly, but also bridge the organic region and the inorganic region in 1–4. Non-covalent interactions such as coordination interaction, π–π stacking interaction and hydrogen bonding assembled 1–4 into 3-D networks together with the electrostatic interactions between Cs⁺, Rb⁺ and the sulfonate anions.     

The synthesis,characterization, and theoretical hydrogen gas adsorption properties of copper(II)-3,3′-thiodipropionate complexes with imidazole derivatives

Three new coordination polymers, [Cu(μ₃-tdp)(im)₂]_n (1), {[Cu(μ₃-tdp)(1-mim)₂]·0.5H₂O}_n (2) and {[Cu₂(μ₃-tdp)₂(4-mim)₄]·H₂O}_n (3) [tdpH₂ = 3,3′-thiodipropionic acid, im = imidazole, 1-mim = 1-methylimidazole and 4-mim = 4-methylimidazole], have been prepared and characterized by spectroscopic techniques (IR and UV–Vis), elemental analyzes, magnetic measurements, thermal analyzes, and single-crystal X-ray diffraction. Complexes 1–3 crystallize in the monoclinic system with space groups of C2/c and P2₁/c, respectively. In 1–3, tdp is a bridging ligand to form 1-D chains, which are extended into a 2-D layer by hydrogen bonding and π···π interactions. The 3,3′-thiodipropionate exhibits an unexpected coordination mode in 1–3. Simulations were used to assess the potential of the complexes in H₂ storage applications.     

Syntheses,crystal structures,and magnetic properties of two new manganese(II) complexes based on biphenyl-2,5,2′,5′-tetracarboxylic acid

Two new complexes, [Mn(H₂bptc)(2,2′-bpy)₂]?·?2H₂O (1) and [Mn₃(Hbptc)₂(2,2′-bpy)₃(H₂O)₈]?·?2H₂O (2) (H₄bptc?=?biphenyl-2,5,2′,5′-tetracarboxylic acid, 2,2′-bpy?=?2,2′-bipyridine), have been synthesized under hydrothermal conditions. Their structures have been characterized by single-crystal X-ray diffraction, elemental analyses, IR spectra, powder X-ray diffraction, and thermogravimetric analyses. Complexes 1 and 2 are both linked into 3-D supramolecular networks by non-covalent interactions (O–H?···?O, C–H?···?O, C–H?···?π, and π?···?π). Complexes 1 and 2 exhibit weak antiferromagnetic interactions.     

1-D wave-like chain,twofold 2-D layer,and chiral 3-D open framework based on multidentate ligand: structural diversities,thermal properties,and photoluminescence

From 1-D to 3-D zinc coordination polymers based on multifunctional flexible 4-(1,2,4-triazole-methylene)-benzonitrile (tzbt), {[Zn(tzbt)₂(bdc)]·2H₂O}_n (1), [Zn(tzbc)₂]_n (2), and [Zn(bpdc)(H₂O)]_n (3) (bdc = 1,4-benzenedicarboxylic acid, tzbc = 4-(1,2,4-triazole-methylene)-benzoic acid, bpdc = 4,4′-biphenyldicarboxylic acid), were synthesized under hydrothermal conditions. The tzbt was synthesized by N-alkylation and hydrolyzed in situ to produce tzbc (in 2). Single-crystal X-ray diffraction analysis reveals that 1 displays 1-D wave-like chains based on [Zn(bdc)]_n. 2 is a chiral twofold interpenetrating 2-D architecture constructed with “V”-shaped tzbc. 3 is a 3-D chiral compound constructed from achiral H₂bpdc with right-handed helical chains. 1–3 display stable blue-emitting luminescence with emission maxima ranging from 383 to 410 nm, depending on ligand-centered π*→π transitions. The effects of different polarity solvents and temperature on luminescence are discussed. TGA and VT-XPRD reveal that 2 has thermal stability to 360 °C.     

Coordination polymers constructed from an asymmetric dicarboxylate and N-donors: preparation,characterization, and properties

Two new coordination polymers with an asymmetric dicarboxylate and 4,4′-bipyridine ligand, {[Co(bpy)(H₂O)₄]·(cpa)·0.5H₂O}_n (1) and {[Ag(cpa)(bpy)][Ag(bpy)]·4H₂O}_n (2) (H₂cpa = 4-(2-carboxyethyl)benzoic acid, bpy = 4,4′-bipyridine), have been hydrothermally synthesized and characterized by elemental analysis, FT-IR spectroscopy, and single-crystal X-ray diffraction. Compound 1 displays a linear chain with guest molecule (cpa)^2? ions existing in the structure. Compound 2 contains two independent units, [Ag(cpa)(bpy)]^– (A) and [Ag(bpy)]⁺ (B), which form a 1-D + 1-D structure. A shows a 1-D chain structure bearing hooks formed by the carboxylates and organized into a tubular structure by hydrogen-bonding interactions. B has linear chains formed from Ag⁺ and bpy. The A and B chains co-crystallize with waters of crystallization to provide two linear [Ag(bpy)]⁺ chains embedded in the tubular structure formed by A via π…π stacking contacts. In 1 and 2, hydrogen-bonding and π…π stacking interactions connect the discrete 1-D chains into 3-D supramolecular structures. The fluorescent properties, TG analysis, and X-ray powder diffraction patterns for 1 and 2 were also measured.     

Synthesis,crystal structures,and photoluminescence of two new zinc complexes based on 2,2′-thiodibenzoic acid

{[Zn₂(tdba)₂(phen)₂(H₂O)₂]?·?2H₂O?·?2DMF} _n (1) and [Zn(tdba)(bpy)] _n (2) (H₂tdba?=?2,2′-thiodibenzoic acid, phen?=?1,10-phenanthroline, bpy?=?2,2′-bipyridine, DMF?=?dimethylformamide) were hydrothermally synthesized, and characterized by single-crystal X-ray diffraction analysis, FT-IR, and elemental analysis. The obtained complexes exhibit different structures. Compound 1 is 0-D with tdba connecting two Zn ions in a μ ₁–η ¹/μ ₁–η ¹ coordination forming a dinuclear molecule. Each molecule is further connected with neighbors via hydrogen-bonding and π?···?π interactions. Compound 2 displays a 1-D structure in which Zn²⁺ centers are connected via tdba anions into 1-D chains propagating along the a-axis; these chains are further packed via π?···?π interactions. In addition, photoluminescence for 1 and 2 has been investigated.     

Diphenylphosphinoderivate von Malein- und Fumarsäureestern: Darstellung,Eigenschaften, Kristall- und Molekülstrukturen

The reaction between 2,3-dichloromaleic acid dialkylester (alkyl=CH₃ and C₂H₅) and diphenyl(trimethylsilyl)phosphine, leading to diphenylphosphine substituted esters of maleic and fumaric acid has been studied. With a molar ratio 1:1 of the components 2-chloro-3-diphenylphosphinomaleic acid dimethylester (3) and-diethylester are obtained as colourless crystalline compounds. From a 1:2 reaction however only bis(diphenylphosphino)fumaric acid dimethylester (colourless crystals) and-diethylester (yellow) can be crystallized, the latter in a partially oxydized form. The presence of bis(diphenylphosphino)maleic acid diester in the oily part of the reaction products has been proved by its chelating with Ni²⁺ and Pd²⁺ to complexes of the compositionMeCl₂·(PP). Pure bis(diphenylphosphino)maleic acid dimethylester (4) could be synthesized by alcoholysis and following methylation of bis (diphenylphosphino)maleic anhydrid. Contrary to this easily chelating and air stable compound the corresponding fumaric acid diesters give no complexes with the metals examined as far and are very sensitive towards oxygen. This sensitivity decreases strongly after oxydation to 2-diphenylphosphino-3-diphenylphosphorylfumaric acid diester, the diethylester of which could be crystallized in pure form.Characteristic vibration bands, uv/vis-absorption and³¹P-nmr peaks are discussed.The result of X-ray diffraction data of3 and4 are reported and conformation, bond lengthes and bond angles of these molecules are given.     

Architectural diversity of six coordination compounds based on (S)-(+)-mandelic acid and different N-donor auxiliary ligands: syntheses,structures, and luminescent properties

Six transition metal coordination compounds with H₂mand and different N-donor ligands, [Co(Hmand)₂(2,2′-bipy)]·H₂O (1), [Ni(Hmand)₂(2,2′-bipy)]·H₂O (2), [Ni(Hmand)₂(bpe)] (3), [Zn(Hmand)₂(2,4′-bipy)(H₂O)]·2H₂O (4), [Zn(Hmand)(bpe)(H₂O)]_n[(ClO₄)]_n·nH₂O (5), and [Zn(Hmand)(4,4′-bipy)(H₂O)]_n[(ClO₄)]_n (6), were synthesized under different conditions (H₂mand = (S)-(+)-mandelic acid, bpe = 1,2-di(4-pyridyl)ethane, 4,4′-bipy = 4,4′-bipyridine, 2,4′-bipy = 2,4′-bipyridine, 2,2′-bipy = 2,2′-bipyridine). Their structures were determined by single-crystal X-ray diffraction analysis and further characterized by elemental analysis, infrared spectra, thermogravimetric analysis, powder X-ray diffraction, and circular dichroism. Compounds 1 and 2 are isostructural (0-D structures), which are extended to supramolecular 1-D chains by hydrogen bonding. Compound 3 exhibits 1-D straight chain structures, which are further linked via hydrogen bond interactions to generate a 3-D supramolecular architecture. Compound 4 displays a discrete molecular unit. Neighboring units are further linked by hydrogen bonds and π–π interactions to form a 3-D supramolecular architecture. Compound 5 displays a 2-D undulated network, further extended into a 3-D supramolecular architecture through hydrogen bond interactions. Compound 6 possesses a 2-D sheet structure. Auxiliary ligands and counteranions play an important role in the formation of final frameworks, and the hydrogen-bonding interactions and π–π stacking interactions contributed to the formation of the diverse supramolecular architectures. Compounds 1, 2, 4, 5, and 6 crystallize in chiral space groups, with the circular dichroism spectra exhibiting positive cotton effects. Furthermore, the luminescent properties of 4–6 have been examined in the solid state at room temperature, and the different crystal structures influence emission spectra significantly.     

Influence of alkyl substituents in 1,3-diethyl-2-thiobarbituric acid on the coordination environment in M(H2O)2(1,3-diethyl-2-thiobarbiturate)2 M = Ca2+, Sr2+

Two new isostructural complexes, [Ca(H₂O)₂(μ₂-Detba-O,O′)₂]_n (1) and [Sr(H₂O)₂(μ₂-Detba-O,O′)₂]_n (2) (HDetba = 1,3-diethyl-2-thiobarbituric acid), were synthesized and characterized by single-crystal and powder X-ray diffraction analysis, TG-DSC, FT-IR, and emission spectroscopy. The single-crystal X-ray diffraction data revealed that 1 and 2 are polymeric where M²⁺ (M = Ca, Sr) is a six-coordinate octahedral binding four Detba^? ions and two water molecules. The octahedra are linked through bridging Detba^? ions forming a 2-D layer. Two intermolecular hydrogen bonds O–H…S in the crystal form a 3-D net. The comparison of M(Detba)₂ and M(Htba)₂ (H₂tba = 2-thiobarbituric acid) structures showed that the coordination number of metals in M(Detba)₂ does not exceed six and there are no π–π interactions, unlike compounds with Htba^?; Detba^? ions are only bridges in HDetba coordination compounds. Thermal decomposition of 1 and 2 includes dehydration, which mainly ends at 200 °C, and organic ligand oxidation at 300–350 °C with a release of CO₂, SO₂, H₂O, NH₃, and isocyanate. Upon excitation at 220 nm, 1 and 2 exhibit an intense emission maximum at 557 nm.     

Ultraviolet light-emitting CdII complexes: synthesis and property studies

Four ultraviolet light-emitting Cd^II complexes, [CdL₁(H₂O)]_n (1), [CdL₁(bpy)(H₂O)₂]_n (2), [CdL₂(H₂O)]_n (3), and [CdL₂(bpy)(H₂O)₂]_n (4), where L₁ = 3,3′-(4-phenyl-4H-1,2,4-triazole-3,5-diyl)dibenzoate, L₂ = 3,3′-(4-(4-fluorophenyl)-4H-1,2,4triazole-3,5-diyl)dibenzoate, and bpy = 2,2′-bipyridine, were hydrothermally synthesized and characterized by single-crystal X-ray diffraction, powder scattering spectra, and infrared spectra. 1–4 possess excellent thermal stability with decomposition temperature of ca. 340 °C. Their powder samples mainly give luminescent spectra at 350, 339, 351, and 339 nm, respectively, which should be attributed to the ligand-centered π*?→?π transfer transitions. Additionally, 1–4 have weak emission bands at 400–500 nm, which are tentatively attributed to the triplet ligand to ligand charge transfer transitions.     

Structural variability of Ag(I) metal–organic networks: C–H⋯π and metal⋯π interactions

The synthesis and X-ray structural characterization of two silver(I) coordination polymers, [Ag₂(bpp)₂(Phdac)]·5H₂O (1) and [Ag₂(bpp)(HSSal)] (2), are reported, where bpp = 4,4′-trimethylene dipyridine, H₂Phdac = 1,4-phenylenediacetic acid, and H₃SSal = 5-sulfosalicylic acid. X-ray crystallography reveals that the structures are stabilized through hydrogen bonding interactions. The C–H?π and metal?π interactions of aromatic molecules play a crucial role in building a layered framework. Intricate combinations of the weak non-covalent interactions have been analyzed to explore cooperativity and competitiveness in the solid-state structures.     

Crystal structures and properties of two Cu(I) complexes based on Keggin-type clusters and diethyl 4,4′-dicarboxy-2,2′-biquinoline acid

Two proton-conductive Cu(I) complexes based on Keggin-type clusters, [Cu(debqdc)₂]₂[HPW₁₂O₄₀]·4H₂O (1), and [Cu(debqdc)₂]₂[HPW₁₂O₄₀]·debqdc·4H₂O (2), where debqdc is diethyl 4,4′-dicarboxy-2,2′-biquinoline, were simply synthesized at room temperature. The products were structurally characterized by elemental analyses, infrared spectroscopy, and single-crystal X-ray diffraction analyses. Single-crystal X-ray diffraction analyses revealed that both complexes crystallized in the triclinic space group P?1 and presented two three-dimensional supramolecular networks with one-dimensional hydrophilic channels via hydrogen-bonding interactions and π–π stacking interactions between the aromatic rings. In the [Cu(debqdc)₂]⁺ ion, debqdc acts as a bidentate nitrogen donor ligand in the chelating fashion. The bulky debqdc ligand constrains the Cu(I) metal center within such a rigid environment in a tetrahedral geometry. The two complexes exhibit good proton conductivities (10^?5 ~ 10^?4 S cm^?1) at 100 °C in the relative humidity range 35 ~ 98%. The luminescence behaviors of these complexes in the solid state at room temperature have also been investigated. Upon excitation at 285 nm, both 1 and 2 display three main emission peaks centered at 470, 520, and 568 nm, respectively.     

Cyanuric chloride reagent as a chloride ion donor: synthesis,crystal structure,and magnetic properties of [Cu2(2-APM)2(μ-Cl)2(μ-OCH3)2]n coordination polymer

A new chloro- and methoxo-bridged Cu(II) coordination polymer, [Cu₂(2-APM)₂(μ-Cl)₂(μ-OCH₃)₂]_n·CH₃OH (1), was prepared using in situ formed chloride by the decomposition of cyanuric chloride and 2-aminopyrimidine (2-APM) as a ligand in methanol. Its solid-state structure has been characterized by elemental analysis and single crystal X-ray diffraction. X-ray crystallographic studies reveal that this compound has an extended 2-D supramolecular architecture directed by strong hydrogen bonds and aromatic π–π stacking interactions. Compound 1 shows an antiferromagnetic coupling exchange with coupling constants of ?58.2 and ?41.4 cm^?1 between adjacent copper(II) ions, in agreement with the intermetallic distances of 3.0405(5) and 3.6073(5)?Å found in the crystal structure.     

A blue luminescent binuclear cadmium-orotate coordination polymer: synthesis,crystal structure,and thermogravimetric analysis

Assembly of orotic acid (H₃Or, 1,2,3,6-tetrahydro-2,6-dioxo-4-pyrimidinecarboxylic) and Cd(NO₃)·6H₂O yielded a coordination polymer, [(Cd(Hor)·2.5H₂O)₂]_n (1), which has been characterized by X-ray single-crystal diffraction, TGA, and ?uorescence spectra. Single-crystal X-ray structural analyses reveal that 1 is a hydrogen-bonded binuclear Cd-orotate coordination polymer in which both Cd²⁺ ions have different coordination environments with identical distorted octahedral geometry. Crystal data for 1: monoclinic, space group P2₁/n, a = 7.0209(10) Å, b = 13.974(2) Å, c = 17.541(3) Å, β = 98.842(2)°, V = 1700.5(4) Å, Z = 4, R1 = 0.0269, wR2 = 0.0612, θ_max = 25.960. The emission spectrum of the Cd-complex recorded with 265 nm excitation wavelength reveals the complex has strong blue luminescence with the peak maximum 420 nm (2.95 eV) as a result of the n–π* and π–π* transitions on the H₃Or ligand.     

A complex based on a decorated Keggin-type cluster from Cu(II) and 4,4′-dimethyl-2,2′-bipyridine: synthesis,structure and proton conductivity

A proton-conductive complex based on decorated Keggin-type cluster, {[Cu(dmbipy)(H₂O)₃]₂[SiW₁₂O₄₀]}·7H₂O (where dmbipy is 4,4′-dimethyl-2,2′-bipyridine) (1), was synthesized by reaction of CuSiW₁₂O₄₀·nH₂O and dmbipy at room temperature. The product was characterized by elemental analysis, infrared spectroscopy, and single-crystal X-ray diffraction analysis. Single-crystal X-ray diffraction analysis at 293 K revealed that 1 crystallized in the monoclinic space group C2/c and has a 3-D supramolecular network with 1-D hydrophilic channels constructed by a decorated Keggin-type cluster, [Cu(dmbipy)(H₂O)₃]₂SiW₁₂O₄₀, and solvent water molecules via hydrogen-bonding interactions. Thermogravimetric analysis suggests that 1 has high-thermal stability and good water binding in 1-D hydrophilic channels from 20 to 100 °C. Compound 1 exhibits good proton conductivities (over 10^?3 S cm^?1) at 100 °C in the relative humidity range 35–98%.     

Copper(I)-1,1,1-tris(diphenylphosphinomethyl)ethane complexes with different coordination modes tuned by auxiliary ligands and their spectroscopic properties

Three mono-, bi- and tetranuclear copper(I) complexes, [Cu(phen)(triphos-O)]BF₄ (1) (phen = 1,10-phenanthroline, triphos = 1,1,1-tris(diphenylphosphinomethyl)ethane), [Cu₂(bipy)(triphos)₂](BF₄)₂ (2) (bipy = 4,4′-bipyridine), and [Cu₄(MeOC^N^N)₄(triphos)₂(bipy)](BF₄)₄ (3) (MeOC^N^N = 6-(4-methoxyphenyl)-2,2′-bipyridine), have been synthesized and characterized by NMR spectroscopy, electrospray ionization, and matrix-assisted laser desorption ionization time-of-flight mass spectrometries, elemental analysis, and X-ray crystal analysis. The crystal structure investigation revealed the copper ions of the complexes have pseudo-tetrahedral coordination geometry. The electronic absorption spectra of 1, 2, and 3 contain low-energy bands at 350–500 and 400–650 nm, which are assigned to d(Cu) → π*(phen or bipy) and a mixture of d(Cu) → π*(MeOC^N^N) and d(Cu) → π*(bipy) transitions, respectively. Complex 2 displays a strong, long-lived solid-state emission with a maximum at 555 nm and lifetime of 13.6 μs at room temperature. Photoinduced electron-transfer properties of 2 and 3 involving nanosecond time-resolved absorption spectroscopy and electron spin resonance techniques were studied.     

Synthesis and crystal structures of 3D supramolecular compounds: [ M (4,4′-bipy)2(H2O)4] · (4,4′-bipy)2 · (3,5-daba)2 · 8H2O ( M =Zn,Mn)

Two new supramolecular compounds [M(4,4′-bipy)₂ (H₂O)₄] ·?(4,4′-bipy)₂ ·?(3,5-daba)₂ ·?8H₂O (M=Zn(1) or Mn(2), 4,4′-bipy =?4,4′-bipyridine, 3,5-daba =?3,5-diaminobenzoic acid anion) were synthesized and characterized by elemental analysis and X-ray crystal diffraction. In [M(4,4′-bipy)₂(H₂O)₄]²⁺, the M(II) is coordinated by two nitrogen atoms from two 4,4′-bipy molecules and four oxygen atoms from four waters to form an octahedral configuration. There exist uncoordinated 4,4′-bipy molecules, 3,5-diaminobenzolate counterions and water guests in the compounds. The 3D structures of the title supramolecular compounds are constructed by rich hydrogen bonds among [M(4,4′-bipy)₂(H₂O)₄]²⁺, uncoordinated 4,4′-bipy molecules, water molecules and 3,5-daba, containing a diverting hexa-member water ring.     

Syntheses and crystal structures of two Co(II) coordination polymers based on 4,6-bis(4-methylbenzoyl)isophthalic acid and 4,4′-bipyridine

Two coordination complexes, [Co₂L₂(4,4′-bpy)₂(H₂O)₄]?·?6H₂O (1) and [CoL(4,4′-bpy)] (2) (H₂L?=?4,6-bis(4-methylbenzoyl)isophthalic acid and 4,4′-bpy?=?4,4′-bipyridine), have been synthesized with the same starting materials under conventional and hydrothermal condition, respectively. Their structures have been characterized by X-ray diffraction, elemental analysis, IR spectra, and thermogravimetric analysis. Complex 1 features a 2-D sheet structure (space group C2/c) with (4,4) grid units. The non-covalent interactions (O–H?·?·?·?O, C–H?·?·?·?π, and weak π??·?·?·?π interactions) extend 1 into a 3-D supramolecular network. Complex 2 displays a (3,5)-connected network (space group P 1) with a (4²?·?6)(4²?·?6⁸) topology.     

Two 5-tetrazolylazo-8-hydroxyquinoline-based Zn(II) and Mn(II) complexes: syntheses,structures and optical properties

Two 5-tetrazolylazo-8-hydroxyquinoline (TTHQ) Zn²⁺ and Mn²⁺ complexes, [Zn(TTHQ)(en)]·2H₂O (en = ethylenediamine) (1) and [Mn₂(TTHQ)₂(H₂O)₆]·2H₂O (2), were synthesized and characterized by single-crystal X-ray diffraction analysis. Stacking (π–π) and hydrogen-bonding interactions are responsible for the stabilization of the supramolecular structures. UV–vis spectral changes and photoluminescent properties of TTHQ, 1 and 2 were investigated and a red emission was found. The hydrogen-bonding interaction energies in 1 and 2 were calculated using density functional theory at the WB97XD/6-31++G level.     

Pyridine effected tunable luminescence properties of a 1D cadmium(II) polymer with tetranuclear second building units

One novel 1D polymer, [Cd₂(m-BrPhHIDC)₂(4,4′-bipy)(H₂O)₂]_n (1) (m-BrPhH₃IDC = 2-(3-bromophenyl)-1H-imidazole-4,5-dicarboxylic acid; 4,4′-bipy = 4,4′-bipyridine), has been hydrothermally synthesised and characterised by single-crystal X-ray diffraction, elemental analysis, IR, powder X-ray diffraction (PXRD) and thermogravimetric analysis. Polymer 1 composed of tetranuclear square [Cd₂(m-BrPhHIDC)₂] second building units and 4,4′-bipy bridges shows the interesting tunable luminescence properties aroused by pyridine. A luminescence enhance mechanism has been proposed.