Preparation,properties and structure of stable ionic dialkylbis(2,2′-bipyridine)cobalt(III) tetraalkylaluminate and related complexes

Two types of dialkylcobalt(III) complexes containing the 2,2′-bipyridine ligand have been isolated as products of the reactions of tris(2,4-pentanedionato)cobalt(III) (Co(acac)₃), 2,2′-bipyridine (bpy), and alkylaluminums in diethyl ether. When high Al/Co ratios (Al/Co > 7) were used, ionic complexes, dialkylbis(2,2′-bipyridine)cobalt(III) tetraalkylaluminates, [CoR₂(bpy)₂][AlR₄] (R = CH₃, C₂H₅) were obtained exclusively. Similar reactions at lower ratios (Al/Co - 1.5–2.0) gave neutral CoR₂(acac)(bpy) (R = CH₃, C₂H₅, n-C₃H₇, i-C₃H₇). These compounds were characterized by IR and NMR spectroscopy as well as by elemental analysis and chemical reactions. Molecular structural analysis of the cationic dimethylcobalt compound confirmed the cis configuration. Stepwise formation of [CoR₂(bpy)₂][AlR₄] from Co(acac)₃ is postulated and the mechanism of the alkylation reaction is discussed.     

Precursor trichloroeth anoato-chromium (III) species in the formation of tris (2,4-pentanedionato) chromium (III)

Two precursor species have been identified as responsible for the catalyzing effect of the trichloroethanoate (TCE) anion on the formation of tris(2,4-pentanedionato)chromium(III), Cr(acac)₃. The first one is the green intermediate species (GIS) identified as tetrahydroxodecakis-μs-trichloroethanoato-trichloroethanoato-tetraaquopentachro-mium(III), Cr₅(OH)₄(CCl₃COO)₁₁(H₂)₄. This appears to be the first pentanuclear species reported among the polynuclear alkanoato metal complexes. It reacts at a rapid rate with the 2,4-penaanedtonate, acac, anion to produce a second precursor, the violet-green intermediate species (VGIS) identified as bis(2,4-pentanedionato)-trichloroethanoato-aquochromium(III), Cr(C₅H₇O₂)₂(CCl₃COO)(H₂O). This is attacked by the remainigg acac anion to ultimaelly produce the Cr(acac)₃. Thus the effect of the TCE anion in facilitating the formation of Cr(acac)₃ is through the ligand coordination catalytic mechanisms.     

Funktionell substituierte zinnorganische verbindungen v. st]Phosphono- Und phosphonylmethyl-triorganostannane

The synthesis of phosphono- and phosphonylmethyl-triorganostannanes R₃SnCH₂P(O)(OR′)R′′ (R′′  OR′, C₆H₅) via an Arbuzov reaction of R₃SnCH₂I with P(OR′)₃ or C₆H₅P(OR′)₂ (R′′  CH₃, C₂H₅) is described. The new compounds have been studied with regard to their behaviour towards electrophilic (Br₂, HCl, HgBr₂) and nucleophilic (NaOH, LiAlH₄, LiR) agents. Their reaction with chlorophenylphosphines followed by reduction with LiAlH₄ yields the unsymmetrical methylenebis(phosphines) C₆H₅P(R)CH₂PH₂ (R  H, C₆H₅). The title compounds add to the carbonyl group of aldehydes and the CN bond of phenylisocyanate.     

trans‐(Methanol)(methyl­di­phenyl­phosphine)­bis­(pentane‐2,4‐dionato)­cobalt(III) hexa­fluoro­phosphate hydrate

The title compound [Co(C₅H₇O₂)₂(C₁₃H₁₃P)(CH₄O)]PF₆·H₂O, (I), which was converted from trans‐[Co(acac)₂(PMePh₂)(H₂O)]PF₆ (acac is pentane‐2,4‐dionato) by recrystallization from aqueous methanol, has been confirmed as have a coordinated methanol ligand. The molecular structure of the complex cation, trans‐[Co(acac)₂(PMePh₂)(MeOH)]⁺, is similar to that of the above aqua complex found in the ClO₄ salt [Kashiwabara et al. (1995). Bull. Chem. Soc. Jpn, 68 , 883–888]. The Co—O bond length for the coordinated methanol is 2.059 (3) Å. There is an intermolecular hydrogen bond between the OH group of the coordinated methanol and one of the O atoms of the acac ligands in an adjacent complex cation [O5?O3′ = 2.914 (4) Å], giving a centrosymmetric dimeric dicationic complex.     

Optisch aktive übergangsmetall-komplexe LXIV. Neue optisch aktive Cp(CO)Fe-acyl-komplexe mit

The novel complexes CpFe(CO)(COR)P(C₆H₅)₂NR'R^* with Cp = C₅H₅,C₉H₇ (indenyl); R = CH₃, C₂H₅, CH(CH₃)₂, CH₂C₆H₅;R` = H, CH<sub>3</sub>, C<sub>2</sub>H<sub>5</sub>, CH<sub>2</sub>C<sub>6</sub>H<sub>5</sub> and R<sup>*</sup> = (S)-CH(CH<sub>3</sub>)(C<sub>6</sub>H<sub>5</sub>), have been synthesized by reaction of CpFe(CO)<sub>2</sub>R wiht P(C<sub>6</sub>H<sub>5</sub>)<sub>2</sub>NR`R^* and characterized analytically as well as spectroscopically. The pairs of diastereoisomers RS/SS have been separated by preparative liquid chromatography and fractional crystallization, respectively. The optically pure complexes (+)₄₃₆- und ()₄₃₆-CpFe(CO)(COR)P(C₆H₅)₂NR`R^* are configurationally stable at room temperature. At higher temperatures they equilibrate with CpFe(CO)₂R and epimerize with respect to the Fe configuration.     

Reaction of [Fe4(μ3-CCH3)(CO)12]− with alkynes: Ethylidyne-alkyne coupling on a tetranuclear iron cluster anion

The [Fe₄(μ₄-η³-C(CH₃)C(R)C(R′)(μ-CO)₂(CO)₉]⁻ cluster anions have been obtained by the reaction of the Fe₄(μ₃-CCH₃)(CO)₁₂⁻ anion with RCCR alkynes in boiling 3-pentanone. In the cases in which R = R′ = C₆H₅ or CH₃, and R = H, R′ = C₆H₅ or t-Bu, only one isomer has been detected. In the case in which R = CH₃, and R′ = C₆H₅, two isomers with the C(CH₃)C(C₆H₅)C(CH₃) and C(CH₃)C(CH₃)C(C₆H₅) fragments have been identified.     

Mass spectrometry of transition metal π-complexes. XV—The effect of substituents on the fragmentation of benchrotrenyls under electron impact

Mass spectra of substituted benchrotrenyls RC₆H₅Cr(CO)₃ where R?H, F, CI, I, CH₃, OCH₃, COOCH₃, C₂H₅, N(CH₃)₂, NH₂, C₆H₅, C(CH₃)₃, p-C₆H₄NH₂, CH₂C₆H₅, CH₂CH₂C₆H₅), 1,3,5-(CH₃)₃C₆H₃Cr(CO)₃ and 1,2,3,5-(CH₃)₄C₆H₂Cr(CO)₃ have been studied. It has been found that for monosubstituted benchrotrenyls there is a linear dependence of the parameter log [Cr]⁺/[RC₆H₅Cr]⁺) on the number of degrees of freedom of the [RC₆H₅Cr]⁺ ion. Decarbonylation of the molecular ions is not affected by the nature of the substituent R. The results are interpreted in terms of the quasi-equilibrium theory of mass spectra.     

Synthesis reactivity and electrochemical properties of substituted cyclopentadienyl cobalt (III) complexes

Cyclopentadienyl cobalt complexes (η⁵‐C₅H₄R) CoLI₂ [L = CO,R=‐COOCH₂CH=CH₂ (3); L=PPh₃, R=‐COOCH₂‐CH=CH₂ (6); L=P(p‐C₆H₄O₃)₃, R = ‐COOC(CH₃) = CH₂ (7), ‐COOCH₂C₆H₅ (8), ‐COOCH₂CH = CH₂ (9)] were prepared and characterized by elemental analyses, ¹H NMR, ER and UV‐vis spectra. The reaction of complexes (η⁵‐C₅H₄R)CoLI₂ [L= CO, R= ‐COOC(CH₃) = CH₂ (1), ‐COOCH₂C₆H₅(2); L=PPh₃, R=‐COOC (CH₃) = CH₂ (4), ‐COOCH₂C₆H₅ (5)] with Na‐Hg resulted in the formation of their corresponding substituted cobaltocene (η⁵‐C₅H₄R)₂ Co[R=‐COOC(CH₃) = CH₂ (10), ‐COOCH₂C₆H₅ (11)]. The electrochemical properties of these complexes 1–11 were studied by cyclic voltammetry. It was found that as the ligand (L) of the cobalt (III) complexes changing from CO to PPh₃ and P(p‐tolyl)₃, their oxidation potentials increased gradually. The cyclic voltammetry of α,α′‐substituted cobaltocene showed reversible oxidation of one electron process.     

The 31P NMR spectra of ArCr(CO)2P(C6H5)3 compounds in neutral and acidic media

The ³¹P NMR spectra of C₆H₅XCr(CO)₂P(C₆H₅)₃ (X = H, CH₃, OCH₃, N(CH₃)₂, COOCH₃) (I), p-C₆H₄X₂Cr(CO)₂P(C₆H₅)₃ (X = COOCH₃)(II) and C₆H₃X₃Cr(CO)₂P(C₆H₅)₃ (X = CH₃) (III) complexes in neutral and acidic media were investigated. The protonation of complexes I and III in trifluoroacetic acid results in the greater upfield shielding of ³¹P{¹H} signal. In this case the complexes I (X = H, CH₃, OCH₃) are completely protonated at the metal, complex I (X = COOCH₃)is partially protonated, while no protonation occurs in the case of complex II.Temperature-dependence of the ³¹P{¹H} NMR spectra was investigated for complexes I (X = H, OCH₃) in a 1/10 mixture of trifluoroacetic acid and toluene and for complexes I (X = COOCH₃) and II in trifluoroacetic acid. The degree of protonation was found to increase with decreasing temperature.     

SYNTHESIS AND CHARACTERISATION OF DIORGANOANTIMONY(III) COMPLEXES OF THIOSEMICARBAZONES

Abstract

The interaction of the sodium salts of thiosemicarbazones with diphenylantimony chloride in 1:1 molar ratio in benzene solution lead to the formation of derivatives, Ph₂Sb[SC(NH₂)NN: C(R)R′] where R = H; R′ [dbnd] C₆H₅, CH₃OC₆H₄, C₆H₅CH[dbnd]CH, and R′ [dbnd] CH₃; R′[dbnd]C₆H₅, CH₃OC₆H₄, C₆H₄CH₃, respectively. The resulting complexes have been characterised on the basis of elemental analyses and molecular weight determination. The mode of bonding of the ligands with the metal atom has been proposed on the basis of I.R., ¹H and ¹³C NMR studies. All these ligands are found to behave as monofunctional bidentate moiety in these complexes.     

H—D scrambling in the ethyl group(s) and 2,2'-bipyridine ligand of ethyl-nickel, -iron and -cobalt complexes in their reactions with molecular deuterium

Reactions of NiMe₂(bipy), (bipy = 2,2'-bipyridine), NiEt₂(bipy), FeEt₂(bipy)₂, CoMe(bipy)₂, CoEt(bipy)₂, NiEt(acac)(PPh₃) (acac = acetylacetonato, PPh₃ = triphenylphosphine), CoMe(PPh₃)₃, CoEt₂(acac)(PPhMe₂)₂, CrMeCl₂(THF)₃ and RhMe(PPh₃)₃ with molecular deuterium have been studied. Reactions of the methyltransition-metal complexes with D₂ gave only CH₃D and CH₄, whereas reactions of the ethyltransition-metal complexes with D₂ gave C₂D₆, C₂HD₅, C₂H₂D₄, C₂H₃D₃, and C₂H₄D₂ in addition to C₂H₅D and C₂H₆. A mechanism comprised of the oxidative addition of D₂, β-elimination and its reverse process, exchange of a hydrido with a deuterido ligand and reductive elimination of the deuterido and ethyl ligands, is proposed to account for the formation of the extensively deuterated ethanes. Hydrogen atoms of 2,2'-bipyridine ligand of the alkyltransition-metal complexes also undergo exchange with D₂, predominantly at the 4- and 6-positions.     

Cyclopentadienyleisen-komplexe mit P(OR)3-liganden; Synthese und spektroskopische charakterisierung

Reactions of reactive cyclopentadienyliron complexes C₅H₅Fe(CO)₂I, [C₅H₅Fe(CO)₂THF]BF₄, [C₅H₅Fe(CO)((CH₃)₂S)₂]BF₄ and [C₅H₅Fe(p-(CH₃)₂C₆H₄)]PF₆ with P(OR)₃ as ligands (R = CH₃, C₂H₅, i-C₃H₇ and C₆H₅) lead to the formation of the complex compounds C₅H₅Fe(CO)_2?n(P(OR)₃)_nI and [C₅H₅Fe(CO)_3?n(P(OR)₃)_n]X (n = 1, 2 and n = 1–3, X = BF₄, PF₆). Spectroscopic investigations (IR, ¹H, ¹³C and ³¹P NMR) indicate an increase of electron density on the central metal with increasing substitution of CO groups by P(OR)₃ ligands. The stability of the compounds increase in the same way.     

Studies on organophosphorus compounds XLVIII Synthesis of Dithioesters from P,S-Containing Reagents and Carboxylic Acids and Their Derivatives

2,4-Bismethylthio-1,3,2,4-dithiadiphosphetane 2,4- disulfide, IIa, is prepared from 0,0-dimethyldithiophosphoric acid, Ia, and P₄S₁₀ at 160°C. 2,4-Bis(4-phenoxyphenyl)-1,3,2,4- dithiadiphsophetane 2,4-disulfide, IIc, and 2,4-bis(4-phenylthiolophenyl)-1,3,2,4-dithiadiphosphetane 2,4-disulfide, IId, are prepared at l60°C from P₄ S₁₀ and diphenylether and diphenylsulfides, respectively. Carboxylic acids RCOOH(R = CH₃ C₂H₅, n-C₃H₇, n-C₄H₉, C₆H₅CH₂, C₆H₈) react with compound Ia at 130°C to give the corresponding methyl dithioesters. Carboxylic acids RCOOH (R = C₆H₈-CH₂, C₆H₈) react with compound Ib at 200°C for 15 min to give the corresponding ethyl dithioesters, while low boiling acids (R = CH₃, C₂H₈, n-C₃H₇) yielded mixtures of the corresponding ethyl dithioester and ethyl carboxylate. Carboxylic acid chlorides RCOCl (R = ClCH₂, C₂H₅, t-C₄H₅ C₆H₅CH₂, C₆H₅, P-NO₂C₆H₄) react with compound IIa at 80°C to give the corresponding methyl dithioesters in good yields. S-Substituted thioesters react with IIC at 85°C to give the corresponding dithioesters in good yields. Dihydro2(3H)-furanone, VI, and 5-methyl-2(3H)-furanone, VII, react with IIa at 80°C; to dihydro-2(3H)-thiophenethione, VIII and 2,2'-dithiobis(5-methyl thiophene),IX, respectively. Also XI reacts with IIa,IIc, and IId to give VIII in nearly quantitative yields.     

Synthese,Struktur und Photochemie von Olefiniridium(I)‐Komplexen mit Acetylacetonatoliganden

Synthesis, Structure, and Photochemical Behavior of Olefine Iridium(I) Complexes with Acetylacetonato Ligands The bis(ethene) complex [Ir(κ²‐acac)(C₂H₄)₂] ( 1 ) reacts with tertiary phosphanes to give the monosubstitution products [Ir(κ²‐acac)(C₂H₄)(PR₃)] ( 2 – 5 ). While 2 (R = iPr) is inert toward PiPr₃, the reaction of 2 with diphenylacetylene affords the π‐alkyne complex [Ir(κ²‐acac)(C₂Ph₂)(PiPr₃)] ( 6 ). Treatment of [IrCl(C₂H₄)₄] with C‐functionalized acetylacetonates yields the compounds [Ir(κ²‐acacR^1,2)(C₂H₄)₂] ( 8 , 9 ), which react with PiPr₃ to give [Ir(κ²‐acacR^1,2)(C₂H₄)(PiPr₃)] ( 10 , 11 ) by displacement of one ethene ligand. UV irradiation of 5 (PR₃ = iPr₂PCH₂CO₂Me) and 11 (R² = (CH₂)₃CO₂Me) leads, after addition of PiPr₃, to the formation of the hydrido(vinyl)iridium(III) complexes 7 and 12 . The reaction of 2 with the ethene derivatives CH₂=CHR (R = CN, OC(O)Me, C(O)Me) affords the compounds [Ir(κ²‐acac)(CH₂=CHR)(PiPr₃)] ( 13 – 15 ), which on photolysis in the presence of PiPr₃ also undergo an intramolecular C–H activation. In contrast, the analogous complexes [Ir(κ²‐acac)(olefin)(PiPr₃)] (olefin = (E)‐C₂H₂(CO₂Me)₂ 16 , (Z)‐C₂H₂(CO₂Me)₂ 17 ) are photochemically inert.     

Basische metalle: LII. Synthese von carbenoid- und ylidcobalt(III)-komplexen aus substitutionslabilen cobalt(I)-vorstufen

The cyclopentadienylcobalt(I) compounds C₅H₅Co(PMe₃)P(OR)₃ (R = Me, Et, Prⁱ) and C₅H₅Co(C₂H₄)L (L = PMe₃, P(OMe)₃, CO) are prepared by ligand substitution starting from C₅H₅Co(PMe₃)₂ and C₅H₅Co(C₂H₄)₂. Whereas the reaction of C₅H₅Co(PMe₃)P(OMe)₃ with CH₂Br₂ mainly gives [C₅H₅CoBr(PMe₃)P(OMe)₃]Br, the dihalogenocobalt(III) complexes C₅H₅CoX₂(PMe₃) (X = Br, I) are obtained from C₅H₅Co(CO)PMe₃ and CH₂X₂. Treatment of C₅H₅Co(CO)PMe₃ or C₅H₅Co(C₂H₄)PMe₃ with CH₂ClI at low temperatures produces a mixture of C₅H₅CoCH₂Cl(PMe₃)I and C₅H₅CoCl(PMe₃)I, which can be separated due to their different solubilities. The same reaction in the presence of ligand L gives the carbenoidcobalt(III) compounds [C₅H₅CoCH₂Cl(PMe₃)L]PF₆ in nearly quantitative yields. If NEt₃ is used as the Lewis base, the ylide complexes [C₅H₅Co(CH₂PMe₃)(PMe₃)X]PF₆ (X = Br, I) are obtained. The PF₆ salts of the dications [C₅H₅Co(CH₂PMe₃)(PMe₃)L]²⁺ (L = PMe₃, P(OMe)₃, CNMe) and [C₅H₅Co(CH₂PMe₃)(P(OMe)₃)₂]²⁺ are prepared either from [C₅H₅Co(CH₂PMe₃)(PMe₃)X]⁺ and L, or more directly from C₅H₅Co(CO)PMe₃, CH₂X₂ and PMe₃ or P(OMe)₃, respectively. The synthesis of C₅H₅CoCH₂OMe(PMe₃)I is also described.     

Derivate des borabenzols: XVI. (Borinato)(cyclobutadien)cobalt-komplexe mit tetramethyl- und tetraphenylcyclobutadien-liganden. Synthese,elektrophile aromatische substitution und ringgliedsubstitution am borinato-liganden

The preparation of (borinato)(cyclobutadiene)cobalt complexes from the reactions of Co(C₅H₅BR)(1,5-C₈H₁₂) with acetylenes C₂R′₂ and of [C₄(CH₃)₄]Co(CO)₂I with Tl(C₅H₅BR) (R,R′ = CH₃, C₆H₅) is described.In electrophilic substitution reactions Co(C₅H₅BCH₃)[C₄(CH₃)₄] (IVa) is more reactive than ferrocene. CF₃CO₂D effects H/D-exchange in the α-position of the borabenzene ring within a few minutes at ambient temperature and in the γ-position within less than four hours Friedel-Crafts acetylation with CH₃COCl/AsCl₃ in CH₂Cl₂ affords the 2-acetyl and the 2,6-diacetyl derivative of IVa. With the more active catalyst AlCl₃, ring-member substitution is effected to give cations [Co(arene)C₄(CH₃)₄]⁺ (arene = C₆H₅CH₃, 2-CH₃C₆H₄COCH₃). Vilsmeier formylation gives the 2-formyl derivative of IVa. The acyl derivatives Co(2-R¹CO-6-R²C₅H₃BCH₃)[C₄(CH₃)₄] (R¹ = CH₃, R² = H, CH₃CO and R¹ = R² = H) transform to the corresponding cations [Co(ortho-R¹R²C₆H₄)C₄(CH₃)₄]⁺ in superacidic media. The mechanistic relationship between acylation and ring-member substitution is discussed in detail.     

Stereoselektive Hydrid-Addition an von N-Methylbenzimidchlorid abgeleitete Carbenchelatkomplexe

Upon reaction with NaBH₄ the carbene chelates [C₅H₅(CO)_xMC(C₆H₅N(CH₃)C(C₆H₅)N(CH₃)]PF₆ (I,M = Mo, x = 2; II,M = Fe, x = 1) are reduced at the carbene carbon with formation of the neutral compounds C₅H₅(CO)_xMC(H)(C₆H₅)N(CH₃)C(C₆H₅)N(CH₃) (III and IV). Depending on the orientation of the incoming H substituent with respect to the C₅H₅ ligand two different isomers A and B are obtained which can be separated by column chromatography. Whereas the H^? addition to the Fe compound II is almost stereospecific (formation of 95% IVB), the stereoselectivity of the H^? addition to the Mo compound I is influenced by a competitive metal centered rearrangement of III in opposite direction. The approach to the equilibrium IIIA/IIIB 85/15 can be measured by ¹H NMR spectroscopy (ΔG³₃₂₈ 26.6 kcal/mol).     

Synthesis and Characterization of Diphenyltin(IV) Dicarboxylates Containing Germanium

Twelve new germanium substituted diphenyltin dipropionates with the general formula (R¹GeCHR²‐CHR³COO)₂SnPh₂ where R¹ = N(CH₂CH₂O)₃, (C₆H₅)₃ and (CH₃C₆H₄)₃, R² = H, CH₃, C₆H₅, p‐CH₃C₆H₄, p‐CH₃OC₆H₄, p‐ClC₆H₄, and R³ = H, CH₃ have been synthesized by the reaction of diphenyltin oxide with a germanium substituted propionic acid. All the compounds were characterized by elemental analysis, IR, multi‐nuclear (¹H, ¹³C, ¹¹⁹Sn) NMR and Mössbauer spectroscopies as well as mass spectrometry. The in vitro antibacterial activity of selected compounds is also reported.     

Synthesis and reactions of some sulfur ylide complexes of palladium

The iodo-bridged sulfur ylide complex [Pd(μ-I)((CH₂)₂(SO)(CH₃))]₂ (1) when treated with dithiolates, acetylacetone and various Lewis bases gave [Pd((CH₂)₂(SO)(CH₃))(S ∼ S)] (S ∼ S = S₂CN(C₂H₅)₂, S₂COC₂H₅ and S₂P(OC₂H₅)₂), [Pd((CH₂)₂(SO)(CH₃))(acac)] (acac = acetylacetonate) and [PdI((CH₂)₂(SO)(CH₃))(base)]a (base = PPh₃, (P(OMe)₃, P(OPh)₃ and C₅H₅N). In the presence of a phase transfer catalyst (PTC). The reactions rates and yields were greatly increased. Reaction of several related sulfur ylide complexes with I₂, HI or aqueous NaOH gave 1. The single crystal structure of [Pd((CH₂)₂(SO)(CH₃))₂] was determined (orthorhombic, Pbcn, a 13.379(2), b 8.081(1), c 9.048(2) Å, V 978.2 ų, Z = 4). The compound has a rather long PdCH₂ bond (2.096(1) Å, mean).     

Carbon-13 chemical shift assignment of some organophosphorus compounds: 1—Dialkyl and diaryl (alkylamido)phosphates with general formula Y2P(X)NHR

Carbon-13 chemical shifts and the POC, POCC, PNC and PNCC coupling constants of 18 compounds containing the amine moiety, and with the general formula Y₂P(X)NHR [Y=C₂H₅O, C₆H₅O, CH₂O, Y₂=1,2-dioxybenzene; X = O or S; R = H, CH₃, C₂H₅, PhCH₂CH₂, (CH₃)₂CH, C(CH₃)₃, C₆H₁₁, C₆H₅, C₆H₅NH] have been determined. The Y₂P(X) group shows a sterically induced effect on the amine moiety; the ¹³C chemical shift of the Y group is, however, almost unaffected on replacing P(O) by a P(S) group.