Anion directed templated synthesis of mono- and di-Schiff base complexes of Ni(II)

Two sets of Schiff base ligands, set-1 and set-2 have been prepared by mixing the respective diamine (1,2-propanediamine or 1,3-propanediamine) and carbonyl compounds (2-acetylpyridine or pyridine-2-carboxaldehyde) in 1:1 and 1:2 ratios, respectively and employed for the synthesis of complexes with Ni(II) perchlorate and Ni(II) thiocyanate. Ni(II) perchlorate yields the complexes having general formula [NiL2](ClO4)(2) (L = L-1 [N-1-(1-pyridin-2-yl-ethylidine)-propane-1,3-diamine] for complex 1, L-2 [N-1-pyridine-2-ylmethylene-propane1,3-diamine] for complex 2 or L-3 [N-1-(1-pyridine-2-yl-ethylidine)-propane-1,2-diamine] for complex 3) in which the Schiff bases are mono-condensed terdentate whereas Ni(II) thiocyanate results in the formation of tetradentate Schiff base complexes, [NiL](SCN)(2) (L=L-4 [N,N'-bis-(1-pyridine-2-yl-ethylidine)-propane-1,3-diamine] for complex 4, L-5 [NN'-bis(pyridine-2-ylmethyline)-propane-1, 3-diamine] for complex 5 or L-6 [NN'-bis-(1-pyridine-2-yl-ethylidine)-propane- 1, 2-diamine] for complex 6) irrespective of the sets of ligands used. Formation of the complexes has been explained by anion modulation of cation templating effect. All the complexes have been characterized by elemental analyses, spectral and electrochemical results. Single crystal X-ray diffraction studies confirm the structures of four representative members, 1, 3, 4 and 5; all of them have distorted octahedral geometry around Ni(II). The bis-complexes of terdentate ligands, I and 3 are the mer isomers and the complexes of tetradentate ligands, 4 and 5 possess trans geometry. (c) 2007 Elsevier Ltd. All rights reserved.

Methylene spacer-regulated structural variation in cobalt(II/III) complexes with bridging acetate and Salen- or Salpn-type Schiff-base ligands

Two linear, trinuclear mixed-valence complexes, [Co-II{(mu-L-1)(mu-OAc)Co-III (OAc)}(2)] (1) and [Co-II(mu-L-2) (mu-OAc)Co-III(OAc)}(2)] (2) and two mononuclear Con' complexes [Co-III{L-3)(OAc)] (3), and [Co-III {L-4}(OAc)] (4) were prepared and the molecular structures of 1, 2 and 4 elucidated on the basis of X-ray crystallography [OAc = Acetate ion, H2L1 = H(2)Salen 1,6-bis(2-hydroxyphenyl)-2,5-diazahexa-1,5-diene, H2L2 H2Me2-Salen = 2,7-bis(2-hydroxyphenyl)-2,6-diazaocta-2,6-diene, H2L3 = H(2)Salpn = 1,7-bis(2-hydroxyphenyl)-2,6-diazahepta1,6-diene, H2L4 = H(2)Me(2)Salpn = 2,8-bis(2-hydroxyphenyl)3,7-diazanona-2,7-dienel. In complexes I and 2, the acetate groups show both monodentate and bridging bidentate coordination modes, whereas chelating bidentate acetate is present in 4. The terminal (CoN2O4)-N-III centres in 1 and 2 exhibit uniform facial arrangements of both non-bridged N2O and bridging O-3 donor sets and the Co-II centre is coordinated to six (four phenoxo and two acetato) oxygen atoms of the bridging ligands. The effective magnetic moment at room temperature corresponds to the presence of high-spin Coll in both 1 and 2. The complexes 1 and 2 are thus Co-III(S = 0)Co-II(S = 3/2)-Co-II(S = 0) trimers. Complexes 3 and 4 are monomeric and diamagnetic containing low-spin Co-III(S = 0) with chelating tetradentate Schiff base and bidentate acetate. Calculations based on DFT rationalise the formation of trinuclear or monomiclear complexes. (C) Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2008).

Structural variations in Ni(II) complexes of salen type di-Schiff base ligands

Three di-Schiff-base ligands, N,N'-bis(salicylidene)-1,3-propanediamine (H(2)Salpn), N,N'-bis(salicylidene)-1,3-pentanedianiine (H(2)Salpen) and N,N'-bis(salicylidine)-ethylenediamine (H(2)Salen) react with Ni(SCN)(2). 4H(2)O in 2:3 molar ratios to form the complexes; mononuclear [Ni(HSalpn)(NCS)(H2O)]center dot H2O (1a), trinuclear [{Ni(Salpen)}(2)Ni(NCS)(2)] (2b) and trinuclear [{Ni(Salen)}(2)Ni(NCS)(2)] (3) respectively. All the complexes have been characterized by elemental analyses, IR and UV-VIS spectra, and room temperature magnetic susceptibility measurements. The structures of la and 2b have been confirmed by X-ray single crystal analysis. In complex la, the Ni(II) atom is coordinated equatorially by the tetradentate, mononegative Schiff-base, HSalpn. Axial coordination of isothiocyanate group and a water molecule completes its octahedral geometry. The hydrogen atom attached to one of the oxygen atoms of the Schiff base is involved in a very strong hydrogen bond with a neighboring unit to form a centrosymmetric dimer. In 2b, two square planar [Ni(Salpen)] units act as bide mate oxygen donor ligands to a central Ni(II) which is also coordinated by two mutually cis N-bonded thiocyanate ligands to complete its distorted octahedral geometry. Complex 3 possesses a similar structure to that of 2b. A dehydrated form of la and a hydrated form of 2b have been obtained and characterized. The importance of electronic and steric factors in the variation of the structures is discussed. (c) 2007 Elsevier Ltd. All rights reserved.

Anion-directed template synthesis and hydrolysis of mono-condensed Schiff base of 1,3-pentanediamine and o-hydroxyacetophenone in Ni-II and Cu-II complexes

Bis(o-hydroxyacetophenone)nickel(II) dihydrate, on reaction with 1,3-pentanediamine, yields a bis-chelate complex [NiL2]center dot 2H(2)O (1) of mono-condensed tridentate Schiff base ligand HL {2-[1-(3-aminopentylimino)ethyl]phenol}. The Schiff base has been freed from the complex by precipitating the Nil, as a dimethylglyoximato complex. HL reacts smoothly with Ni(SCN)(2)center dot 4H(2)O furnishing the complex [NiL(NCS)] (2) and with CuCl2 center dot 2H(2)O in the presence of NaN3 or NH4SCN producing [CuL(N-3)](2) (3) or [CuL(NCS)] (4). On the other hand, upon reaction with Cu(ClO4)(2)center dot 6H(2)O and Cu(NO3)(2)center dot 3H(2)O, the Schiff base undergoes hydrolysis to yield ternary complexes [Cu(hap)(pn)(H2O)]ClO4 (5) and [Cu(hap)(pn)(H2O)]NO3 (6), respectively (Hhap = o-hydroxyacetophenone and pn = 1,3-pentanediamine). The ligand HL undergoes hydrolysis also on reaction with Ni(ClO4)(2)center dot 6H(2)O or Ni(NO3)(2)center dot 6H(2)O to yield [Ni(hap)(2)] (7). The structures of the complexes 2, 3, 5, 6, and 7 have been confirmed by single-crystal X-ray analysis. In complex 2, Ni-II possesses square-planar geometry, being coordinated by the tridentate mono-negative Schiff base, L and the isothiocyanate group. The coordination environment around Cu-II in complex 3 is very similar to that in complex 2 but here two units are joined together by end-on, axial-equatorial azide bridges to result in a dimer in which the geometry around Cu-II is square pyramidal. In both 5 and 6, the Cu-II atoms display the square-pyramidal environment; the equatorial sites being coordinated by the two amine groups of 1,3-pentanediamine and two oxygen atoms of o-hydroxyacetophenone. The axial site is coordinated by a water molecule. Complex 7 is a square-planar complex with the Ni atom bonded to four oxygen atoms from two hap moieties. The mononuclear units of 2 and dinuclear units of 3 are linked by strong hydrogen bonds to form a one-dimensional network. The mononuclear units of 5 and 6 are joined together to form a dimer by very strong hydrogen bonds through the coordinated water molecule. These dimers are further involved in hydrogen bonding with the respective counteranions to form 2-D net-like open frameworks. ((C) Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2008).

The Crucial Role of Polyatomic Anions in Molecular Architecture: Structural And Magnetic Versatility of Five Nickel(II) Complexes Derived from A N,N,O-Donor Schiff Base Ligand

A series of five Ni(II)-complexes containing the same tridentate Schiff base but different monoanionic ligands (N-3(-), NO3-, PhCOO- and NO2-)reveals that the competitive as well as the cooperative role of the monoanions and phenoxo group in bridging the metal ions play the key role in the variation of molecular architecture.

Facile strategies for the synthesis and crystallization of linear trinuclear nickel(II)-Schiff base, complexes with carboxylate bridges: Tuning of coordination geometry and magnetic properties

Three new linear trinuclear nickel(II) complexes, [Ni-3(salpen)(2)(OAc)(2)(H2O)(2)]center dot 4H(2)O (1) (OAc = acetate, CH3COO-), [Ni-3(salpen)(2)(OBz)(2)] (2) (OBz=benzoate, PhCOO-) and [Ni-3(salpen)(2)(OCn)(2)(CH3CN)(2)] (4) (OCn = cinnamate, PhCH=CHCOO-), H(2)salpen = tetradentate ligand, N,N'-bis(salicylidene)-1,3-pentanediamine have been synthesized and characterized structurally and magnetically. The choice of solvent for growing single crystal was made by inspecting the morphology of the initially obtained solids with the help of SEM study. The magnetic properties of a closely related complex, [Ni-3(salpen)(2)(OPh)(2)(EtOH)] (3) (OPh = phenyl acetate, PhCH2COO-) whose structure and solution properties have been reported recently, has also been studied here. The structural analyses reveal that both phenoxo and carboxylate bridging are present in all the complexes and the three Ni(II) atoms remain in linear disposition. Although the Schiff base ligand and the syn-syn bridging bidentate mode of the carboxylate group remain the same in complexes 1-4, the change of alkyl/aryl group of the carboxylates brings about systematic variations between six- and five-coordination in the geometry of the terminal Ni(II) centres of the trinuclear units. The steric demand as well as hydrophobic nature of the alkyl/aryl group of the carboxylate is found to play a crucial role in the tuning of the geometry. Variable-temperature (2-300 K) magnetic susceptibility measurements show that complexes 1-4 are antiferromagnetically coupled (J = -3.2(1), -4.6(1). -3.2(1) and -2.8(1) cm(-1) in 1-4, respectively). Calculations of the zero-field splitting parameter indicate that the values of D for complexes 1-4 are in the high range (D = +9.1(2), +14.2(2), +9.8(2) and +8.6(1) cm(-1) for 1-4, respectively). The highest D value of +14.2(2) and +9.8(2) cm(-1) for complexes 2 and 3, respectively, are consistent with the pentacoordinated geometry of the two terminal nickel(II) ions in 2 and one terminal nickel(II) ion in 3. (C) 2009 Elsevier Ltd. All rights reserved.

Use of a reduced Schiff-Base ligand to prepare novel chloro-bridged chains of rare Cu(II) trinuclear complexes with mixed azido/oxo and chloro/oxo bridges

Two mixed bridged one-dimensional (1D) polynuclear complexes, [Cu3L2(mu(1,1)-N-3)(2)(mu-Cl)Cl](n) (1) and {[Cu3L2(mu-Cl)(3)Cl]center dot 0.46CH(3)OH}(n), (2), have been synthesized using the tridentate reduced Schiff-base ligand HL (2-[(2-dimethylamino-ethylamino)-methyl]-phenol). The complexes have been characterized by X-ray structural analyses and variable-temperature magnetic susceptibility measurements. In both complexes the basic trinuclear angular units are joined together by weak chloro bridges to form a 1D chain. The trinuclear structure of 1 is composed of two terminal square planar [Cu(L)(mu(1,1)-N-3)] units connected by a central Cu(II) atom through bridging nitrogen atoms of end-on azido ligands and the phenoxo oxygen atom of the tridentate ligand. These four coordinating atoms along with a chloride ion form a distorted trigonal bipyramidal geometry around the central Cu(II). The structure of 2 is similar; the only difference being a Cl bridge replacing the mu(1,1)-N-3 bridge in the trinuclear unit. The magnetic properties of both trinuclear complexes can be very well reproduced with a simple linear symmetrical trimer model (H = JS(i)S(i+1)) with only one intracluster exchange coupling (J) including a weak intertrimer interaction (.j) reproduced with the molecular field approximation. This model provides very satisfactory fits for both complexes in the whole temperature range with the following parameters: g = 2.136(3), J = 93.9(3) cm(-1) and zj= -0.90(3) cm(-1) (z = 2) for 1 and g = 2.073(7), J = -44.9(4) cm(-1) and zJ = -1.26(6) cm(-1) (z = 2) for 2.

Mono-aqua-bridged dinuclear complexes of Cu(II) containing NNO donor Schiff base ligand: Hydrogen-bond-mediated exchange coupling

Two new mono-aqua-bridged dinuclear Cu(II) complexes of tridentate NNO Schiff bases, [Cu-2(mu-H2O)L-2(1)(H2O)(2)](BF4)(2)center dot 2H(2)O (1) and [Cu-2(mu-H2O)L-2(2)(H2O)(2)](BF4)(2)center dot 2H(2)O (2) where HL1 = 2-[1-(2-dimethylamino-ethylimino)-ethyl]-phenol and HL2 =2-[(2-dimethylamino-ethylimino)-methyl]-phenol were synthesized. Both the complexes were characterized by single-crystal X-ray diffraction analyses and variable-temperature magnetic measurements. For both the complexes each Cu(II) ion is in a square-pyramidal environment being bonded to three atoms from the tridentate NNO Schiff base and a terminal H2O molecule in the equatorial plane; a second H2O ligand acts as a bridge between the two Cu(II) centres through the axial positions. Hydrogen bonds between the terminal H2O ligand and the Schiff base of the adjacent centre complete the intra-dimer linkages. Variable-temperature (4-300 K) magnetic susceptibility measurement shows the presence of significant antiferromagnetic coupling for both the complexes (J = -12.2 and -12.5 cm(-1), respectively, for 1 and 2), mediated mainly through the intra-dimer H-bonds.

Synthesis and characterization of Cu(II) complexes of tetradentate and tridentate symmetrical Schiff base ligands involving o-phenelenediamine, salicylaldehyde and diacetylmonoxime

A mononuclear complex [CuL] (1), a binuclear complex [Cu2LCl2(H2O)] (2), a trinuclear complex [Cu3L2](ClO4)(2) (3) involving o-phenylenediamine and salicylaldehyde and another binuclear complex of a tridentate ligand (H2L1) [Cu2L (2) (1) ](CH3COO)(2) (4) involving o-phenylenediamine and diacetylmonoxime have been synthesized, where H2L = N,N'-o-phenylenebis(salicylideneimine) and H2L1 = 3-(2-aminophenylimino)butan-2-one oxime. All the complexes have been characterized by elemental analyses, spectral and magnetic studies. The binuclear complex (2) was characterized structurally where the two Cu(II) centers are connected via an oxygen-bridged arrangement.

Functional model for catecholase-like activity: A mechanistic approach with manganese(III) complexes of salen type Schiff base ligands

Three new Mn(III) complexes [MnL1(OOCH)(OH2)] (1), [MnL2(OH2)(2)][Mn2L22(NO2)(3)] (2) and [Mn2L21(NO2)(2)] (3) (where H2L1 = H(2)Me(2)Salen = 2,7-bis(2-hydroxyphenyl)-2,6-diazaocta-2,6-diene and H2L2 = H(2)Salpn = 1,7-bis(2-hydroxyphenyl)-2,6-diazahepta-1,6-diene) have been synthesized. X-ray crystal structure analysis reveals that 1 is a mononuclear species whereas 2 contains a mononuclear cationic and a dinuclear nitrite bridged (mu-1 kappa O:2 kappa O') anionic unit. Complex 3 is a phenoxido bridged dimer containing terminally coordinated nitrite. Complexes 1-3 show excellent catecholase-like activity with 3,5-di-tert-butylcatechol (3,5-DTBC) as the substrate. Kinetic measurements suggest that the rate of catechol oxidation follows saturation kinetics with respect to the substrate and first order kinetics with respect to the catalyst. Formation of bis(mu-oxo)dimanganese(III,III) as an intermediate during the course of reaction is identified from ESI-MS spectra. The characteristic six line EPR spectra of complex 2 in the presence of 3,5-DTBC supports the formation of manganese(II)-semiquinonate as an intermediate species during the catalytic oxidation of 3,5-DTBC.

Synthesis, crystal structures, magnetic properties and catecholase activity of double phenoxido-bridged penta-coordinated dinuclear nickel(II) complexes derived from reduced Schiff-base ligands: mechanistic inference of catecholase activity

Three double phenoxido-bridged dinuclear nickel(II) complexes, namely [Ni-2(L-1)(2)(NCS)(2)] (1), [Ni-2(L-2)(2)(NCS)(2)] (2), and [Ni-2(L-3)(2)(NCS)(2)] (3) have been synthesized using the reduced tridentate Schiff-base ligands 2-[1-(3-methylamino-propylamino)-ethyl]-phenol (HL1), 2-[1-(2-dimethylamino-ethylamino)-ethyl]-phenol (HL2), and 2-[1-(3-dimethylarnino-propylamino)-ethyl]-phenol (HL3), respectively. The coordination compounds have been characterized by X-ray structural analyses, magnetic-susceptibility measurements, and various spectroscopic methods. In all complexes, the nickel(II) ions are penta-coordinated in a square-pyramidal environment, which is severely distorted in the case of 1 (Addison parameter tau = 0.47) and 3 (tau = 0.29), while it is almost perfect for 2 (tau = 0.03). This arrangement leads to relatively strong antiferromagnetic interactions between the Ni(II) (S = 1) metal centers as mediated by double phenoxido bridges (with J values of -23.32 (1), -35.45 (2), and -34.02 (3) cm(3) K mol(-1), in the convention H = -2JS(1)S(2)). The catalytic activity of these Ni compounds has been investigated for the aerial oxidation of 3,5-di-tert-butylcatechol. Kinetic data analysis following Michaelis-Menten treatment reveals that the catecholase activity of the complexes is influenced by the flexibility of the ligand and also by the geometry around the metal ion. Electrospray ionization mass spectroscopy (ESI-MS) studies (in the positive mode) have been performed for all the coordination compounds in the presence of 3,5-DTBC to characterize potential complex-substrate intermediates. The mass-spectrometry data, corroborated by electron paramagnetic resonance (EPR) measurements, suggest that the metal centers are involved in the catecholase activity exhibited by the complexes.

Synthesis, crystal structure, and catecholase activity of three trinuclear heterometallic NiII2-MnII complexes derived from a salen-type Schiff base ligand

Three new trinuclear heterometallic nickel(II)manganese(II) complexes, [(NiL)2Mn(NCS)2] (1), [(NiL)2Mn(NCO)2] (2), and [{NiL(EtOH)}2Mn(NO2)2]center dot 2EtOH (3), have been synthesized by using [NiL] as the so-called ligand complex [where H2L = N,N'-bis(salicylidene)-1,3-propanediamine] and have been structurally characterized. Crystal structure analyses revealed that complexes 1 and 2 are angular trinuclear species, in which two terminal four-coordinate square planar [NiL] moieties are coordinated to a central MnII through double phenoxido bridges. The MnII is in a six-coordinate distorted octahedral environment that is bonded additionally to two mutually cis nitrogen atoms of terminal thiocyanate (in 1) and cyanate (in 2). In complex 3, in addition to the double phenoxo bridge, the two terminal NiII ions are linked to the central MnII by means of a nitrite bridge (1?N:2?O) that, together with a coordinated ethanol molecule, gives rise to an octahedral environment around the NiII ions and consequently the structure becomes linear. Catecholase activity of these three complexes was examined by using 3,5-di-tert-butylcatechol (3,5-DTBC) as the substrate. All three complexes mimic catecholase activity and the rate of catechol oxidation follows saturation kinetics with respect to the substrate and first-order kinetics with respect to the catalyst. The EPR spectra of the complexes exhibit characteristic six line spectra, which indicate the presence of high-spin octahedral MnII species in solution state. The ESI-MS positive spectrum of 1 in the presence of 3,5-DTBC has been recorded to investigate possible complexsubstrate intermediates.

Complexes of NiX2 (X=Cl− and NO3−) with a NNO donor Schiff base: anion dependent structural variations and spectroscopic behaviour

Two new nickel(11) complexes, [NiLL'(H2O)(2)Cl] (1) and [{NiLL'(H2O)](2)(mu-H)]NO3·H2O(2), have been synthesized using a tridentate Schiff base ligand, HL, 2-[(2-dimethylamino-ethylimino)-methyl]-phenol, along with Cl- or NO3(-) as an anionic co-ligand or counter anion (where L'H = salicylaldehyde). Both complexes have been characterized by X-ray crystallography. The structural analyses reveal that complex 1 is mononuclear whereas 2 is a hydrogen-bridged dinuclear complex. The Ni(II) ions possess a distorted octahedral geometry in both structures. Both complexes show negative solvatochromic behaviour with increasing donor number (DN) of the solvent. In more coordinating solvents, like DMSO or methanol, the colour of the solutions is green, whereas in less coordinating solvents, like dichloromethane (DCM) or acetonitrile, it is red.

Synthesis, crystal structures and magnetic properties of two bis(μ-phenoxido)dicopper(II) complexes derived from reduced Schiff base ligands

Two phenoxido bridged dinuclear Cu(II) complexes, [Cu-2(L-1)(2)(NCNCN)(2)] (1) and [Cu-2(L-2)(2)(NCNCN)(2)]center dot 2H(2)O (2) have been synthesized using the tridentate reduced Schiff-base ligands 2-[1-(2-dimethylamino-ethylamino)-ethyl]-phenol (HL1) and 2-[1-(3-methylamino-propylamino)-ethyl]-phenol (HL2), respectively. The complexes have been characterized by X-ray structural analyses and variable-temperature magnetic susceptibility measurements. Both the complexes present a diphenoxido bridging Cu2O2 core. The geometries around metal atoms are intermediate between trigonal bipyramid and square pyramid with the Addison parameters (tau) = 0.57 and 0.49 for 1 and 2, respectively. Within the core the Cu-O-Cu angles are 99.15 degrees and 103.51 degrees and average Cu-O bond distances are 2.036 and 1.978 angstrom for compounds 1 and 2, respectively. These differences have marked effect on the magnetic properties of two compounds. Although both are antiferromagnetically coupled, the coupling constants (J = -184.3 and -478.4 cm (1) for 1 and 2, respectively) differ appreciably.

Structural and magnetic studies of Schiff base complexes of nickel(ii) nitrite: change in crystalline state, ligand rearrangement and a very rare μ-nitrito-1κO:2κN:3κO′ bridging mode

Four new nickel(II) complexes, [Ni2L2(NO2)2]·CH2Cl2·C2H5OH, 2H2O (1), [Ni2L2(DMF)2(m-NO2)]ClO4·DMF (2a), [Ni2L2(DMF)2(m-NO2)]ClO4 (2b) and [Ni3L¢2(m3-NO2)2(CH2Cl2)]n·1.5H2O (3) where HL = 2-[(3-amino-propylimino)-methyl]-phenol, H2L¢ = 2-({3-[(2-hydroxy-benzylidene)-amino]-propylimino}-methyl)-phenol and DMF = N,N-dimethylformamide, have been synthesized starting with the precursor complex [NiL2]·2H2O, nickel(II) perchlorate and sodium nitrite and characterized structurally and magnetically. The structural analyses reveal that in all the complexes, NiII ions possess a distorted octahedral geometry. Complex 1 is a dinuclear di-m2-phenoxo bridged species in which nitrite ion acts as chelating co-ligand. Complexes 2a and 2b also consist of dinuclear entities, but in these two compounds a cis-(m-nitrito-1kO:2kN) bridge is present in addition to the di-m2-phenoxo bridge. The molecular structures of 2a and 2b are equivalent; they differ only in that 2a contains an additional solvated DMF molecule. Complex 3 is formed by ligand rearrangement and is a one-dimensional polymer in which double phenoxo as well as m-nitrito-1kO:2kN bridged trinuclear units are linked through a very rare m3-nitrito-1kO:2kN:3kO¢ bridge. Analysis of variable-temperature magnetic susceptibility data indicates that there is a global weak antiferromagnetic interaction between the nickel(II) ions in four complexes, with exchange parameters J of -5.26, -11.45, -10.66 and -5.99 cm-1 for 1, 2a, 2b and 3, respectively