Ruthenium(II) complexes incorporating tridentate Schiff base ligands: synthesis,spectroscopic, redox,catalytic and biological properties

A series of new diamagnetic ruthenium(II) complexes of the type [RuCl(CO)(B)(L)] (where B = PPh₃, AsPh₃ or Py; L = monobasic tridentate Schiff base ligands derived from o‐aminophenol or o‐aminothiophenol with ethylacetoacetate or ethylbenzoylacetate) have been synthesized and these complexes were characterized by physico‐chemical and spectroscopic methods. Cyclic voltammograms of all the complexes show quasi‐reversible oxidation in the range 0.24–1.05 V and the quasi‐reversible reduction in the range ? 0.14 to ? 0.51 V. The observed redox potentials show little variation with respect to the replacement of triphenyl phosphine/arsine by pyridine. The complexes were tested as catalysts in the oxidation of primary and secondary alcohols using molecular oxygen at room temperature and also in C? C coupling reactions. Further, the antibacterial properties of the free ligands and their metal complexes were evaluated against certain bacteria such as Escherichia coli and Staphylococcus aureus. Copyright © 2010 John Wiley & Sons, Ltd.     

Ruthenium(II) phenylazopyridinearylazoimidazoles: Synthesis, spectral studies and redox properties

Tris-chelate complex [Ru(Pap)(RAaiR′)₂](ClO₄)₂ (I, II, III/a, b, c) (where RAaiR′ = 1-alkyl-(2-arylazo)imidazole, R = H, Me, Cl (a, b, c); R′ = Me, Et, CH₂Ph (I, II, III), and Pap = phenylazopyridine) was prepared by silver assisted synthetic route. IR spectra of the complexes support Ru-azo nitrogen π-bonding interaction. ¹H NMR spectra suggest that there are two types of streochemical orientation of RAaiR′ around ruthenium(II). Cyclic voltammetry of the complexes shows one metal oxidation Ru(II)/Ru(III) at 1.4–1.5 V and three successive ligand reduction couples at the negative side of the reference potential in the range from −0.5 to −0.56, −0.7 to −0.8, and from −1.25 to −1.40 V, respectively. The text was submitted by the author in English.     

Synthesis and characterization of chiral polymer complexes incorporating polybinaphthyls,bipyridine, and Eu(III)

Chiral conjugated polymers P‐1 and P‐2 were synthesized by the polymerization of (S)‐3,3′‐diiodo‐2,2′‐bisbutoxy‐1,1′‐binaphthyl and (S)‐6,6′‐dibromo‐2,2′‐bisbutoxy‐1,1′‐binaphthyl, respectively, with 5,5′‐divinyl‐2,2′‐bipyridine through a Heck cross‐coupling reaction. Chiral polymer complexes P‐C‐1 and P‐C‐2 were obtained by the bipyridine chelating coordination of P‐1 and P‐2 with Eu(TTA)₃·2H₂O (where TTA is 2‐thenoyltrifluoroacetonate). Polymers P‐1 and P‐2 and polymer complexes P‐C‐1 and P‐C‐2 exhibited intense circular dichroism signals, with negative and positive Cotton effects in their circular dichroism spectra. The chiral polymers showed strong green‐blue fluorescence because of the efficient energy migration from the extended π‐electronic structure of the conjugated polymer main to the chiral binaphthyl core. The chiral polymer complexes could have not only polymer fluorescence but also the characteristic fluorescence of Eu(III) (⁵D₀→⁷F₂) at a different excited wavelength. These kinds of chiral polymer complexes incorporating polybinaphthyls, bipyridine, and Eu(III) moieties are expected to provide an understanding of the relationship between the structure and properties of chiral polymer complexes. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 650–660, 2007     

Ruthenium (II) polypyridyl complexes based on bipyridine and two novel diimine ligands with carrier-transporting unit: synthesis, photoluminescence and redox properties

A series of ruthenium (II) complexes, [Ru(bpy)₂L]X₂ (L = L1, L2; X = Cl⁻, PF₆⁻, SCN⁻), were synthesized based on bipyridine and two novel diimine ligands L1 and L2 (L1 = 1-(4-5′-phenyl-1,3,4-oxadiazolylphenyl)-2-pyridinyl-benzoimidazole, L2 = 1-(4-carbazolylphenyl)-2-pyridinylbenzimidazole); and the crystal structure of [Ru(bpy)₂L1]Cl₂ was also described. [Ru(bpy)₂(Pybm)]X₂ (Pybm = 2-(2-pyridine)benzimidazole) complexes were also prepared as reference samples. In the UV-vis absorption spectra there are one strong π → π* transition and two dπ (Ru) → π* transitions. By comparisons of photoluminescence properties between [Ru(bpy)₂L]X (L = L1, L2) and the reference complexes we find that the complexes with carrier-transporting groups of carbazole and oxadizole have the higher emission intensity and quantum efficiency. One reversible oxidation process in the range 0.80-1.00 V exists in each of the complexes which is assigned to the metal oxidation, [Ru(III)(bpy)₂L]²⁺ + e⁻?[Ru(II)(bpy)₂L]⁺.     

Synthesis, structure, spectroscopic properties, and electrochemical oxidation of ruthenium(II) complexes Incorporating monocarboxylate bipyridine ligands

[Ru(bpy)(2)(Mebpy-COOH)](PF(6))(2).3H(2)O (1), [Ru(phen)(2)(Mebpy-COOH)](ClO(4))(2).5H(2)O (2), [Ru(dppz)(2)(Mebpy-COOH)]Cl(2).9H(2)O (3), and [Ru(bpy)(dppz)(Mebpy-COOH)](PF(6))(2).5H(2)O (4) (bpy = 2,2'-bipyridine, Mebpy-COOH = 4'-methyl-2,2'-bipyridine-4-carboxylic acid, phen = 1,10-phenanthroline, dppz = dipyrido[3,2,-a;2',3-c]phenazine) have been synthesized and characterized spectroscopically and by microanalysis. The [Ru(Mebpy-COOH)(CO)(2)Cl(2)].H(2)O intermediate was prepared by reaction of the monocarboxylic acid ligand, Mebpy-COOH, with [Ru(CO)(2)Cl(2)](n), and the product was then reacted with either bpy, phen, or dppz in the presence of an excess of trimethylamine-N-oxide (Me(3)NO), as the decarbonylation agent, to generate 1, 2, and 3, respectively. For compound 4, [Ru(bpy)(CO)Cl(2)](2) was reacted with Mebpy-COOH to yield [Ru(bpy)(Mebpy-COOH)(CO)Cl](PF(6)).H(2)O as a mixture of two main geometric isomers. Chemical decarbonylation in the presence of dppz gave 4 also as a mixture of two isomers. Electrochemical and spectrophotometric studies indicated that complexes 1 and 2 were present as a mixture of protonated and deprotonated forms in acetonitrile solution because of water of solvation in the isolated solid products. The X-ray crystal structure determination on crystals of [Ru(bpy)2(MebpyCOO)][Ru(bpy)(2)(MebpyCOOH)](3)(PF(6))(7), 1a, and [Ru(phen)(2)(MebpyCOO)](ClO(4)).6H(2)O, 2a, obtained from solutions of 1 and 2, respectively, revealed that 1a consisted of a mixture of protonated and deprotonated forms of the complex in a 1:3 ratio and that 2a consisted of the deprotonated derivative of 2. A distorted octahedral geometry for the Ru(II) centers was found for both complexes. Upon excitation at 450 nm, MeCN solutions of the protonated complexes 1-4 were found to exhibit emission bands in the 635-655 nm range, whereas the corresponding emission maxima of their deprotonated forms were observed at lower wavelengths. Protonation/deprotonation effects were also observed in the luminescence and electrochemical behavior of complexes 1-4. Comprehensive electrochemical studies in acetonitrile show that the ruthenium centers on 1, 2, 3, and 4 are oxidized from Ru(II) to Ru(III) with reversible potentials at 917, 929, 1052, and 1005 mV vs Fc(0/+) (Fc = ferrocene), respectively. Complexes 1 and 2 also exhibit an irreversible oxidation process in acetonitrile, and all compounds undergo ligand-based reduction processes.     

Synthesis,spectroscopic and redox properties of nickel(II) salicylaldimine complexes containing sterically hindered phenols

The preparation and spectroscopic characterization of a series of new bis[N-(2,6-di-t-butyl-1-hydroxyphenyl)salicylaldiminato]nickel(II) complexes, [Ni(L^X)₂], bearing one or two OH and MeO substituents on the salicylaldehyde moiety, as well as radical species generated from these compounds by the oxidation with PbO₂, are reported. The [Ni(L^X)₂] chelates, which appear to be tetrahedral in the solid state and in dioxane solution, are converted into a square-planar configuration in non-donor solvents. The OH-substituted complexes, unlike their MeO analogues, form six-coordinate adducts in pyridine, DMF and DMSO. These new compounds, unlike their analogues with electron-withdrawing substituents (Cl, Br, NO₂), are easily oxidized by PbO₂ to produce Ni^II-stabilized phenoxy radicals in which the unpaired electrons are delocalized over the ligand and do not couple with the second radical center. No e.s.r. signals were observed that could be attributed to a M = ±2 transition of the triplet state biradicals.     

Synthesis, spectroscopic, redox, catalytic and antimicrobial properties of some ruthenium(II) Schiff base complexes

A new series of mixed ligand semicarbazone or thiosemicarbazone complexes of Ru(II) having the general formula [RuCO(EPh₃)(B)L] (where E = P or As; B = PPh₃, AsPh₃ or Pyridine; L = dibasic tridentate ligand derived by the condensation of ethylacetoacetate/methylacetoacetate and thiosemicarbazide/semicarbazide) have been synthesized and characterized by physico-chemical, spectroscopic and electrochemical studies. A comparative study on the catalysis of oxidation of benzyl alcohol, cyclohexanol, cinnamyl alcohol, n-butanol, n-propanol and iso-butyl alcohol has been done with N-methylmorpholine-N-oxide and molecular oxygen as co-oxidants. Catalytic activity studies of the complexes in coupling reactions have been carried out. The antibacterial properties of the complexes have also been examined.     

Ruthenium(II)-arylazoimidazole-8-hydroxyquinolinate complexes: Synthesis,spectral study (H,C, COSY,HMQC-NMR) and redox properties

The reaction of [Ru(OH₂)₂(RaaiR′)₂]²⁺ (RaaiR′ = 1-alkyl-2-(arylazo)imidazole, p-R-C₆H₄-N=N-C₃H₂NN(1)-R′, R = H (1), Me (2), Cl (3); R′ = Me (a), Et (b), CH₂Ph (c)) with 8-quinolinol (HQ) in acetone solution followed by the addition of NH₄PF₆ has afforded violet coloured mixed ligand complexes of the composition [Ru(Q)(RaaiR′)₂](PF₆). The maximum molecular peak of 1b is observed at m’z 790 (50%) in the ESI mass spectrum. Ir spectra of the complexes show -C=N- and -N=N- stretching near at 1590 and 1370 cm⁻¹. The ¹H NMR spectral measurements suggest methylene, -CH₂−, in RaaiEt gives a complex AB type while in RaaiCH₂Ph it shows AB type quartets. Considering the arylazoimidazole and oxine moitie there are twenty different carbon atoms in the molecule which gives a total of twenty different peaks in the C¹³ NMR spectrum of complex 1a. In the ¹H-¹H COSY spectrum of the present complexes, absence of any off-diagonal peaks extending from δ = 14.12 and 9.55 ppm confirm their assignment of no proton on N(1) and N(3) respectively. Contour peaks in the ¹H-¹³C HMQC spectrum in the present complexes, the absence of any contours at δ = 157.12, 160.76, 155.67 ppm and 157.68–160.2 ppm assign them to the C(2), C(6), C(g) and C(h), C(i) carbon atoms respectively. The solution structure and stereoretentive transformation in each step have been established from n.m.r. results. Cyclic voltammograme show a Ru(III)/Ru(II) couple at 1.0–1.1 V versus SCE along with three successive ligand reductions.     

Synthesis,crystal structures,and characterization of copper(II) carboxylate complexes incorporating 1,10-phenanthroline and bipyridine

A series of Cu(II) carboxylate complexes (carboxylate?=?2-fluorobenzoic acid (2-HFBA) or 4-fluorobenzoic acid (4-HFBA)) containing either one chelating 1,10-phenanthroline (phen) or 2,2′-bipyridine (bipy) have been synthesized and characterized by single-crystal X-ray diffraction, IR spectroscopy, and thermal analyses. In [Cu(bipy)(H₂O)(2-FBA)₂] (1), [Cu(bipy)(H₂O)(4-FBA)₂] (3), and [Cu(phen)(H₂O)(2-FBA)₂] (4), Cu is five-coordinate in a square pyramidal geometry and four-coordinate in [Cu(phen)(2-FBA)₂] (2). The four complexes are extended into 1-D chains through hydrogen-bonding and π?···?π interactions in 1 and 4, only hydrogen-bonding in 2, and π?···?π interactions in 3. These contacts lead to aggregation and supramolecular self-assembly.     

Synthesis, characterization and some properties of amide-linked porphyrin-ruthenium(II) tris(bipyridine) complexes

A new molecular dyad, comprised of a zinc-porphyrin and a ruthenium(II) tris(bipyridine) complex linked through an amide bond has been synthesized and characterized by ¹H, ¹³C NMR, UV-vis, mass-spectrometry and elemental analysis. The electrochemistry as well as the steady-state emission properties were investigated. The redox behavior of the dyad exhibits a favorable reversible characteristic. Substantial quenching of porphyrin emission was found when the Q band of 5 and 5-Zn was selectively photoexcited. This observation suggests a quenching mechanism with possible intramolecular electron transfer or energy transfer between the Ru(bpy)₃ moiety and the porphyrin free-base or Zn porphyrin moieties.     

Aryl-diamide bridged binuclear ruthenium (II) tris(bipyridine) complexes: Synthesis, photophysical, electrochemical and electrochemiluminescence properties

Several new symmetrical aromatic hydrocarbon bridged bipyridine ligands and their binuclear Ru (II) complexes have been designed, synthesized and characterized on the basis of ¹H NMR, MS and HRMS. Their absorption and emission properties, electrochemical behaviors and electrochemical luminescence were investigated. All ruthenium complexes show characteristic MLCT absorption and similar redox potential. Among the three complexes reported, 4c has the best electrochemical luminescence property.     

Synthesis, spectroscopic and structural properties of uranyl complexes based on bipyridine N-oxide ligands

By using 2,2′-bipyridine N-oxide (bipyO) and 2,2′-bipyridine N,N′-dioxide (bipyO₂), three new uranyl complexes [UO₂(bipyO)SO₄]·H₂O (1), [UO₂(bipyO)(OH)(NO₃)]₂·H₂O (2) and [UO₂(bipyO₂)H₂O](ClO₄)₂·(3) were synthesized using uranyl salts including non-coordinating or weakly coordinating power of the ClO₄⁻ anion and the strongly coordinating power of NO₃⁻ and SO₄²⁻ anions. All of the compounds were characterized by CHN microanalytical procedures, infrared and luminescence spectroscopy and by single crystal X-ray diffraction. Spectroscopic studies indicate that the bipyO is bound to the uranyl group via the nitrogen and oxygen atoms. Structural analyses revealed that overall bonding pattern is different in each case: 1 is a polymer; in 2 dimeric complex molecules are formed, whereas 3 is composed of monomers. In all of the complexes, the uranium atom is in a seven-coordinate environment.     

Synthesis, spectroscopic and redox properties of the copper(II) complexes of N-(di-methylphenyl)-3,5-Bu2t-salicylaldimines

A series of copper(II) complexes (CuL2x) with new N-di-methylphenyl-3,5-Bu2t-salicylaldimines (L(x)H) were prepared and characterized by IR, UV/vis, 1H NMR, ESR, cyclic voltammetry techniques and chemical oxidation. L(x)H ligands have been found selectively bind to a Cu(II), rather than to Ni(II), Co(II), Mn(II), VO(IV), Zn(II) and Cd(II). ESR examinations of the CuL2x complexes demonstrate that they exist in magnetically diluted mononuclear or coupled triplet-state structures in the solid. The temperature dependent (113-283 K) intensity of the powder ESR spectra for some CuL2x is characteristic of ferromagnetic coupling (J > 0). The reduction potentials of CuL2x in DMSO are sensitive to aniline moieties. Chemical oxidation of CuL2x with (NH4)2[Ce(NO3)6] in CHCl3 and MeCN solutions at 300 K affords gradually disappearance of their ESR signals and dramatic changes in the electronic spectra as well as the appearance of new maximum bands at 530-672 (CHCl3) and 670-700 nm (MeCN), suggesting generation of Cu(II)-phenoxyl radical species.     

Palladium(II)-dppe-arylazoimidazole complexes: Synthesis,and spectroscopic characterization

Reaction of [Pd(dppe)Cl₂/Br₂] with AgOTf in a dichloromethane medium followed by ligand addition led to [Pd(dppe)(OSO₂CF₃)₂] and then [Pd(dppe)(RaaiR)](OSO₂CF₃)₂ [RaaiR′ = p-R-C₆H₄-N=N-C₃H₂-NN-1-R′, (1–3), abbreviated as a N,N′-chelator, where N(imidazole) and N(azo) are represented by N and N′, respectively; R = H (a), Me (b), Cl (c) and R′ = Me (1), CH₂CH₃ (2), CH₂Ph (3), OSO₂CF₃ is the triflate anion, dppe = 1,2-bis-(diphenylphosphinoethane)]. ³¹P “¹H” NMR confirmed that due to the two phosphorus atom interaction in the azoimine symmetrical environment one sharp peak was formed. The ¹H NMR spectral measurements suggest that azo-imine link with lot of phenyl protons in the aromatic region. ¹³C (¹H) NMR spectrum, ¹H, ¹H COSY and ¹H, ¹³C HMQC spectrum assign the solution structure and stereo-retentive conformation in each complex.     

Synthesis, photophysical, photochemical, and redox properties of nitrospiropyrans substituted with Ru or Os tris(bipyridine) complexes

Photochromic nitrospiropyrans substituted with 2,2'-bipyridine (bpy), [Ru(bpy)3]2+, and [Os(bpy)3]2+ groups were synthesized, and their photophysical, photochemical, and redox properties investigated. Substitution of the spiropyran with the metal complex moiety results in strongly decreased efficiency of the ring-opening process as a result of energy transfer from the excited spiropyran to the metal center. The lowest excited triplet state of the spiropyran in its open merocyanine form is lower in energy than the excited triplet MLCT level of the [Ru(bpy)3]2+ moiety but higher in energy than for [Os(bpy)3]2+, resulting in energy transfer from the excited ruthenium center to the spiropyran but inversely in the osmium case. The open merocyanine form reduces and oxidizes electrochemically more easily than the closed nitrospiropyran. Like photoexcitation, electrochemical activation also causes opening of the spiropyran ring by first reducing the closed form and subsequently reoxidizing the corresponding radical anion in two well-resolved anodic steps. Interestingly, the substitution of the spiropyran with a Ru or Os metal center does not affect the efficiency of this electrochemically induced ring-opening process, different from the photochemical path.     

New trinuclear carbonato-bridged copper(II) complexes: Synthesis,crystal structure,and spectroscopic properties

New trinuclear carbonato-bridged copper(II) complexes, [Cu₃(Bipy)₆(μ₃-CO₃)](CF₃SO₃)₄(H₂O)_0.5 (I) and [Cu₃(Phen)₆(μ₃-CO₃)](CF₃SO₃)₄(H₂O)_0.5 (II) (Bipy = 2,2′-bipyridine and Phen = 1,10-phenanthroline), have been synthesized and characterized by X-ray crystallography. In the trinuclear units, a carbonate anion triply bridges three Cu atoms in a μ₃-η¹:η¹:η¹-CO₃ mode. The environment around each copper(II) center is five-coordinate ranging between intermediate to distorted square-pyramidal geometry. In the crystal packing, the molecule of I is involved in a variety of intra/intermolecular non-covalent interactions such as intra/intermolecular stacking and CH···π interactions between the pyridine groups of the chelated ligand, leading to a one-dimensional arrangement of I. In complex II, the molecule is involved in both intra- and intermolecular Phen-Phen π-stacking, forming a three-dimensional network. The spectroscopic (IR, diffuse reflectance, and EPR spectra) properties and the preliminary results of magnetic measurements of both complexes are investigated and compared to other closely related trinuclear copper(II) complexes.     

Synthesis and electronic characterization of bipyridine dithiolate rhodium(III) complexes

Five new mixed diimine 1,1'-dithiolate or dithiocarbamate ligand complexes of the form [Rh(bpy)2(SS)][PF6]n, where bpy = 2,2'-bipyridine and SS = various substituted dialkyldithiocarbamates or 1,1'-dithiolates, were synthesized from cis-[Rh(bpy)2(OTf)2][OTf]. The triflate ligands are easily displaced by other ligands and allow these syntheses to proceed in high yields (80-90% overall) under relatively mild reaction conditions and to give high purity products. Electrochemistry shows irreversible two-electron reduction of Rh(III) to Rh(I) and a concomitant loss of one bipyridine ligand; this is followed by reversible one-electron reduction of the remaining 2,2'-bipyridine ligand. The electronic characterizations of these complexes are consistent with significant delocalization of the sulfur electron density onto the empty metal d orbitals. The 1,1'-dithiolate ligands induce larger red shifts in the absorption and emission spectra than the dithiocarbamates as the 1,1'-dithiolates have a more extensive conjugation system.     

Ruthenium(II) bipyridine complexes: from synthesis and crystal structures to electrochemical and cytotoxicity investigation

Complexes 1–4, [Ru(L)(bpy)₂]PF₆, where bpy = 2,2′-bipyridine; HL = 3-methylpyridine-2-carboxylic acid (HL1), 6-methylpyridine-2-carboxylic acid (HL2), 5-bromopyridine-2-carboxylic acid (HL3) and 6-bromopyridine-2-carboxylic acid (HL4), were synthesized and characterized. The electrochemical character of the complexes was investigated by cyclic voltammetry revealing two reversible reduction waves in the negative range of potentials, most likely due to a reduction of the bipyridine moiety. Cytotoxicity studies by MTT assay for 72 h of drug action revealed that 2–4 exhibited moderate activity in cervical human tumor cells (HeLa). Complex 2 exhibited low activity in colon cancer LS-174 cells (180 ± 10), while all complexes were devoid of activity in lung cancer A549 and non-tumor MRC-5 cells, up to 200 μM. Combinational studies of the most active complex 2, with pharmacological modulators of cell redox status, L-buthionine-sulfoximine (L-BSO) or N-acetyl-L-cysteine (NAC), showed that when L-BSO potentiated, 2 induced a sub-G1 peak of the cell cycle in the HeLa cell line. UV–vis and cyclic voltammetry were performed in order to investigate the binding mode of 2 to DNA and suggested intercalation for the complex–DNA interaction.     

Synthesis,Characterization and reactivities of Schiff-base complexes of Ruthenium(III)

Schiff-base complexes of ruthenium (1–5) have been synthesized using Schiff-base ligands derived by condensation of either 1,2-phenylenediamine with aldehydes (salicyldehyde, 2-pyridinecarboxaldehyde) or acetylacetone with amines (2-aminophenol, 2-aminomethylpyridine). All complexes were characterized by analytical, spectroscopic, conductance, magnetic moment and electrochemical studies. At room temperature, complexes 1–5 catalyze the oxidation of both saturated and unsaturated hydrocarbons using tert-butylhydroperoxide (t-BuOOH). A mechanism involving formation of and transfer from a reactive high valency Ru(V)-oxo species as the catalytic intermediate is proposed for the processes.     

Synthesis,molecular geometry,spectroscopic studies and thermal properties of Co(II) complexes

Co(II) complexes (1‐4) were prepared and characterized by elemental analyses, infrared spectra, spectral studies, magnetic susceptibility measurements, X‐ray diffraction analysis and thermogravimetric analysis (TGA). The X‐ray diffraction patterns of Co(II) complexes were observed many peaks which indicate the polycrystalline nature. The thermodynamic parameters were calculated by using Coats–Redfern and Horowitz–Metzger methods. The bond length, bond angle and quantum chemical parameters of the Co(II) complexes were studied and discussed. The Co(II) complexes were tested against various Gram‐positive bacteria, Gram‐negative bacteria and fungi. It was found that the Co(II) complex (1) has more antifungal activity than miconazole (antifungal standard drug) against P. italicum at all concentration. The Co(II) complex ( 2 ) has more antibacterial activity than the penicillin against K. pneumoniae at all concentration. The interaction between Co(II) complexes and calf thymus DNA show hypochromism effect. The relationship between the values of HOMO–LUMO energy gap (?E) and the values of intrinsic binding constant (K_b) is revealed increasing of HOMO–LUMO energy gap accompanied by the decrease of K_b.