Monomeric copper(II) and nickel(II) complexes of N,N,N′,N′-tetrakis [(2-benzimidazolyl)methyl]-1,2-cyclohexanediamine], a chelating ligand containing imidazole groups

Summary Cu^II and Ni^II coordination compounds with N,N,N,N-tetrakis[(2-benzimidazolyl)methyl]-1,2-cyclohexanediamine (CDTB) have been prepared and characterized. The crystal structure of [Cu(CDTB)](ClO₄)₂ has been determined. The geometry around the Cu atom is highly irregular and can best be described as a cis-distorted octahedron, with four short CuN bond distances of 1.988(3) Å and 2.028(3) Å, and two very long CuN bond lengths of 2.543(4) A. The cis NCuN chelate angles in the complex range from 68.8(2) for N(1)CuN(1) to 141.03° for N(4)CuN(1). The cyclic voltammogram of the complex shows a fully reversible one-electron redox wave at E _1/2 = 0.162V versus standard calomel electrode, corresponding to the Cu^I/II redox couple. The structure of [Ni(CDTB)](NO₃)₂ ·EtOH has also been determined. The geometry around the Ni atom in this compound can be described as distorted octahedral, with N(4), N(4), N(1), N(1) as the ligating atoms in the basal plane, with cis chelate angles ranging from 79.37(10) to 120.9(2)° with the trans N(2)NiN(2) angle at 175.1(2)°. The structural differences in these two compounds are undoubtedly electronic rather than steric.     

Influence of heme periphery on the electronic structure and Mössbauer parameters of hemoglobin

For the five-coordinated complexes of ferroprotoporphynynn with imidazole, a quantum-chemical analysis of the electronic structure and Mossbauer spectral parameters has been canied out. Peripheral substituents (CH3, Cf13, C₂H₄COOH) were introduced into the porphynin macrocycle to model the real chemical structure of protopo'phynynn in the heme group of desoxyhemoglobin. The calculations have shown that near the occupation border in the complaes there are MO which are due to the -systems of the CH= CM₂ and CH₂CH₂COOH substituents. The orientalion of the vinyl fragments has a considerable effect on the populations of the Fe d-orbitals and the quadrupole splitting E_Q for the⁵B₁ and⁵B₂ terns.Institute of Biophysics, Ministry of Health, Russian Federation. Translated fromZhurnal Strukturmoi Khimii, Vol. 34, No. 5, pp. 90–93, September–October, 1993.Translated by L. Smolina     

Polymeric membrane sodium-selective electrodes based on calix[4]arene ionophores

Six kinds of tetra alkylester type calix[4]arene derivatives, (R₁=R₂=CH₃1, C₂H₅2, C₃H₇3,n-C₄H₉4,t-C₄H₉5,n-C₁₀H₂₁6), a diethyl-didecyl mixed ester type (R₁=C₂H₅, R₂ =C₁₀H₂₁7), and three kinds of lower rim bridged types (R₁=C₂H₅, R₂–R₂=(CH₂)₁₀8, (CH₂)₁₂9, (CH₂)₂(OCH₂CH₂)₃10) were characterized by electrochemical measurement to elucidate the effect of the length of the alkyl group of alkoxycarbonyl substituents on Na⁺ selectivity. To obtain excellent Na⁺ selective ionophores, introduction of short chain alkyl groups rather than long chain ones, such as a decyl group, and maintenance of sufficient solubility of the calix[4]arene derivatives in the membrane solvent are required concurrently. Among the calix[4]arenes tested, 25,26,27,28-tetrakis[(ethoxycarbonyl)methoxy]-p-tert-butylcalix[4]arene2, and the diethyl-didecyl mixed ester type derivative7 are the best ionophores for a Na⁺ selective electrode. On the other hand, sodium selectivity of the bridged type derivative9 is comparable or even superior to that of the known bis(12-crown-4).This paper is dedicated to the commemorative issue on the 50th anniversary of calixarenes.     

Concerning the absorption and emission properties of phenanthro[1,10,9,8,o,p,q,r,a]perylene-7,14-dione

Summary In contrast to hitherto published data, phenanthro[1,10,9,8,o,p,q,r,a]perylene-7,14-dione, the fundamental chromophoric system of hypericin type compounds, exhibits an absorption with a long wavelength band at 423 nm in aprotic solvents like dimethylsulfoxide (7000). Its fluorescence in these solvents is below the detection limit. In protic solvents like methanol, the long wavelength absorption is bathochromically shifted to 546 nm, and a fluorescence at 565 nm is observed. This behavior was interpreted from the reversal ofn – * and – * transitions. The data have not been recorded yet due to the very low solubility of this compound. Its monoprotonation in ground and excited states is characterized bypK _a andpK* _a values of –6 and 2; diprotonation occurs at apK _a=–7.

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Absorptions- und Emissions-Eigenschaften von Phenanthro[1,10,9,8,o,p,q,r,a]perylen-7,14-dion (Kurze Mitt.)

Zusammenfassung Im Gegensatz zu bislang publizierten Daten zeigt Phenanthro[1,10,9,8,o,p,q,r,a]perylen-7,14-dion, das fundamentale chromophore System der Hypericintyp-Verbindungen, in aprotischen Lösungsmitteln wie Dimethylsulfoxid eine Absorption mit einer langwelligen Bande bei 423 nm (7000). In diesen Lösungsmitteln ist Fluoreszenz nicht nachweisbar. In protischen Lösungsmitteln wie Methanol wird die langwellige Bande bathochrom verschoben (546 nm) und bei 565 nm tritt Fluoreszenz auf. Dieses Verhalten wurde mit der Umkehr in der Reihenfolge vonn – * und – * Übergängen interpretiert. Die Daten wurden wegen der extremen Schwerlöslichkeit dieser Verbindung bislang nicht erhalten. Die Monoprotonierung im Grund- und Anregungszustand ist durchpK _a- undpK* _a -Werte von –6 und 2 charakterisiert; die Diprotonierung tritt beipK _a=–7 ein.

     

The deprotonation and protonation equilibria of a hypericin derivative in aqueous solution

Summary A hypericin derivative ,'-appended at the methyl groups with two polyethylene glycol moieties (about 23 units long) and capped with acetyl groups was synthesized starting from emodin. This derivative proved to be soluble in water and was investigated by means of spectrophotometric titrations and electrophoresis experiments. Deprotonation at thebay-region hydroxyl group was observed atpK _a=1.6. This was followed by a second deprotonation step of aperi-hydroxyl group at apK _a value of 9.4. This derivative could be protonated at the carbonyl group characterized by apK _a value of –5.7. FrompK _a determinations in water-ethanol mixtures the correspondingpK _a values of hypericin itself determined in such mixtures were extrapolated to the aqueous phase. This resulted in estimatedpK _a values of 1.8, 9.2, and –6.

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Deprotonierungs- und Protonierungsgleichgewichte eines Hypericinderivates in wäßriger Lösung

Zusammenfassung Ein an den Methylgruppen von Hypericin mit endständig acetylierten Polyethylenglykolketten (ungefähr 23 Einheiten lang) ,'-disubstituiertes Derivat wurde ausgehend von Emodin synthetisiert. Dieses Derivat ist wasserlöslich, und es wurde mit Hilfe von spektrophotometrischen Titrationen und Elektrophorese untersucht. Die Deprotonierung derbay-Hydroxylgruppe erfolgt beipK _a=1.6. Diese wird von einem zweiten Deprotonierungsschritt an einerperi-Hydroxylgruppe bei einempK _a-Wert von 9.4 gefolgt. Dieses Derivat konnte an der Carbonylgruppe protoniert werden, was durch einenpK _a-Wert von –5.7 charakterisiert ist. Ausgehend vonpK _a-Messungen in Wasser-Ethanol-Mischungen wurden die entsprechendenpK _a-Werte auch für das Hypericin selbst in wäßriger Phase extrapoliert. Dies führte zu geschätztenpK _a-Werten von 1.8, 9.2 und –6.

     

Factors affecting adsorption of organic solutes on cellulose acetate in an aqueous solution system

Summary The adsorption properties of esters, aldehydes, ethers and amides on cellulose acetate, which is commonly used as a reverse osmosis membrane material, in an aqueous solution system were measured by high-performance liquid chromatography. The adsorption property was characterized with the specific retention volume. For a noncyclic homologous series the logarithm of the specific retention volume was linearly correlated with the logarithm of the partition coefficient between 1-octanol and water. The fact that the slopes of these regression lines are almost identical confirms that the dominant effect on adsorption is the hydrophobic interaction between cellulose acetate and the solute molecule. The intercept represents the effect of the polar groups on adsorption. The effect of the polar group decreases as follows: C(O)O, CO, HCON > CH₃CON > OH, O.     

Studies in isodielectric media. Part IV. Thermodynamics of protonation ofp-nitroaniline in ethylene glycol—Diethylene glycol mixtures at 25°C

The thermodynamic ionisation constant ofp-nitroanilinium ion was determined spectrophotometrically at 25°C in the near isodielectric mixtures of ethylene glycol (EG) and diethylene glycol (DEG) over the complete range of solvent compositions. thepK of the ion decreases continuously with the addition of diethylene glycol, passes through a minimum around 80 wt% of the same solvent and then increases. The variation of pK (pK _{mixed solvent}–pK _EG) with solvent composition was analyzed in terms of the changes inGibbs energies of transfer of the different species involved in the ionisation process in these mixtures.

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Untersuchungen in isodielektrischen Medien, 4. Mitt.: Thermodynamik der Protonierung von p-Nitroanilin in Ethylenglykol—Diethylenglykol-Mischungen bei 25°C

Zusammenfassung Die thermodynamischen Ionisierungskonstanten desp-Niroanilinium-Ions wurde spektrophotometrisch bei 25°C in den annähernd isodielektrischen Mischungen von Ethylenglykol—Diethylenglykol (EG—DEG) über den gesamten Bereich der Lösungsmittelzusammensetzungen gemessen. DerpK des Ions sinkt kontinuierlich mit der Zugabe von Diethylenglykol und geht bei etwa 80 Gew.%DEG durch ein Minimum. Die Änderung von pK (pK _{Lösungsm.-Gemisch}-pK _EG) mit der Lösungsmittelzusammensetzung wird als Wechsel in denGibbs-Energien des Transfers der verschiedenen in den Ionisierungsprozess verwickelten Spezies erklärt.

     

Effects of ionization on the phase behavior of poly(<Emphasis Type="Italic">N</Emphasis>-isopropylacrylamide-co-acrylic acid) and poly(<Emphasis Type="Italic">N</Emphasis>,<Emphasis Type="Italic">N</Emphasis>-diethylacrylamide-co-acrylic acid) in water

Phase transitions of poly(N-isopropylacrylamide-co-acrylic acid) (PiPA-AA) and poly(N,N- diethylacrylamide-co-acrylic acid) (PdEA-AA) in water have been investigated by means of turbidimetry, Fourier transform infrared (FTIR) spectroscopy and differential scanning calorimetry (DSC). The phase transition temperatures (T_p) of these copolymers increase with the degree of ionization () of the acrylic acid (AA) units, which in turn is dependent on the pH of the solutions. Apparent values of pK_a for the AA units, determined from the pH dependencies of T_p, are 4.7 and 5.4 for PiPA-AA and PdEA-AA, respectively. Differences between T_p for PiPA-AA and T_p for PiPA homopolymer (T_p) are +1.5 and –0.2 °C/mol% of AA at =1 and 0, respectively. The values of T_p for PdEA-AA are +2.6 (ionic) and –0.5 (nonionic)°C/mol%, indicating that the incorporated AA units have a larger effect on PdEA than on PiPA. DSC measurements performed with each of these copolymers at different pH values show a linear relationship between T_p and the enthalpy of transition (H). IR measurements of PiPA-AA show that the profiles of IR bands from both iPA and AA units exhibit critical changes at T_p of the copolymer. Heating the solution above T_p leads to shifts of the amide II, C–H stretch, and C–H bend bands from the iPA units toward lower wavenumbers, as well as a shift of the amide I band from the iPA units toward higher wavenumbers. A decrease in the intensity of the symmetric C=O stretch IR band from carboxylate anions (1560 cm^–1), and an increase in the intensity of the C=O stretch band from COOH groups (1705 cm^–1) suggest that a partial protonation of the carboxylate groups (COO^–+H⁺COOH) takes place upon the phase transition.     

Preparation of BaCe0.8Gd0.2O3−δ by the citrate method and its application in the synthesis of ammonia at atmospheric pressure

BaCe_0.8Gd_0.2O_3– is a kind of high-temperature proton conductor. A precursor of BaCe_0.8Gd_0.2O_3– solid electrolyte was synthesized by the citrate method and characterized by thermal analysis (thermogravimetric analysis–differential thermal analysis), X-ray diffraction and scanning electron microscopy. Using the sintered samples as a solid electrolyte and silver–palladium alloy as electrodes, we synthesized ammonia from nitrogen and hydrogen at atmospheric pressure in the solid-state proton-conducting-cell reactor. The rate of evolution of ammonia was up to 3.09×10^–9 mol s^–1 cm^–2.     

Mean amplitudes of vibration for PMo12O40 3− and its fragments

Mean amplitudes of vibration () are calculated for all 80 distance types in PMo₁₂O₄₀ ^3–. The values are discussed and some of them compared with the corresponding values calculated for, five different fragments of the structure. Reasonable values (<0.12 Å at 298 K) are found even for extremely long distances, e.g. 0.078 Å at 298 K for the longest oxygen-oxygen distance (10.4 Å). The values for bonded distances as well as a number of nonbonded distances have comparable magnitudes in the fragments and the whole structure; in other cases the fragment values are substantially higher.

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Mittlere Schwingungsamplituden für PMo₁₂O₄₀ ^3– und Fragmente

Zusammenfassung Mittlere Schwingungsamplituden () für alle 80 Typen von Abständen in PMo₁₂O₄₀ ^3– wurden berechnet. Die Werte werden diskutiert und einige werden mit denen von fünf verschiedenen Fragmenten der untersuchten Struktur verglichen. Es wurden auch für extrem große Distanzen plausible -Werte (<0,12 Å bei 298 K) gefunden (z. B. 0,078 Å bei 298 K für die größte, O–O-Distanz 10,4 Å). Die, -Werte für Bindungslängen und auch für einige Abstände von nicht aneinander gebundenen Atomen weisen in den Fragmenten und in der Gesamtstruktur vergleichbare Größe auf; in anderen Fällen sind die Fragment-Werte allerdings bedeutend höher.

     

Thermodynamics of the Second Dissociation Constant of N-tris[Hydroxymethyl]-4-amino-butanesulfonic Acid (TABS) from 5 to 55°C

N-tris[Hydroxymethyl]-4-aminobutanesulfonic acid (TABS) has been investigated for the determination of the values of the second dissociation constant, pK ₂, in water at 12 temperatures in the range 5–55°C, including 37°C. This zwitterionic compound is useful as a secondary pH standard in the range of pH (7–9) for physiological applications. The electromotive force (emf) measurements have been carried out using a hydrogen gas electrode and a silver–silver chloride electrode. The values of pK ₂ are fitted as a function of temperature with the following results: pK ₂ = 1671.305/T+14.8737–2.04383 ln T, where T is the thermodynamic temperature in Kelvins. The experimental values of pK ₂ are 8.834 ± 0.0005 and 8.539 ± 0.0004 at 25 and 37°C, respectively. The related thermodynamic quantities, G°, H°, S°, and C _p ° characterizing the dissociation process have been derived from the pK ₂ and its temperature coefficients.     

Spectrophotometric and potentiometric determination of acidic constants of oxo-phenyl pyridinium monoxime and dioxime

The UV absorption spectra of 1-(1-hydroxyimino-2-oxo-2-phenyl) pyridinium chloride (compound I) and 1-(1-hydroxyimino-2-oxo-2-phenyl)-4-hydroxyiminomethyl pyridinium chloride (compound II) in water solution at differentpH values have been measured. The spectral changes, with changingpH, in aqueous solutions are attributed to the dissociation of individual functional groups of the compounds. The mixed acidic constants (pKa) of the investigated monoxime and dioxime, have been determined spectrophotometrically in the series ofBritton-Robinson's buffer solutions in thepH range 3.0–5.19 and 7.70–9.90 (t=25±0.5°C,I=0.2). The followingpKa values have been obtained for monoximepKa ₁=4.30 and for dioximepKa ₁=4.28,pKa ₂=8.36.Thermodynamic acidic constants (pKa) have been determined on the basis of potentiometric titrations and they have been found to bepKa ₁=4.32 for compound I andpKa ₁=4.27,pKa ₂=8.51 for compound II. The values obtained by transferringpKa intopKa are in good agreement with the values obtained potentiometrically.

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Spektrophotometrische und potentiometrische Bestimmung der Aciditätskonstanten von Oxo-Phenyl-Pyridinium-Monooxim und -Dioxim

Zusammenfassung Die UV-Absorptionsspektren von 1-(1-Hydroxyimino-2-oxo-2-phenyl)-pyridiniumchlorid (Verbindung I) und 1-(1-Hydroxyimino-2-oxo-2-phenyl)-4-hydroxyiminomethylpyridiniumchlorid (Verbindung II) wurden in wäßrigen Lösungen bei verschiedenenpH-Werten aufgenommen. Die Änderungen in den Spektren, die in wäßrigen Lösungen mit derpH-Änderung entstehen, können der Dissoziation der einzelnen funktionellen Gruppen der untersuchten Verbindungen zugeschrieben werden. Die Mischaciditätskonstanten (pKa) des untersuchten Monooxims und Dioxims wurden spektrophotometrisch in einer Reihe vonBritton-Robinson-Pufferlösungen inpH-Intervallen 3.0–5.19 und 7.70–9.90 (t=25±0.5°C;I=0.2) bestimmt: für das MonooximpKa ₁=4.30 und für DioximpKa ₁=4.28 undpKa ₂=8.36. Die thermodynamischen Aciditätskonstanten (pKa) wurden aufgrund der potentiometrischen Titration berechnet:pKa ₁=4.32 für die Verbindung I undpKa ₁=4.27 undpKa ₂=8.51 für die Verbindung II. Die durch ÜbertragungpKa inpKa erhaltenen Werte sind mit den über die potentiometrische Methode erhaltenen Werten in guter Übereinstimmung.

     

Die Phase La2U2N5

In the system U–La–N a new phase of composition La₂U₂N₅ was observed. The differaction pattern of this phase can be indexed with a tetragonal unit cell:a=8.43 Å,c=8.50 Å andc/a=1.008. The pseudocubic sub-cell withaca/2 is closely related to the CsCl-type.

Auszug aus der von der Technisch-Naturwissenschaftlichen Fakuktät der TU Wien approbierten Diplomarbait des Herrn Dipl.-Ing.J. Waldhart.     

Optisch aktive,aromatische Spirane, 8. Mitt.: Darstellung optisch aktiver, 5, 5′, 6′-trisubstituierter 2,2′-Spirobiindane bekannter Chiralität und enantiomerer Reinheit

Starting from (+) (2R) methyl 5-ethyl-2,2-spirobiindane-5-carboxylate of known enantiomeric purity 79 optically active, configurationally correlated 5,5,6-trisubstituted 2,2-spirobiindanes (2–7) were prepared for the purpose of testing a shortened polynomal Ansatz for chirality functions. Their optical rotations and¹H-nmr spectra are reported.In this context several 6-substituted 5-ethylindanes (1) were prepared as model compounds for synthetic transformations.

     

Spectrophotometric studies,stability constants and thermodynamics for complexes ofo-hydroxyacetophenone isobutyroylhydrazone with some bivalent transition metal ions

Summary The u.v. spectra ofo-hydroxyacetophenone isobutyroylhydrazone (HAIBuH) were investigated in pure organic solvents as well as in Britton Robinson buffer solutions of varyingpH values. The interaction ofHAIBuH with Co(II), Ni(II) and Cu(II) were studied spectrophotometrically. The optimumpH favouring the formation of the highly coloured complexes are 8.5, 8.0 and 7.5 for Co(II), Ni(II) and Cu(II), respectively. The stoichiometries of these complexes were determined and indicated the formation of 1:2 (metal:ligand) complexes of Co(II) and Ni(II) and a 1:1 complex of Cu(II). The dissociation constantspK ^H ofHAIBuH and the overall stability constants log of their complexes were determined at different temperatures (293, 303 and 313 K). The corresponding thermodynamic parameters (G, H and S) in 20% (v/v) ethanol-water mixture were derived and discussed.

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Spektrophotometrische Untersuchungen, Stabilitätskonstanten und Thermodynamik der Komplexe vono-Hydroxyacetophenonisobutyroylhydrazon mit einigen bivalenten Übergangsmetallionen

Zusammenfassung Die UV-Spektren vono-Hydroxyacetophenon-isobutyroylhydrazon (HAIBuH) wurden in reinen organischen Solventien und in Britton-Robinson-Pufferlösungen von verschiedenempH gemessen. Die Wechselwirkung vonHAIBuH mit Co(II), Ni(II) und Cu(II) wurde spektrophotometrisch untersucht. Die optimalenpH-Werte zur maximalen Ausbildung der starkgefärbten Komplexe sind 8.5, 8.0 bzw. 7.5 für Co(II), Ni(II) bzw. Cu(II). Für die Stöchiometrien wurde ein Metall: Ligand-Verhältnis 1:2 für Co(II) und Ni(II) und 1:1 für Cu(II) bestimmt. Die DissoziationskonstantenpK ^H vonHAIBuH und die Gesamtstabilitätskonstanten log der Komplexe wurden bei verschiedenen Temperature bestimmt (293, 303 und 313 K) und die entsprechenden thermodynamischen Parameter (G, H und S) in 20% (v/v) Ethanol-Wasser-Mischung errechnet und diskutiert.

     

Rate Constant for the Reaction of the OH-Radical with CH2F2

The rate constant value of k ₁ = (6.05 ± 0.20)×10⁹ cm³ mol^–1 s^–1 (with ± 1 error) has been determined for the reaction OH + CH₂F₂ (1) by applying the discharge-flow/resonance-fluorescence method at 298 K.     

Fluorescence behaviour of polychlorinated dibenzofurans in organized molecular systems. Analytical applications

Fluorescence characteristics of several polychlorinated dibenzofurans (PCDFs) of toxicological and environmental interest in the presence of cationic, anionic, neutral surfactants, -cyclodextrin and -cyclodextrin were examined. The fluorescence enhancement of 2,3,7,8-tetrachlorodibenzofuran (TTCDF) in the presence of polyoxyethylene(10) lauryl ether (C₁₂E₁₀) medium was utilized to establish a sensitive spectrofluorimetric method for determination of TTCDF. The optimization of variables as the concentration of surfactant, percentage of organic solvent and temperature, and effect of possible interferences from other PCDFs, polychlorinated dibenzo-p-dioxins (PCCDs), polychlorinated biphenyls (PCBs) and Arochlors were investigated. The method, which has a detection limit of 1.30 ng ml^–1, has been applied to the determination of TTCDF in sea water with acceptable recoveries.     

Gas chromatographic determination of the free energy of sorption of methylene units ofN-alkylsubstituted six-membered cyclic amines

The free energy of sorption of methylene units, G(CH₂), for the homologous series ofN-alkylsubstituted morpholines, thiomorpholines, piperidines and 2-methyl-, 3-methyl-, 4-methyl- and 2,6-dimethylpiperidines was determined. It was shown that the dependence of these values on the number of CH₂ units in the carbon chain is not linear. Universal equations for calculating the values of the energy contribution depending on the number of CH₂ units in the carbon chain were obtained. Abnormally high values of free energy of sorption of the first CH₂ unit were found in all series studied and reasons for the anomaly are discussed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 437–439, March, 1994.This work was made possible by the financial support of Russian Foundation for Basic Research, project No. 93-03-4969,     

Force constant calculations of the LAM-1 modes ofn-alkanes and their substituted α-Monohalo- and α,ω-dihalo- species in their extended zig-zag planar configurations as found in urea inclusion compounds

Force constants were determined for the C₈, C₁₀, C₁₂ and C₁₄ series ofn-alkanes C _n H_{2n + 2} using an approximate SVFF calculation and observed LAM = 1 wave numbers. In this calculation the hydrogen atoms were neglected and only the carbon backbone chain and terminal atoms were considered; this was valid since only low-frequency vibrations were under consideration. Using force constant transfer, the wavenumbers of the LAM = 1 accordion modes for the analogous -C_n H_2n + 1 X and ,-C_n H_2nX₂ species, where X = C1, Br or I were calculated. For -chloroalkanes and ,-dichloroalkanes, them = 1 accordion modes are calculated to be in the 220–130 cm^–1 and 200–120 cm^–1 regions, respectively. For the bromo- and iodo-analogues them = 1 accordion modes are calculated to be in the 200–100 cm^–1, 150–90 cm^–1 and in the 170–100, 135–80 cm^–1 regions, respectively.