Wingtip Position Research Articles

Motor output and control input in flapping flight: a compact model of the deforming wing kinematics of manoeuvring hoverflies.

Insects are conventionally modelled as controlling flight by varying a few summary kinematic parameters that are defined on a per-wingbeat basis, such as the stroke amplitude, mean stroke angle and mean wing pitch angle. Nevertheless, as insects have tens of flight muscles and vary their kinematics continuously, the true dimension of their control input space is likely to be much higher. Here, we present a compact description of the deforming wing kinematics of 36 manoeuvring Eristalis hoverflies, applying functional principal components analysis to Fourier series fits of the wingtip position and wing twist measured over 26 541 wingbeats. This analysis offers a high degree of data reduction, in addition to insight into the natural kinematic couplings. We used statistical resampling techniques to verify that the principal components (PCs) were repeatable features of the data, and analysed their coefficient vectors to provide insight into the form of these natural couplings. Conceptually, the dominant PCs provide a natural set of control input variables that span the control input subspace utilized by this species, but they can also be thought of as output states of the flight motor. This functional description of the wing kinematics is appropriate to modelling insect flight as a form of limit cycle control.

Synthesis, structure and reactivity of tetranuclear square-type complexes of rhenium and manganese bearing pyrimidine-2-thiolate (pymS) ligands: versatile and efficient precursors for mono- and polynuclear compounds containing M(CO)3 (M = Re, Mn) fragments

Reactions of M(2)(CO)(10) (M = Re, Mn) with pyrimidine-2-thiol (pymSH) in the presence of Me(3)NO afford the tetranuclear square-type complexes [M(4)(CO)(12)(micro-kappa(3)-pymS)(4)] (, M = Re; , M = Mn). Both consist of four M(CO)(3) (M = Re, Mn) units, pairs of which are joined by tridentate pyrimidine-2-thiolate ligands. Treatment of with a variety of donor ligands results in cleavage of the square to afford mononuclear species with either a mono- or bidentate pyrimidine-2-thiolate ligand. Triphenylphosphine reacts with to give [Mn(CO)(3)(PPh(3))(kappa(2)-pymS)] () in which the pyrimidine-2-thiolate coordinates in a bidentate fashion. With diamines [M(CO)(3)(kappa(2)-L)(kappa(1)-pymS)] () (M = Re, Mn; L = 2,2'- bipy, 1,10-phen, en) result in which the pyrimidine-2-thiolate binds in a monodentate fashion through sulfur. With diphosphines, complexes with different stoichiometries and pyrimidine-2-thiolate binding modes are obtained depending on the nature of the metal and diphosphine. With dppm and dppe, gives [Re(CO)(2)(kappa(1)-pymS)(kappa(2)-dppm)] () and [Re(CO)(2)(kappa(2)-pymS)(kappa(1)-dppe)(2)] (), respectively, whereas affords [Mn(CO)(2)(kappa(2)-pymS)(kappa(1)-dppm)(2)] () and [Mn(CO)(2)(kappa(2)-pyS)(kappa(2)-dppe)] () under similar conditions. Reactions of with [Os(3)(CO)(10)(NCMe)(2)] affords mixed-metal butterfly clusters [MOs(3)(CO)(13)(micro(3)-kappa(2)-pymS)] () in which the group 7 metal occupies a wing-tip position and the pyrimidine-2-thiolate ligand caps a triangular Os(2)M face. With Ru(3)(CO)(12), carbon-sulfur bond cleavage occurs to give the tetranuclear clusters [MRu(3)(CO)(14)(micro(4)-S)(micro-kappa(1):eta(1)-pym)] () bearing both the extruded sulfur and the heterocyclic ring. The molecular structures of , and have been established by X-ray diffraction allowing the binding mode of the pyrimidine-2-thiolate ligands to be probed.

Synthesis and molecular structure of mixed alkyne-cyclopentadienyl clusters via the ionic coupling of [Os 3(CO) 9(R 2C 2)] 2− with [Ru(η 5-C 5H 5)(MeCN) 3] + and the reaction [Os 3RuH(η 5-C 5H 5)(CO) 10(MeCN)] with alkynes (R 2C 2) (R = Me, Ph)

The ionic coupling reaction of the dianion [Os 3(CO) 9(R 2C 2)] 2− (R = Me, Ph) with two equivalents of the monocation [Ru(η 5-C 5H 5)(CH 3CN) 3] + affords the neutral clusters [Os 3Ru 2(CO) 9(R 2C 2)(η 5-C 5H 5) 2] [R = Me, 1 and R = Ph, 2] in ca. 80% yield. An X-ray crystallographic study of 1 confirms that these clusters exhibit a capped pseudo-octahedral Os 3Ru 2C 2 core, with the alkyne bonded parallel to the hinge bond of the capped butterfly metal geometry in a μ 4–η 2 manner, the Ru atoms adopting the wing-tip and capping positions. Reaction of the activated cluster [Os 3RuH(η 5-C 5H 5)(CO) 10(MeCN)] ( 3) with RCCR (R = Me, Ph) affords the related clusters [Os 3RuH(CO) 9(η 5-C 5H 5)(R 2C 2)] (R = Me, 4 and R = Ph, 5) in ca. 35% yield. The reaction with PhCCPh also produces [Os 3Ru(CO) 8(η 5-C 5H 5)(PhCCPh)(PhCC(H)Ph)] ( 6) in ca. 15% yield. An X-ray crystallographic study shows that this cluster has a pseudo-octahedral Os 3RuC 2 core, with the Ru(η 5-C 5H 5) unit adopting the wing-tip position, the alkyne bonded in a μ 4–η 2 arrangement and the ethenyl ligand bridging an Os–Os edge in a μ 2–η 1:η 2 configuration.

Rational synthesis of tricobalt-molybdenum and -tungsten butterfly clusters with alkyne ligands

The heterometallic alkyne complexes [CoM(μ-R 1CCR 2)(CO) 5Cp] (M=Mo, W; R 1=R 2=CO 2Me, CO 2Et; R 1=H, R 2=CO 2Me) react with dicobalt octacarbonyl in refluxing toluene to give the 60-electron tetranuclear clusters [Co 3M(μ 4-R 1C 2R 2)(CO) 9Cp] in moderate to good yields. The clusters consist of a butterfly-type metal core in which the molybdenum (or tungsten) atom occupies a wing-tip position, as shown by X-ray analysis of three of the complexes.

Molecular structure of a new palladium-containing vinylidene cluster [η2-Ph2P(CH2)3PPh2]PdFe3(μ4-C=CHPh)(CO)9

The structure of the vinylidene cluster [η2-Ph2P(CH2)3PPh2]PdFe3(μ4-C=CHPh)(CO)9 was established by X-ray diffraction analysis. The metal core of the molecule has a butterfly shape with the Pd atom occupying a wingtip position. The C(1)=C(2)HPh ligand is σ-bound to three atoms of the Fe2Pd triangle through the C(1) atom and is η2-coordinated to the Fe atom located in the second wingtip position via the C(1)=C(2) double bond. The Pd atom is chelated by the diphosphine ligand.

Complexes with Platinum−Ruthenium Bonds: Synthesis, Structure, and Fluxionality of Pt3Ru Cluster Complexes

The reaction of [Pt3(μ3-CO)(μ-dppm)3][PF6]2, 1, dppm = Ph2PCH2PPh2, with [HRu(CO)4]- initially gives [Pt3(μ-H)(μ-dppm)3{Ru(CO)4}]+, 2, which contains a PtRu(μ-H) unit. In solution, complex 2 rearranges to the cluster [Pt3Ru(μ-H)(CO)2(μ-CO)2(μ-dppm)3]+, 3, which has been characterized by X-ray structure determination to have a butterfly structure with ruthenium at a wingtip position and which contains a Pt2(μ-H) unit. Both complexes 2 and 3 exhibit fluxionality, which is defined by low-temperature NMR studies.

Complexes of Ir3(CO)3(η5-C9H7)3with Metal Fragment Electrophiles

The reactions of C3v Ir3(μ-CO)3(η5-C9H7)3 (1) with various metal electrophiles yield the cationic tetranuclear clusters [Ir3{M(PPh3)}(CO)3(η5-C9H7)3][PF6] (2, M = Cu; 3, M = Ag; 5, M = Au), [Ir3Tl(μ-CO)3(η5-C9H7)3][PF6] (4), and [Ir3(HgR)(CO)3(η5-C9H7)3][PF6] (6, R = Ph; 7, R = W(CO)3(η5-C5H5)). Compounds 5−7 are best prepared via compound 4. The structures of compounds 4 and 5 have been determined by X-ray diffraction. The C3v symmetry of the parent cluster 1 is maintained in the structure of 4. The molecule consists of a triangle of iridium atoms, each edge of which has a bridging carbonyl oriented out of the plane in the same direction and each vertex of which has an η5-indenyl ligand oriented toward the opposite side of the plane. The thallium atom adopts a face-capping mode of coordination on the same side of the triiridium plane as the three indenyl ligands and is encapsulated by the phenylene portions of the indenyl groups. The molecular structure of 5 consists of a AuIr3 butterfly framework with a hinge angle of 153.63(3)° and the gold atom in a wingtip position. Each CO ligand is bonded in a terminal mode to one iridium center, with one CO ligand ‘down' relative to the Ir3 plane and two CO ligands ‘up', flanking the Ir−Ir edge bridged by the Au(PPh3)+ fragment. The indenyl ligands take up positions opposite those of the CO ligands at each iridium center. The infrared and 1H NMR spectra of compounds 2, 3, 5, 6, and 7 are all very similar and are fully consistent with the solid-state structure of 5.

Tetranuclear and Octanuclear Manganese Carboxylate Clusters: Preparation and Reactivity of (NBu(n)(4))[Mn(4)O(2)(O(2)CPh)(9)(H(2)O)] and Synthesis of (NBu(n)(4))(2)[Mn(8)O(4)(O(2)CPh)(12)(Et(2)mal)(2)(H(2)O)(2)] with a "Linked-Butterfly" Structure.

The reaction of Mn(O2CPh)2·2H2O and PhCO2H in EtOH/MeCN with NBun4MnO4 gives (NBun4)[Mn4O2(O2CPh)9(H2O)] (4) in high yield (85−95%). Complex 4 crystallizes in monoclinic space group P21/c with the following unit cell parameters at −129 °C: a = 17.394(3) A, b = 19.040(3) A, c = 25.660(5) A, β = 103.51(1)°, V = 8262.7 A3, Z = 4; the structure was refined on F to R (Rw) = 9.11% (9.26%) using 4590 unique reflections with F > 2.33σ(F). The anion of 4 consists of a [Mn4(μ3-O)2]8+ core with a “butterfly” disposition of four MnIII atoms. In addition to seven bridging PhCO2- groups, there is a chelating PhCO2- group at one “wingtip” Mn atom and terminal PhCO2- and H2O groups at the other. Complex 4 is an excellent steppingstone to other [Mn4O2]-containing species. Treatment of 4 with 2,2-diethylmalonate (2 equiv) leads to isolation of (NBun4)2[Mn8O4(O2CPh)12(Et2mal)2(H2O)2] (5) in 45% yield after recrystallization. Complex 5 is mixed-valent (2MnII,6MnIII) and contains an [Mn8O4]14+ core that consists of two [Mn4O...

Characterization, redox properties and structures of the iron nitridocarbonyl clusters [Fe4N(CO)11{PPh(C5H4FeC5H5)2}]–, [Fe6N(CO)15]3–and [Fe6H(N)(CO)15]2–

The redox condensation of [Fe2(CO)8]2– with [Fe4N(CO)12]– yielded the cluster [Fe6N(CO)15]3–. Single-crystal X-ray analysis showed it to possess an octahedral metal cage, with an interstitial nitride ligand. Under the D3 idealized symmetry, all iron vertices are equivalent, being bound to one edge-bridging and two terminal carbonyls. The ion [Fe6N(CO)15]3– can be oxidized to [Fe5N(CO)14]– or protonated to the hydridic dianion [Fe6H(N)(CO)15]2–. The molecular structure of the latter was determined, and is strikingly similar to that of the parent trianion. Small deformations of the ligand shell or elongations of the Fe–Fe distances are not sufficient to determine the location of the hydride. Electrochemical experiments were consistent with the chemical findings, showing that [Fe6N(CO)15]3– undergoes three irreversible one-electron oxidation steps, ultimately generating [Fe5N(CO)14]–. A lifetime of about 15 s was evaluated for the transient radical [Fe6N(CO)15]2–. Thermal activation induces substitution of one carbonyl ligand of [Fe4N(CO)12]– by PPh(C5H4FeC5H5)2, yielding [Fe4N(CO)11{PPh(C5H4FeC5H5)2}]–, the molecular structure of which was also determined. The cluster adopts a butterfly arrangement of iron atoms, having an exposed µ4-N atom and the phosphine ligand at a wingtip position. Cyclic voltammetry showed that communication between the two ferrocenyl units of the ligand PPh(C5H4FeC5H5)2 is rather low in the free state, and is notably improved by co-ordination to the tetrairon cluster. The 15N-labelled [Fe6N(CO)15]3– and [Fe6H(N)(CO)15]2– complexes were synthesized, and the NMR chemical shifts and IR bands of the interstitial µ6-N ligands measured.

Exo-2-(η6-Hexamethylbenzene)-endo-2-chloro-2-ruthena-arachno-tetraborane(8)

The compound exo-2-(η 6 -hexamethylbenzene)-endo-2-chloro-2-ruthena-arachno-tetraborane, [RuCl(C 12 H 18 )(B 3 H 8 )], is based on a four-vertex butterfly structure with an Ru atom occupying a wing-tip position. The Ru atom is coordinated to the [B 3 H 8 ] moiety via an Ru-μ-H-B bridge to each of the two B atoms in the hinge positions. Additionally, the Ru atom is ligated by a hexahapto-hexamethylbenzene and a Cl atom. The compound is in a conformation with the Cl atom in the endo position and the η 6 -arene in the exo position.

Interaction of metal cluster ketenylidenes, [M3(CO)9(CCO)]2- (M = iron, ruthenium) with the soft electrophiles copper(I) iodide and CuPR3+

The reaction of [Fe 3 (CO) 9 (C α C β O)] 2- (I) with CuI yields a metal butterfly cluster III with the CCO ligand intact and Cu in a wingtip position. The X-ray structure determination also reveals a Cu-Cα distance of 2.008 (5) A

Reactions of a cobalt-molybdenum and related cobalt-tungsten tetrahedral clusters with phenylacetylene: formation of tetrametallic alkyne clusters or cluster fragmentation?

The reactions of the tetrahedral mixed-metal clusters CO~M(CO)~~(~~-C~ H~M~) (M = Mo, la; M = W, lb), Co,W,(p-CO),(C0)7(?s-CSH4Me)2 (2), and COW,(CO)~(~~-C~H ~M~)~ (3) with PhC2H have been investigated. la affords the cluster CO,MO(CO)~(~~-~~-P~C~H)(~~-C~H~M~) (5) when treated with this alkyne. The structure of 5 was established by an X-ray diffraction study. It consists of a Co,Mo butterfly core with the molybdenum atom in a wing-tip position. A p4-PhC2H ligand interacts with all the metals. 5, C23H1309C03Mo, crystallizes in the monoclinic space group P21/n (No. 14) with a = 9.272 (2) %I, 6 = 14.608 (2) A, c = 17.752(3) A, (3 = 95.132(9)', V = 2394 (1) A3, and Z = 4. The structure was refined to R = 0.030 and R, = 0.040 using the 2235 unique data with I > 34). The cluster CO~W,(~-CO)~(CO),(~~-C~H~M~)~ (2) affords CO~W,(~,-~*-P~C~H)(CO)~(~~-C~H,M~)~ (7), which has a Co2W2C2 butterfly core geometry, when treated with PhC2H. In contrast, its tricobalt-tungsten analogue CO~W(CO)~~(~~-C~ H~M~) (lb) and the sterically congested tritungsten cluster COW,(C0)9($-CsH4Me)3 (3) rupture when treated with PhC2H. The products included PhC2H oligomers, the cobalt tungstenacycle (~s-CsH4Me)(OC)2W(r-~z,~4-C(Ph)C(H)C(H)C(Ph)~Co(CO)2

Chemistry of polynuclear metal complexes with bridging carbene or carbyne ligands. Part 70. Tetranuclear metal compounds with rhenium–molybdenum or –tungsten bonds. Crystal structures of [Mo2Re2(µ3-CC6H4Me-4)2(µ-CO)2(CO)7(η-C5H5)2]·1.5CH2Cl2and [W2Re2(µ-H)(µ3-σ:σ′:η2-CCH2)(µ3-CMe)(µ-CO)(CO)8(η-C5H5)2

Reactions between the compounds [M(CC6H4Me-4)(CO)2(η-C5H5)](M = Mo or W) and [Re2(µ-H)(µ-σ:η-CHCHBun)(CO)8] afford the tetranuclear metal complexes [M2Re2(µ3-CC6H4Me-4)2(µ-CO)2(CO)7(η-C5H5)2]. The corresponding reaction between [W(CMe)(CO)2(η-C5H5)] and the dirhenium compound yields a mixture of the cluster compounds [W2Re2(µ3-CMe)2(µ-CO)2(CO)7(η-C5H5)2], [W2Re2(µ-H)(µ3-σ:σ′:η2-CCH2)(µ3-CMe)(µ-CO)(CO)8(η-C5H5)2], and [WRe2(µ3CMe)(CO)10(η-C5H5)]. The molecular structures of [Mo2Re2(µ3-CC6H4Me-4)2(µ-CO)2(CO)7(η-C5H5)2]·1.5CH2Cl2 and [W2Re2(µ-H)(µ3-σ:σ′:η2-CCH2)(µ3-CMe)(µ-CO)(CO)8(η-C5H5)2] have been established by X-ray diffraction studies. Crystals of the former contain two very similar crystallographically independent molecules in the asymmetric unit and there are three molecules of CH2Cl2 of crystallisation. The structure has a tetrahedral core of metal atoms (mean metal–metal separations 2.914 A) with two of the faces of the tetrahedron capped by p-tolylmethylidyne ligands and two of the Mo–Re edges of the tetrahedron asymmetrically bridged by CO groups [Mo–C–O 155(3) and 157(3)°]. Each rhenium atom carries three orthogonal terminal CO ligands, with the remaining CO group being terminally attached to a molybdenum atom. As expected, the C5H5 moieties ligate the Mo atoms. In [W2Re2(µ-H)(µ3-σ:σ′:η2-CCH2)(µ3-CMe)(µ-CO)(CO)8(η-C5H5)2] the four metal atoms adopt a near-planar ‘butterfly’ arrangement, having a W–Re spine [2.923(1)A] and with a W and a Re atom at the wing-tip positions. The W2Re triangle is capped by a CMe group which lies perceptibly closer to the tungsten atoms than the rhenium. On the other side of the W2Re2 plane, the WRe2 triangle is triply bridged by the CCH2 group. The latter is σ bonded to the W and Re atoms which form the spine of the butterfly, and is η2-co-ordinated to the Re atom at the wing-tip position. A CO ligand asymmetrically bridges [W–C–O 159(2)°] the W–Re edge of the WRe2 triangle and, although not located by X-ray diffraction, the hydrido ligand must bridge the Re–Re edge [3.023(1)A], since the latter is perceptibly longer than the other metal–metal separations (mean 2.951 A). Each rhenium atom is ligated by three terminal CO groups, and the tungsten atom is co-ordinated by two such groups. There is a C5H5 ligand bonded to each tungsten centre. The 1H and 13C-{1H} n.m.r. spectra of the new compounds are reported and discussed.

Chemistry of the unsaturated cluster compound [Os3Pt(µ-H)2(CO)10{P(cyclo-C6H11)3}]; X-ray crystal structures of [Os3Pt(µ-H)2(CO)11{P(cyclo-C6H11)3}], [Os3Pt(µ-H)4(CO)10{P(cyclo-C6H11)3}], and [Os3Pt(µ-H)2(µ-CH2)(CO)10–{P(cyclo-C6H11)3}](two isomers)

Reactions of the unsaturated cluster compound [Os3Pt(µ-H)2(CO)10{P(cyclo-C6H11)3}] with hydrogen and with diazomethane have been investigated, and the structures of the products determined by X-ray diffraction. The structure of the previously prepared carbon monoxide adduct [Os3Pt(µ-H)2(CO)11{P(cyclo-C6H11)3}] has also been established. The latter species, which is formed in a readily reversed reaction, has a ‘butterfly’ arrangement of the metal atoms with the platinum atom at a wing-tip position. One hydrido-ligand bridges the Os–Os vector of the body of the butterfly, and the other an Os–Pt edge. The latter is cis to the P (cyclo-C6H11)3 group on the platinum, which also carries a CO ligand. The osmium atom at the other wing-tip is ligated by four CO groups, and the remaining two Os are each terminally bonded to three carbonyls. The hydrogen adduct [Os3Pt(µ-H)4(CO)10{P(cyclo-C6H11)3}] is also formed reversibly but in contrast with the product from carbon monoxide has a closo-tetrahedral metal core. The hydrido-ligands occupy edge-bridging sites on the cluster framework, with two bridging Os–Pt vectors [cis to the P(cyclo-C6H11)3 ligand on platinum] and two bridging Os–Os vectors. Thus the M4 tetrahedron has D2d symmetry with two short unbridged edges and four longer bridged edges. Diazomethane readily adds to [Os3Pt(µ-H)2(CO)10{P(cyclo-C6H11)3}] to give the complex [Os3Pt(µ-H)2(µ-CH2)-(CO)10{P(cyclo-C6H11)3}] which exists as an equilibrium mixture of two isomeric forms (orange-yellow and red crystals). Both species have a closo distorted tetrahedral geometry for the metal atoms, with the methylene group bridging an Os–Os edge cisoid to the P(cyclo-C6H11)3 ligand on the platinum in the orange-yellow form and transoid to the phosphine group in the red isomer. The relative positions of the hydrido-ligands also differ. In the orange-yellow form they bridge the remaining two Os–Os edges, while although not located directly in the red isomer, being assigned on potential-energy grounds, they bridge an Os–Os edge and the Os–Pt edge cis to the P(cyclo-C6H11)3 ligand. N.m.r. studies reveal that the two isomers maintain these solid-state structures in solution. The mechanism of formation of the two isomers is discussed in the context of the orange-yellow form being the kinetically controlled product, which after several days in solution establishes a 1 : 4 equilibrium with the red form.