Equilibrium and structural studies of silicon(IV) and aluminium(III) in aqueous solution—10. A potentiometric study of aluminium(III) pyrocatecholates and aluminium(III) hydroxo pyrocatecholates in 0.6 M Na(Cl)

Equilibria between aluminium(III), pyrocatechol (1,2-dihydroxybenzene, H₂L) and OH⁻ were studied in 0.6 M Na(Cl) medium at 25°C. The measurements were performed as emf titrations (glass electrode) within the limits 1.5 ≤ − log[H⁺] ≤ 9; 0.0005 ≤ B ≤ 0.015 M; 0.006 ≤ C ≤ 0.03 M and 2 ≤ C/B ≤ 30 (B and C stand for the total concentrations of aluminium(III) and pyrocatechol respectively). All data can be explained with a main series of complexes: A1L⁺, log β_−2,1,1 = − 6.337 ± 0.005; A1L₂⁻, log β_−4,1,2 = −15.44 ± 0.017 and A1L₃³⁻, log β_−6,1,3 = − 28.62 ± 0.024 together with two minor species: Al(OH)L₂²⁻, log β_−5,1,2 = − 23.45 ± 0.079 and Al₃(OH)₃L₃, log β_−9,3,3 = − 29.91 ± 0.066. Of the two, the latter probably is a type of average composition complex principally occurring at low C/B quotients. The first acidity constant for pyrocatechol as determined in separate experiments is log β_−1,0,1 = − 9.198 ± 0.001. The standard deviations given are 3σ(log β p,q,r). Data were analyzed with the least squares computer program LETAGROPVRID. In a model calculation using kaolinite as solid phase, we compared the complexation ability of this system with that of the system Al³⁺-OH⁻-salicylic acid, reported earlier in this series.     

Conformational study on dipeptides containing phenylalanine: A DFT approach

DFT calculations has been done applying 6-31G^* basis set on a series of dipeptides where the N-terminus position is fixed with phenylalanine and the C-terminus is varied with eight different amino acids. Different geometrical parameters (bond angle, bond length, geometry around -carbon atom) are thoroughly investigated to study the effect of amino acid sequence on dipeptide. Dihedral angle data analysis shows the deviation of amide plane from planarity, which is due to the combined effect of the steric hindrance of –R group and hydrogen bonding. The λ_max value for phenylalanine has been calculated, which shows good agreement with the experimental value. A rigid potential energy scan is performed on phenylalanine by rotating –CH₂Ph, –COOH and –NH₂ groups separately to get some idea about the conformational stability.     

Coordination geometry of chromium(VI) species. The first example of cis-bridging chromate ions in helically structured catena(μ-CrO4-O,O′)[Ni(HIm)3H2O]

Nickel(II) chromate complex with imidazole (HIm) was isolated from the [Ni²⁺–HIm–CrO₄²⁻] system in various experimental conditions, i.e. reagent molar ratios and nickel(II) salts. The catena(μ-CrO₄-O,O′)[Ni(HIm)₃H₂O] (1) crystallizes in monoclinic crystal system—space group P2₁/n with cell parameters: a=11.784(2), b=8.899(2), c=13.934(3) (Å), β=95.19(3) (°). The unit cell contains two independent helixes, left- and right-handed, stabilized by intrahelical and interhelical hydrogen bonds (HB) and π–π interactions. The cis coordination of the CrO₄²⁻ anions and the HB systems appeared to be the main determinants of the helical architecture. To the best of our knowledge the cis-chromate coordination was observed for the first time. The cis coordination causes the distortion of the nickel octahedron, which was analysed by 4 K single crystal electronic spectra with D_4h symmetry approximation (gaussian resolution and crystal field parameters). This symmetry was also confirmed with the polarised electronic spectra. The magnetic properties of the complex suggest the occurrence of weak intrachain antiferromagnetic interactions between the magnetic Ni^II center. The computational DFT studies of complex 1 assuming three possible isomers mer[(HIm)₃]–cis[(CrO₄²⁻)₂], mer–trans and fac–cis suggested that the main contribution to the stability of 1 might have interhelical and intrahelical hydrogen bonds.     

Structure cristalline et conformation en solution aqueuse de la carnosine (β-alanyl-L-histidine)

Carnosine (β-alanyl-L-histidine) is a biologically active molecule involved in muscular metabolism. It crystallises in the C; space group with a = 24.725 Å b = 5,427 Å c = 8,004 Å β = 100,2° (Z = 4)

In the crystal, acid and basic groups are engaged in hydrogen bonds whose strength is evaluated through IR frequencies. Molecular conformation in the solid state is defined by τ₁ = /t-177° τ₂ = −38° φ = −96° ψ = +131° χ₁ = 181° χ₂₁ = 62°

NMR study of carnosine in aqueous solution indicates that rotation about CH₂-CH₂ is free and that the other angles take the following values: Ø −150° or −90° and X₁ = 165° or 315°. Infrared and Raman spectra suggest that τ₂ undergoes small changes when going from crystal to solution while ψ is close to +150°.     

Kinetische und mechanistische untersuchungen von Übergangsmetall-komplex-reaktionen : III. Abhängigkeit des gleichgewichts der addition von tributylphosphan an pentacarbonyl(arylmethoxycarben)wolfram vom substituenten am ring

The reaction of pentacarbonyl(arylmethoxycarbene)tungsten, (CO)₅W[C(OCH₃(p-C₆H₄R)] [R = OCH₃ (a), CH₃ (b), H (c), Br (d), CF₃ (e)], with tributylphosphane at low temperatures results in a reversible addition of the phosphane to the carbene carbon atom. The addition—dissoziation equilibrium is not only dependent on the temperature but also to a strong degree on the nature of the substituent R. ΔG, ΔH and the equilibrium constant K increase in the series from R = OCH₃ to R = CF₃. With the exception of R = OCH₃ the substituents b to e form an isentropic class. For all substituents (a to e) a linear dependency from Jaffés σ-constants was observed for ΔH. Good linear correlation for the substituents b to e was also found for log K and σ as well as for log K and the CO-force constants k_cis and k_trans.     

E-2-benzylidenebenzocyclanones. II. IR and mass spectrometric investigations

A series of E-2-benzylideneindanones (a) -tetralones (b) and -benzosuberones (c) with OCH₃ (2–4), NO₂ (5–7) and F (8–10) substituents in ortho, meta or para position was studied by IR and mass spectrometry. The most important IR bands were assigned and stated correlations between some frequencies and the stereostructure or conjugation feature of the molecules investigated. IR spectra were also analyzed in order to find frequencies characteristic of the size of the alkanone ring. The mass spectrometric investigation aimed at determining fragmentation pathways and finding correlations between them and the ring size of the alkanone ring or the position of the substituents.     

Preparation, properties, and reactions of metal-containing heterocycles: Part CV. Synthesis and structure of polyoxadiphosphaplatinaferrocenophanes

A series of novel heterobimetallic crown ether-like polyoxadiphosphaplatinaferrocenophanes cis-[1,1′-Fc(CH₂O(CH₂CH₂O)_nCH₂CH₂PPh₂)₂]PtCl₂ (n=1–3) (4a–c) was synthesized in good yield by cyclization of the bis(phosphine) ligands 1,1′-Fc(CH₂O(CH₂CH₂O)_nCH₂CH₂PPh₂)₂ (n=1–3) (3a–c) and (PhCN)₂PtCl₂ under high dilution conditions in CH₂Cl₂. The bisphosphines 3a–c are obtained by reaction of the corresponding diols 1,1′-Fc(CH₂O(CH₂CH₂O)_nCH₂CH₂OH)₂ (n=1–3) (1a–c) with: (i) CH₃SO₂Cl in CH₂Cl₂ and (ii) LiPPh₂ in THF. Although the X-ray crystal structure of 4a shows that the cavity is large enough for the encapsulation of small metal cations, inclusion experiments of 4a–c with Group 1 cations, and Mg²⁺, or NH₄⁺ in solution applying NMR titration and cyclovoltammetric methods reveal no evidence for the formation of host–guest complexes for 4a,b. In the case of 4c only the addition of Na⁺ or K⁺ leads to an insignificant effect.     

X-ray study of the hetero ring flexibility in trans-5,6- trimethylene- and tetramethylene-5,6-dihydro 2-phenyl-[4H]-1,3-thiazines

The structures to two 1,3-thiazine derivatives differing only in the number of CH₂ groups in their trans fused hydrocarbon ring (_n = 3 for I and n = 4 for II) have been established by X-ray crystallography from diffractometer data. Crystals of I (trans-5,6- trimethylene-5,6-dihydro-2-phenyl-[4H] - 1,3-thiazine) are triclinic, space group P with a = 7.661(1), b = 8.282(1), c = 9.566(2) Å, = 91.75(1), β = 100.72(1), γ = 105.45(1)° Z = 2, D_c = 1.260 g cm^-3. Crystals of II (trans-5,6-tetramethylene-5,6-dihydro-2-phenyl [4H]-1,3-thiazine) are monoclinic, space group P2₁/c with a = 7.914(2), b = 19.362(13), c = 8.440(1) Å, β = 109.16(2)°C Z = 4, D_c = 1.258 g cm^-3. The structures determined by Patterson (I) and direct (II) methods were refined to R = 0.050 for 1330 reflections of I and R = 0.082 for 1012 reflections of II. The proper treatment of the positional disorder of the carbon atoms (C(5) and C(6)) forming the trans ring junction in I discovered two discrete conformations with a ratio of 1:2. The opposite chirality of atoms C(51) and C(52), and C(61) and C(62), indicates a simultaneous configurational disorder with a pattern of total disorder: A A . The puckering parameters of the hetero rings in the same enantiomers of molecules IA, IB and II indicate a connection between the conformers: ⁵E(II)→⁵H₆(IB)→E₆IA) via pseudorotation. Their relationship is discussed and compared with the conformational freedom of the analogous 1,3-oxazine derivatives.     

The vibrational state distributions in both products of the reaction: O(P) + NO2 → O2 + NO

A laser pulse-and-probe method has been used to determine the nascent vibrational populations in NO(v=0–4) and O₂(v=6–11) formed in the thermal reaction: O(³P) + NO₂ → O₂(v) + NO(v). A frequency-tripled Nd: YAG laser is used to photolyse NO₂, diluted tenfold in Ar, and laser-induced fluorescence spectroscopy in the NO A ²Σ⁺-X ²Π and O₂ B ³Σ⁻_u -X ³Σ⁻_g electronic band system is used both to follow the kinetics of individual vibrational states and to determine the nascent vibrational distributions. The majority of the NO product is formed in v = 0 and the average vibrational yield is ≈ 4.6%. The O₂ populations fall monotonically from v = 6 to 11 in a distribution close to what is expected on prior grounds. Based on a surprisal analysis, the average vibrational energy yield in O₂ is ≈ 26%. The nature of the reaction dynamics is discussed.     

Studies on organolanthanide complexes : LXIII. Synthesis, spectroscopic and X-ray crystallographic characterization of new early organolanthanide, organoyttrium hydride and organoholmium hydroxide complexes

Organolanthanide chloride complexes [(CH₃OCH₂CH₂C₅H₄)₂Ln(μ-Cl)]₂ (Ln = La, Pr, Ho and Y) react with excess NaH in THF at 45°C to give the dimeric hydride complexes [(CH₃OCH₂CH₂C₅H₄)₂Ln(μ-H)]₂, which have been characterized by IR, ¹H NMR, MS and XPS spectroscopy, elemental analyses and X-ray crystallography. [(CH₃OCH₂CH₂C₅H₄)₂Y(μ-H)]₂ crystallizes from THF/n-hexane at −30°C, in the triclinic space group P1 with a = 8.795(2) Å, b = 11.040(1) Å, c = 16.602(2) Å, = 93.73(1)°, β = 91.82(1)°, γ = 94.21(1)°, D_c = 1.393 gcm⁻³ for Z = 2 dimers. However, crystals of [(CH₃OCH₂CH₂C₅H₄)₂Ho(μ-OH)]₂ were obtained by recrystallization of holmium hydride in THF/n-hexane at −30°C, in the orthorhombic space group Pbca with a = 11.217(2) Å, b = 15.865(7) Å, c = 17.608(4) Å, D_c = 1.816 gcm⁻³ for Z = 4 dimers. In the complexes of yttrium and holmium, each Ln atom of the dimers is coordinated by two substituted cyclopentadienyl ligands, one oxygen atom and two hydrogen atoms (for the Y atom) or two hydroxyl groups (for the Ho atom) to form a distorted trigonal bipyramid if the C(η⁵)-bonded cyclopentadienyl is regarded as occupying a single polyhedral vertex.     

Dynamic behaviour and X-ray analysis of chiral η-allylpalladium complexes. II

The DANTE technique and NOESY two-dimensional method have been employed to observe the isomerization of the chiral cationic complex [Pd(η³-CH₂CMeCH₂(P-P′)]⁺ (1a), where P-P′ = the chiral chelating ligand (S)(N-diphenylphosphino)(2-diphenylphosphinoxymethyl)pyrrolidine. The rate constant was found to be 0.5 s⁻¹ in CHCl₃ at 295 K and 1.50 s⁻¹ in the presence of added free ligand. In the latter case the epimerization proceeds by a π-σ-π mechanism via the intermediacy of a primary η¹-allylpalladium complex. Although the intermediate was not detected, the NMR findings reveal that it has the allylic terminus η¹-bonded to palladium. The structure of 1a in its PF₆⁻ salt has been determined. The compound crystallizes in the orthorhombic space group P2₁2₁2₁ with a 10.029(4) b 19.203(8) c 36.115(6) Å, Z = 8, R = 0.0572 and R_w = 0.0712 for 3716 observed reflections with I > 3σ(I).     

The organic ligands as template: the synthesis, structures and properties of a series of the layered structure rare-earth coordination polymers

A series of new 2D-layered structural rare-earth coordination polymers with the general formal [Ln(C₈H₄O₅)(H₂O)₅]·(H₂O)·(C₈H₄O₅)_1/2 (Ln=Eu for (1); Gd for (2); Tb for (3); Dy for (4); and Er for (5)) have been yielded by hydrothermal synthesis. The coordination polymers crystallize in monoclinic space group C/2c with a=19.838(16), b=10.529(8), c=17.752(14) Å, β=107.503(14)° for (1), with a=19.823(7), b=10.552(4), c=17.762(6) Å, β=107.443(6)° for (2), with a=19.770(4), b=10.519(2), c=17.698(4) Å, β=107.52(3)° for (3), with a=19.632(2), b=10.492(2), c=17.617(3) Å, β=107.470(12)° for (4), with a=19.648(7), b=10.480(3), c=17.598(6) Å, β=107.502(6)° for (5), respectively. And the metal ions (Ln³⁺) are located in nine-member coordination environment. The carboxyl groups from 5-hydroxyisophthalate chelate the metal ions to form 1D helical cation chains. It is interesting that these helical cation chains are arranged to form 2D anion–cation layers by the uncoordinated ligands' anions as template. And the luminescence properties of the rare-earth ions are studied in the paper.     

Equilibrium diagram of KPO3–Y(PO3)3 system, chemical preparation and characterization of KY(PO3)4

Microdifferential thermal analysis (μ-DTA), X-ray diffraction (XRD) and infrared (IR) spectroscopy were used for the first time to investigate the liquidus and solidus relations in the KPO₃–Y(PO₃)₃ system. The only compound observed within the system was KY(PO₃)₄ melting incongruently at 1033 K. An eutectic appears at 13.5 mol% Y(PO₃)₃ at 935 K, the peritectic occurs at 1033 K and the phase transition for potassium polyphosphate KPO₃ was observed at 725 K. Three monoclinic allotropic phases of the single crystals were obtained. KY(PO₃)₄ polyphosphate has the P2₁ space group with lattice parameters: a=7.183(4) Å, b=8.351(6) Å, c=7.983(3) Å, β=91.75(3)° and Z=2 is isostructural with KNd(PO₃)₄. The second allotropic form of KY(PO₃)₄ belongs to the P2₁/n space group with lattice parameters: a=10.835(3) Å, b=9.003(2) Å, c=10.314(1) Å, β=106.09(7)° and Z=4 and is isostructural with TlNd(PO₃)₄. The IR absorption spectra of the two forms show a chain polyphosphates structure. The last modification of KYP₄O₁₂ crystallizes in the C2/c space group with lattice parameters: a=7.825(3) Å, b=12.537(4) Å, c=10.584(2) Å, β=110.22(7)° and Z=4 is isostructural with RbNdP₄O₁₂ and contains cyclic anions. The methods of chemical preparations, the determination of crystallographic data and IR spectra for these compounds are reported.     

Influence of operating conditions on the retention of phosphate in water by nanofiltration

The objective of this study was to investigate the retention of phosphate anions, H₂PO₄⁻ and HPO₄²⁻, by nanofiltration. The first part of this study deals with the characterisation of the NF200 membrane used in permeation experiments with aqueous solutions of neutral organic and charged inorganic solutes. In the second part the effects of feed pressure, ionic strength, concentration and pH on the retention of phosphate anions were investigated. Results show that the membrane is negatively charged, its pore radius is around 0.5 nm and the retention order for the salts tested was R(Na₂SO₄) > R(NaCl) > R(CaCl₂). The retentions of phosphate anions are in the order of 85% for H₂PO₄⁻ and 96% for HPO₄²⁻. They are relatively high when compared to retentions of other anions with the same charge. The retentions of phosphate anions, particularly the monovalent species, depend on the chemical parameters (feed concentration, ionic strength, and pH) and applied pressure. The experimental data were analysed using the Speigler–Kedem model and the transport parameters, i.e., the reflection coefficient (σ) and solute permeability (P_s) have been determined.     

Oxygen abstraction from tetrahydrofuran by molybdenum-iodide complexes. X-ray molecular structure of [Mo2(μ-O)(μ-I)(μ-O2CCH3)I2(THF)4][MoOI4(THF)] (THF = tetrahydrofuran)

The interaction between Mo₂(O₂CCH₃)₄, Me₃SiI and I₂ in THF resulted in oxygen abstraction from the solvent and formation of [Mo₂(μ-O)(μ-I)(μ-O₂CCH₃) I₂(THF)₄]⁺[MoOI₄(THF)]⁻ and I---(CH₂)₄---I. The molybdenum complex has been characterized by X-ray diffractometry. Crystal data: triclinic, space group P , a = 13.827(3) Å; b = 15.803(7) Å; c = 9.950(3) Å; = 93.34(4)°; β = 102.40(2)°; γ = 90.09(2)°; V = 2120(2) Å₃; Z = 2; d_calc = 2.559 g cm⁻³; R = 0.0476 (R_w = 0.0613) for 370 parameters and 3938 data with F₀²> 3σ(F₀²). The metal-metal distance in the cation is 2.527(2) Å and indicates a strong interaction. The magnetic behavior is consistent with the assignment of one unpaired electron to the Mo₂⁷⁺ core of the cation and one to the d¹ Mo(V) center of the anion. The interaction between Mo(CO)₆ and I₂ in THF also results in the formation of 1,4-diiodobutane.     

Structural characteristics of pyrocarbon-fumed silica

Two series of pyrocarbon/fumed silica (CS) samples at different carbon concentrations C_C=0.5–64 wt.% (first series, CSI) and 2.6–53 wt.% (second series, CSII) synthesised by means of pyrolysis of CH₂Cl₂ at fumed silica substrate (S_BET=297 (CSI) and 232 (CSII) m² g⁻¹) under slightly different conditions were studied by using TEM, FTIR-PAS, DTG, and nitrogen adsorption–desorption methods. On methylene chloride carbonisation, disordered carbon deposits can form mainly in the inter-particle volume of secondary particles (aggregates of primary particles and agglomerates of aggregates) covering the surfaces of primary silica particles; therefore, marked reduction of the pore (gaps between primary particles) volume and the specific surface area is observed with increasing C_C. Estimation of distributions of the pore f_SCD(R_p) and particle f(a) sizes using a self-consistent method with binary regularisation with respect to both f_SCD(R_p) and f(a) shows that the average size of particles increases (silica particles are covered by pyrocarbon) and individual pyrocarbon particles (up to 50 nm according to TEM) also appear. Structural parameters of carbosils are characterised by nonlinear changes with increasing carbonisation time. Surface functionalities on CS samples correspond to aromatic and twinned CC bonds with contribution of oxygen-containing groups.     

Ferroelectric liquid crystals induced by dopants with axially chiral 2,2'-spirobiindan-1,1'-dione cores: diether vs. diester side-chains

A series of axially chiral 5,5'- and 6,6'-dialkanoyloxy-2,2'-spirobiindan-1,1'-dione dopants, (R)-2 and (R)-4a-4c were synthesized in optically pure form and their ferroelectric polarization powers, δ_p, measured in four liquid crystal hosts with isotropic (I)-nematic (N)-smectic A (SmA)-smectic C (SmC) phase sequences. The results show that the sign of polarization P _S induced by (R)-2 and (R)-4a-4c follows the same trend as that previously reported for the 5,5'- and 6,6'-diheptyloxy-2,2'-spirobiindan-1,1'-dione dopants, (R)-1 and (R)-3. The polarization induced by (R)-2 in the host DFT is below detection limits, and the sign of P _S was found to invert as a function of temperature at mole fractions as low as 0.01. On the other hand, the polarization power of the 6,6'-diheptanoyloxy dopant (R)-4b in the host NCB76 is -1449 nC cm^-2, the fourth highest value reported so far, and more than three times the δ_p value of the 5,5'-diheptanoyloxy analogue (R)-2 in that host (+474 nC cm^-2). Results of ²H NMR experiments suggest that (R)-4b exerts stronger local perturbations in NCB76 than (R)-2, and that these perturbations may be chiral in nature.     

The electrostatic potential at atomic sites as a reactivity index in the hydrogen bond formation

The paper reviews results from computational studies by molecular orbital and density functional theories on several series of hydrogen bonded complexes. These studies aim at quantifying the reactivity of molecules for the complexation process. Excellent linear relationships are found between the electrostatic potential values at the sites of the electron donor and electron accepting atoms and the energy of hydrogen bond formation (ΔE). The series studied are: (a) complexes of R–CHO and R–CN molecules with hydrogen fluoride; (b) complexes of mono-substituted acetylene derivatives with ammonia; (c) (HCN)_n hydrogen bonded cluster for n=2–7. All 22 studied complexes of carbonyl and nitrile compounds with hydrogen fluoride fall in the same dependence between the energy of hydrogen bond formation and the electrostatic potential at the atomic site of the carbonyl oxygen and nitrile nitrogen atoms, with linear regression correlation coefficient r=0.979. In the case of complexes of mono-substituted acetylene and diacetylene derivatives with NH₃, the correlation coefficient for the dependence between the electrostatic potential at the acidic hydrogen atom and ΔE equals 0.996. For the series of hydrogen bonded (HCN)_n clusters, the correlation coefficient for the relationship between the electrostatic potential at the end nitrogen atom and ΔE is r=0.9996. Similarly, the analogous relationship with the electrostatic potential at the end hydrogen atom has a regression coefficient equal to 0.9994. The dependencies found are theoretically substantiated by applying the Morokuma energy decomposition scheme. The results show that the molecular electrostatic potential at atomic sites can be successfully used to predict the ability of molecules to form hydrogen bonds.     

Hydrogenmaleato bridged supramolecular double chains via π–π stacking interactions: syntheses, crystal structures and magnetic properties of ∞[Cu(phen)X(HL)2/2] with X=Cl (1), NO3 (2) and H2L=maleic acid

Two novel hydrogen maleato (HL) bridged Cu(II) complexes _∞¹[Cu(phen)Cl(HL)_2/2] 1 and _∞¹[Cu(phen)(NO₃)(HL)_2/2] 2 were obtained from reactions of 1,10-phenanthroline, maleic acid with CuCl₂·2H₂O and Cu(NO₃)₂·3H₂O, respectively, in CH₃OH/H₂O (1:1 v/v) at pH=2.0 and the crystal structures were determined by single crystal X-ray diffraction methods. Both complexes crystallize isostructurally in the monoclinic space group P2₁/n with cell dimensions: 1 a=8.639(2) Å, b=15.614(3) Å, c=11.326(2) Å, β=94.67(3)°, Z=4, D_calc=1.720 g/cm³ and 2 a=8.544(1) Å, b=15.517(2) Å, c=12.160(1) Å, β=90.84(8)°, Z=4, D_calc=1.734 g/cm³. In both complexes, the square pyramidally coordinated Cu atoms are bridged by hydrogen maleato ligands into 1D chains with the coordinating phen ligands parallel on one side. Interdigitation of the chelating phen ligands of two neighbouring chains via π–π stacking interactions forms supramolecular double chains, which are then arranged in the crystal structures according to pseudo 1D close packing patterns. Both complexes exhibit similar paramagnetic behavior obeying Curie–Weiss laws χ_m(T−θ)=0.414 cm³ mol⁻¹ K with the Weiss constants θ=−1.45, −1.0 K for 1 and 2, respectively.