Spectral properties and solution behavior of gold(III) coordination compounds with water-soluble porphyrins

Gold(III) coordination compounds with three water-soluble porphyrins―5,10,15,20-tetrakis(4-sulfonatophenyl)porphyrin (H₂TSPP^4–), 5,10,15,20-tetrakis(4-N-methylpyridyl)porphyrin (H₂TMPyP⁴⁺), and 5,10,15,20-tetrakis(4-N,N,N-trimethylaminophenyl)porphyrin (H₂TTMAPP⁴⁺)―have been studied. Complex [Au(TTMAPP)]⁵⁺ has been prepared for the first time. The analysis of coordination-induced shifts of proton signals in NMR spectra and intensities of Q bands in absorption spectra indicates the high degree of bond covalence in the studied metal porphyrins and a partial transfer of electron density from porphyrin to gold ion. The cationic complexes [Au(TMPyP)]⁵⁺ and [Au(TTMAPP)]⁵⁺ in aqueous solutions has been found to exist in monomeric form, while anionic complex [Au(TSPP)]^3– undergoes dimerization upon growth of concentration and solution ionic strength. Equilibrium constant for dimerization has been calculated, the constant has been found to decrease when temperature rises. Thermodynamic parameters of dimerization process have been determined: ΔH° =–31.8 kJ/mol and ΔS° =–13.8 J/mol K.     

Solubility enhancement of phenanthrene using novel chelating surfactant

A novel chelating surfactant denoted as sodium N-lauroyl ethylenediamine triacetate (N-LED3A) with both surface activity and chelation functions was studied for phenanthrene (PHE) solubilisation ability. The critical micelle concentration (CMC) of N-LED3A was measured, and the effects of the initial N-LED3A concentration, temperature, pH value and coexisting ions (Na⁺, Ca²⁺ and Cu²⁺) on PHE solubilisation by N-LED3A were investigated. The results demonstrated that PHE solubility was efficiently enhanced by N-LED3A, especially with N-LED3A concentrations above the CMC, which was 707 mg L^?1 when measured at 25°C. The temperature influenced the apparent PHE solubility slightly and the apparent solubility of PHE was significantly affected by the pH. Na and Ca were shown to increase the PHE solubility, while Ca exhibited a better promoting ability than Na⁺. A suitable quantity of Cu could significantly enhance the solubilisation capacities of N-LED3A at pH 5. The mechanism of the interaction between Cu⁺ and N-LED3A was further confirmed by Fourier transform infrared spectroscopy (FTIR). These results reveal that Cu²⁺ can be chelated with N-LED3A to form a chelate complex. The results implied that N-LED3A had the potential to remediate soils contaminated by both organics and heavy metals.     

Synthesis,crystal structure,and fluorescence properties of a two-dimensional copper(II) complex with Schiff base

A new Schiff base ligand C₁₉H₁₃NO₅(H₂L) was synthesized using 2-aminoterephthalic acid and 2-hydroxy-1-naphthaldehyde. A complex of this ligand [Cu(C₁₉H₁₁NO₅)(C₂H₆O)] _n was synthesized and characterized by IR, UV, fluorescence spectroscopy and X-ray diffraction single-crystal analysis. The crystal crystallizes in the monoclinic system, space group Pbca with a = 8.7745(18), b = 18.613(4), c = 24.644(5) Å, V = 4024.9(14) ų, Z = 8, F(000) = 1816, S = 1.009, ρ _calcd = 1.462 g cm^?3, μ = 1.122 mm^?1, the final R = 0.0477 and wR = 0.1594 for 4609 observed reflections (I > 2σ(I)). The Cu(II) is five-coordinated by one N atom and two O atoms from the Schiff base ligand and two carboxylate O atoms from another two ligands to form a distorted square-pyramidal geometry. Each ligand serves as a bridging ligand to link Cu²⁺ ions, leading to a two-dimensional coordination polymer. The fluorescence properties of the ligand and complex were also studied. The ligand shows strong fluorescence, and the fluorescence intensity is weakened after the Cu(II) complex formed.     

Syntheses,Structures, and Properties of Two Coordination Polymers Based on 2-Pyrimidineamidoxime

Two coordination polymers, {[Cd(L¹)₂(L₂)] · 0.25H₂O} _n (I) and {[Cd(L¹)(L₃)H₂O] · 2H₂O} _n (II) (L¹ = 2-pyrimidineamidoxime, L² = 4-sulfobenzoate dianion and L³ = 5-sulfosalicylate dianion), has been synthesized and structurally characterized by single-crystal X-ray diffraction (CIF files CCDC nos. 1565646 (I) and 1565728 (II)). Complex I crystallizes in monoclinic space group P2₁/n with a = 10.1462(3), b = 16.0152(5), c = 14.0349(5) Å, β = 93.267(3)°, V = 2276.87(13) ų, C₆₈H₆₆N₃₂O₂₉S₄Cd₄, M = 2373.36, ρ_calcd = 1.731 g/cm³, μ(MoK_α) = 1.109 mm^?1, F(000) = 1186, GOOF = 0.806, Z = 1, the final R¹ = 0.0287 and wR² = 0.0733 for I > 2σ(I). Complex II crystallizes in monoclinic space group P2₁ with a = 6.882(2), b = 17.138(2), c = 7.883(2) Å, β = 103.83(3)°, V = 902.8(4) ų, C₁₂H₁₆N₄O₁₀SCd, M = 520.75, ρ_calcd = 1.916 g/cm³, μ(MoK_α) = 1.388 mm^?1, F(000) = 520, GOOF = 1.047, Z = 2, the final R¹ = 0.0739 and wR² = 0.2041 for I > 2σ(I). Crystal structural analysis reveals that complex I possesses the corrugated 1D chain structure extending along the \([\bar 101]\) direction. However, complex II displays a 2D coordination network lying on the ab crystal plane, which can be simplified as a binodal 3-connected 6³ topological network by considering Cd²⁺ ions and L³ ligands as 3-connected nodes. Their photoluminescent and thermal properties were also investigated.     

Azidokomplexe in nichtwäßrigen Lösungsmitteln, 3. Mitt.: Ti(III), V(III) und Cr(III) in Acetonitril,Propandiol-1,2-carbonat und Trimethylphosphat

Ions of Ti(III), V(III) and Cr(III) seem to be converted to the following azido complexes in acetonitrile, propanediol-1,2-carbonate and trimethylphosphate: [Ti(N₃)₂]⁺ (inTMP), Ti(N₃)₃ (probably distorted octahedral inAN, PDC andTMP, low solubility inTMP), [Ti(N₃)₄]^? (probably tetragonal inAN, probably octahedral inTMP), [Ti(N₃)₆ ^3? (probably distorted octahedral inAN andPDC); [V(N₃)]²⁺ (inAN, PDC andTMP), V(N₃)₃ (octahedral inAN, PDC andTMP, low solubility inTMP), [V(N₃)₄]^? (inPDC), [V(N₃)₆]^3? (octahedral inAN andPDC); [Cr(N₃)]²⁺ (inTMP), [Cr(N₃)₂]⁺ (octahedral inAN andPDC), Cr(N₃)₃ (octahedral inAN, PDC andTMP), [Cr(N₃)₆]^3? (octahedral inAN andPDC).     

A thermodynamic study of interaction of Ag+, Mg2+, Ca2+, and K+ cations with 4-hydroxyphenyl-2,5-bis(2-benzofuranyl)pyridine in some binary mixed non-aqueous solvents

In the present work the complexation process between Ag⁺ and Mg²⁺ cations and 4-hydroxyphenyl-2,5-bis(2-benzofuranyl)pyridine (HBFPY) ligand was studied in pure dimethylformamide (DMF), ethanol (EtOH), acetonitrile (AN) and in (DMF-EtOH), (AN-EtOH) and (DMF-AN) binary mixed solvent solutions at different temperatures using the conductometric method. Also in this work the complexation reaction between Ca²⁺, K⁺ cations and HBFPY ligand, was studied in pure dimethylformamide (DMF), propanol (PrOH), 1,4-dioxane (DOX), ethanol (EtOH) and in DMF-PrOH, DMF-DOX and DMF-EtOH binary mixed solvent solutions at different temperatures using the conductometric method. The conductance data show that the stoichiometry of the complexes formed between this ligand and the studied cations is 1 : 1 [ML]. In most cases, addition of HBFPY to solutions of these cations, causes a continuous increase in the molar conductivities which indicates that the mobility of complexed cations is more than the uncomplexed ones. The stability constants of the complexes were obtained from fitting of molar conductivity curves using a computer program, GENPLOT. The stability constant of [Mg(HBFPY)]²⁺ complex in various neat solvents at 15°C decreases in order: EtOH > DMF > AN and the stability constant of [Ag(HBFPY)]⁺ complex in various neat solvents at 35°C decreases in order: DMF > EtOH. The values of standard enthalpy changes (ΔH° _c ) for complexation reactions were obtained from the slope of the Van’t Hoff plots and the changes in standard entropy (ΔS° _c ) were calculated from the relationship ΔH° _c,295.15= ΔH° _c –298.15ΔS° _c .     

Study of variation in thermophysical properties of RE<Subscript>6</Subscript>UO<Subscript>12</Subscript>(s) along the lanthanide series

The novel ligand N,N,N′′′′,N′′′′-tetrabutyl-N′′′,N′′′-(N″,N″-diethyl)-ethidene bisdiglycolamide (TBEE-BisDGA) and other eight analogous extractants have been synthesized and characterized by NMR and HRMS. The solvent extraction of Th⁴⁺, UO₂ ²⁺ and Eu³⁺ from nitric acid solution using the above BisDGA extractants was investigated in 1-dodecanol at 30 ± 1 °C. The extractants exhibited higher affinity toward Th⁴⁺ than UO₂ ²⁺ and Eu³⁺ in the present system. The maximum value of separation factor SF _Th(IV)/U(VI) and SF _{Th(IV)/Eu(III)} is 78.5 and 53.3 respectively for TBEE-BisDGA, 88.1 and 69.5 respectively in the case of TB ^i-PE-BisDGA at 3 M HNO₃ solution.     

Phthalocyanines and Related Compounds: XL. Synthesis of β-Diethylaminoethyl-substituted Octa-4,5-carboxyphthalocyanine Tetraimides and Their Quaternary Salts

Cobalt, zinc, hydroxoaluminum, and iron complexes of N,N′,N″,N?-tetrakis(β-diethylaminoethyl) phthalocyanine-2,3 : 9,10 : 16,17 : 23,24-tetrakis(dicarboxamide) were synthesized and were converted into the corresponding water-soluble quaternary salts by treatment with methyl iodide, methyl p-toluenesulfonate, diethyl and dimethyl sulfates, and trimethyl phosphate. The electronic absorption spectra of the quaternary salts indicated their considerable aggregation in aqueous solution; the degree of aggregation decreases in going to solutions in ethanol and disappears in DMSO.     

Synthesis,structural and spectroscopic properties of asymmetric Schiff bases derived from 2,3-diaminopyridine

Two Schiff base derivatives, 4-(2-amino-3-pyridyliminomethyl)phenol (I) and 3-(2-amino-3-pyridyliminomethyl)nitrobenzene (II), were synthesised and characterised by spectroscopy. The structure of I was determined by single crystal X-ray diffraction studies. The asymmetric Schiff base derived from 2,3-diaminopyridine selectively recognise transition and heavy metal cations, and some anion. Ligands I and II form stable complexes with Cu²⁺, Zn²⁺, Pb²⁺, Al³⁺ whereas ligand I also binds F~ ions. The stoichiometry for the host: cation is 1: 1 and 2: 1. The addition of F~ ion in CH₃CN to ligand I causes a colour change of the solution from colourless to yellow. The binding behaviour of ligand I towards several ions was investigated using density functional theory calculations.     

Synthesis,crystal structures,and catalytic property of dioxomolybdenum(VI) complexes with hydrazone ligands derived from 3,5-Di-<Emphasis Type="Italic">tert</Emphasis>-butylsalicylaldehyde

Two new dioxomolybdenum(VI) complexes, [MoO₂L¹(MeOH)] (I) and [MoO₂L²] (II), where L¹ and L² are the anionic forms of N'-(2-hydroxy-3,5-di-tert-butylbenzylidene)-4-methoxybenzohydrazide and 2-amino-N'-(2-hydroxy-3,5-di-tert-butylbenzylidene)benzohydrazide, respectively, have been synthesized and characterized by elemental analysis, FT-IR spectra, and single crystal X-ray determination (CF files CCDC nos. 1448089 (I), 1487063 (II)). The crystal of I is monoclinic: space group P21/n, a = 7.353(1), b = 24.758(3), c = 13.891(2) Å, β = 101.013(2)°, V = 2482.3(6) Å3, Z = 4, R ₁ = 0.0848, wR ₂ = 0.2050. The crystal of II is monoclinic: space group P2₁/c, a = 6.752(1), b = 16.947(1), c = 19.510(1) Å, β = 96.891(2)°, V = 2216.5(4) Å3, Z = 4, R ₁ = 0.0670, wR ₂ = 0.1638. The Mo atom in complex I is in octahedral coordination, with three donor atoms of the hydrazone ligand, two oxo groups, and one methanol O atom. The Mo atom in complex II is in square pyramidal coordination, with three donor atoms of the hydrazone ligand, and two oxo groups. The complexes have interesting catalytic properties for sulfoxidation reactions.     

Synthesis and sorption properties of layered hydrous manganese dioxide saturated with <Emphasis Type="Italic">s</Emphasis>-, <Emphasis Type="Italic">p</Emphasis>-, and <Emphasis Type="Italic">d</Emphasis>-metal cations

Layered compounds based on hydrous manganese dioxide (hereafter, Mn-phases) saturated with s-metal (Ba²⁺), p-metal (Pb²⁺), and d-metal (Mn²⁺, Co²⁺, Ni²⁺, Cu²⁺, Zn²⁺, and Cd²⁺) cations, analogues of manganese minerals of oceanic ferromanganese formations (vernadite, birnessite, buserite-I, and asbolan), were prepared at 4–6°C. All Mn-phases have poorly ordered structures. The sorption properties of phase compounds were studied in relation to alkali-metal (Na⁺ and K⁺) and other s-, p-, and d-metal cations. The exchange capacities of Mn-phases for alkali cations are very low, within 0.02–0.10 mg-equiv/g; for the other cations, the exchange capacities are 0.13–4.20 mg-equiv/g. The sorption of divalent metal cations depends on the phase and chemical composition of the Mn-phase.     

Chloro- und Azidokomplexe des Vanadyl(IV)-Ions in Acetonitril,Propandiol-1,2-carbonat,Trimethylphosphat und Dimethylsulfoxid

The formation of chloro- and azidocomplexes of VO²⁺(IV) is investigated in acetonitrile (AN), propanediol-1,2-carbonate (PDC), trimethyl phosphate (TMP) by spectrophotometric, potentiometric and conductometric methods. The following coordination forms are indicated: [VOCl]⁺ inAN, PDC andDMSO), [VOCl₂] (inAN, PDC andTMP), [VOCl₃]^? (inPDC andTMP[?]), [VOCl₄]^2? (inAN, PDC andTMP); [VON₃]⁺ (inAN, PDC andDMSO), [VO(N₃)₂] (inAN, PDC, TMP andDMSO), [VO(N₃)_2+n]^n? (inAN, PDC, TMP andDMSO). The results are interpreted by the donor numbers and sterical properties of the solvent molecules.     

Synthesis,characterization, and crystal structures of dioxomolybdenum(VI) complexes with O,N,N type tridentate hydrazone ligands as catalyst for oxidation of olefins

The preparation of Mo(VI) hydrazone complexes, cis-[MoO₂L¹(CH₃OH)] (I) and cis-[MoO₂L₂(CH₃OH)] (II), derived from N'-(3-bromo-2-hydroxybenzylidene)-2-chlorobenzohydrazide (H₂L¹) and N'-(3-bromo-2-hydroxybenzylidene)-4-bromobenzohydrazide (H₂L²), respectively, is reported. The complexes were characterized by elemental analyses, infrared and electronic spectroscopy, and single crystal structure analysis (CIF files ССDС nos. 1426875 (I), 1426871 (II)). The Mo atoms are coordinated by two cis terminal oxygen, ONO from the hydrazone ligand, and methanol oxygen. Even though the hydrazone ligands and the coordination sphere in both complexes are similar, the unit cell dimensions and the space groups are different. Complex I crystallized as orthorhombic space group Pca21 with unit cell dimensions a = 27.887(2), b = 8.0137(7), c = 15.544(1) Å, V = 3473.8(5) ų, Z = 8, R ₁ = 0.0450, wR ₂ = 0.0539. Complex II crystallized as triclinic space group P1, with unit cell dimensions a = 8.2124(4), b = 8.5807(5), c = 12.9845(8) Å, α = 83.366(2)°, β = 79.201(2)°, γ = 80.482(2)°, V = 883.03(9) Å3, Z = 2, R ₁ = 0.0278, wR ₂ = 0.0569. The complexes were tested as catalyst for the oxidation of olefins, and showed effective activity.     

Synthesis,crystal structures,and catalytic oxidation of olefins of dioxomolybdenum(VI) complexes with aroylhydrazone ligands

Two Mo(VI) aroylhydrazone complexes, cis-[MoO₂(L¹)(CH₃OH)] (I) and cis-[MoO₂(L²)(CH₃OH)] (II), derived from 2-bromo-N'-(3,5-dibromo-2-hydroxybenzylidene)benzohydrazide (H₂L¹) and 2-bromo-N'-(2-hydroxy-4-methoxybenzylidene)benzohydrazide (H₂L²), respectively, are reported. The complexes were characterized by elemental analyses, infrared and electronic spectroscopy, and single crystal structure analysis (CIF files CCDC nos. 1443679 (I) and 1443678 (II)). The Mo atoms are coordinated by two cis terminal oxygen, ONO from the aroylhydrazone ligand, and methanol oxygen. Complex I crystallized as monoclinic space group P2₁/_c with unit cell dimensions a = 8.075(2), b = 13.905(1), c = 16.448(1) Å, β = 91.282(2)°, V = 1846.5(4) ų, Z = 4, R ₁ = 0.0859, wR ₂ = 0.2066. Complex II crystallized as triclinic space group P \(\overline 1 \), with unit cell dimensions a = 8.0824(6), b = 10.5919(8), c = 10.7697(8), α = 96.432(2)°, β = 97.438(2)°, γ = 103.119(2)°, V = 880.8(1) ų, Z = 2, R ₁ = 0.0271, wR ₂ = 0.0571. The complexes were tested as catalyst for the oxidation of olefins and showed effective activity.     

Effect of donor and acceptor properties of solvents on the kinetics of photoreduction of sterically hindered <Emphasis Type="Italic">о</Emphasis>-benzoquinones

Effect of the solvent nature on the kinetics of photoreduction of 3,6-di-tert-butyl-1,2-benzoquinone and its six derivatives in the presence of N,N-dimethylaniline and 4-(N,N-dimethylamino)benzaldehyde has been investigated. It has been found that for the о-quinone—amine pair, for which the free energy change of electron transfer is ΔG_e > +0.11 eV, the rate constant of о-quinone photoreduction k_H decreases proportionally to the increase in the acceptor number of the solvent. For the о-quinone—amine pair with ΔG_e < +0.11 eV, the k_H value decreases proportionally to the increase in the donor number of the solvent. It has been established that the enhancement of the electron-acceptor properties of the solvent leads to the emergence of kinetic isotope effect for the reactant pairs of 3,6-di-tert-butyl-1,2-benzoquinone and 4,5-dimethoxy-3,6-di-tert-butyl-1,2-benzoquinone with N,N-di-methylaniline (ΔG_e = +0.11 and +0.22 eV, respectively).     

Synthesis,crystal, and molecular structure of coordination polymers constructed by self-assembly of NiN<Subscript>4</Subscript> cores with 2,2′-iminodibenzoate and nitroprusside ions

Two coordination compounds of compositions [Ni(L¹)(idba)(H₂O)]·1.5 H₂O (1) and [Ni(L²)Fe(CN)₅NO]·C₂H₅OH (2) where L¹ is N, N′-bis(3-aminopropyl)ethylenediamine, L² is 2,12-dimethyl-3,7,11,17-tetraazabicyclo[11.3.1]heptadeca-1(17),2,11,13,15-pentaene, and idba^2? is 2,2′-iminodibenzoate have been synthesized and characterized by elemental analysis, IR spectroscopy, thermal analysis, and single-crystal X-ray diffraction. Complex 1 crystallizes in the monoclinic space group P2₁/n (No. 14) with a=9.810(2) Å, b=10.230(2) Å, c=25.350(5) Å, V=2543.6(9) Å³, Z=4, and R=0.0727. The nickel atom is six-coordinated by four N atoms of amine and two O atoms of water and idba^2?. The molecular packing of the complex comprises of an infinite one-dimensional layered network in which the molecules in the crystal are held together by a system of hydrogen bonding. Complex 2, however, crystallizes in the space group C2/c (No. 15) of the monoclinic system with a=19.7990(4) Å, b=14.9440(3) Å, c=19.8800(3) Å, V=5115.90(17) Å³, Z=4, and R=0.0540. The Ni ion in compound 2 has a slightly distorted octahedral arrangement of the N₄ donor atoms of primary ligand L² and two N-donor atoms of the secondary nitroprusside ligand. The structure of 2 displays an extended one-dimensional network formed by linear [—Ni—NC—Fe—CN—] units. A cyclic voltammetric study shows that compound 1 undergoes a quasireversible oxidation attributable to Ni²⁺ → Ni³⁺ in the range 300–420 mV vs SCE.     

Influence of the Molecular Mass of Poly(<Emphasis Type="Italic">N</Emphasis>-vinylpyrrolidone) on Formation of Cu<Subscript>2</Subscript>O Nanoparticles During Reduction of Divalent Copper Ions with <Emphasis Type="Italic">tert</Emphasis>-Butylamine Borane in Polymer Solution

The process of reduction of divalent copper ions with tert-butylamine borane in dilute aqueous solutions of poly(N-vinylpyrrolidone) is investigated. The influence of polymer molecular mass on properties of the resultant Cu₂O sols is studied. It is shown that Cu₂O nanoparticles with an average diameter of 6–8 nm independent of polymer molecular mass and a relatively narrow size distribution of particles are formed in the systems under study. The contour length of macromolecules and the hydrodynamic diameter of a poly(N-vinylpyrrolidone) macromolecular coil are compared with the diameter of Cu₂O particles. Poly(N-vinylpyrrolidone) with M ≥ 1 × 10⁴ can be used to produce Cu₂O nanoparticles. Poly(N-vinylpyrrolidone) with M > 4 × 10⁴ should be used for the formation of long-living Cu₂O sols.     

Synthesis,structure, and antimicrobial activity of methyl (4-alkanoyl-1,5-diaryl-2-hydroxy-3-oxo-2,3-dihydro-1<Emphasis Type="Italic">H</Emphasis>-pyrrol-2-yl)acetates

Reactions of methyl 3,4,6-trioxoalkanoates (3,4-dihydroxy-6-oxo-2,4-alkadienoates) with mixtures of aromatic aldehydes and arylamines or with the corresponding N-(arylmethylidene)anilines afforded methyl (4-alkanoyl-1,5-diaryl-2-hydroxy-3-oxo-2,3-dihydro-1H-pyrrol-2-yl)acetates. The product structure was discussed on the basis of their IR, ¹H NMR, and mass spectra and X-ray diffraction data, and their antimicrobial activity against Staphylococcus aureus P-209 and Escherichia coli M₁₇ was evaluated.     

Synthesis of Cu(II) and Mn(III) Complexes Involving Derivatives of Pyridine

Two complexes with derivatives of pyridine as ligands were synthesized and characterized. From the reaction of 2-pyridinecarboxaldehyde oxime with Cu(OAc)₂ · H₂O afforded the complex C₂₀H₃₀N₆O₁₂Cu₃ (I), and the use of 3-hydroxy-2-pyridinecarboxylic acid with anhydrous MnCl₂ · 4H₂O led to the formation of another complex C₁₂H₁₄N₂OCl₂Mn (II). They were characterized by X-ray diffraction (CIF files CCDC nos. 568718 (I) and 1568880 (II)), NMR, IR and elemental analysis. For I: terigonal, space group R\(\bar 3\)/H, a = 42.548(3), c = 10.2774(9) Å, V = 16113(2) ų, Z = 18, ρ_calcd = 1.367 Mg/m³, the final R factor was R₁ = 0.0945, 6662 for reflections were observed with I > 2σ(I), wR = 0.162 for all data. For II: triclinic, Pī, a = 5.6174(9), b = 7.7259(13), c = 9.7160(16) Å, α = 70.444(3)°, β = 88.009(3)°, γ = 89.818(3)°, V = 397.09(11) ų, Z = 1, ρ_calcd = 1.840 Mg/m³, the final R factor was R₁ = 0.0281, 4280 for reflections were observed with I > 2σ(I), wR = 0.0775 for all data.