Synthesis of Me2LSn(o-CH3-C2B10H10): Crystal structure of Sn ← O intramolecularly coordinated organotin compound containing 1-methyl-o-carborane

The synthesis and molecular structure of Me₂LSn(1-Me-1,2-C₂B₁₀H₁₀) (3), L is 2,6-(t-BuOCH₂)₂C₆H₃⁻, the precursor for the synthesis of other Sn ← O intramolecularly coordinated organotin(IV) compounds containing 1-methyl-o-carborane (1-Me-1,2-C₂B₁₀H₁₁) is reported. Compound 3 was characterized by the help of ¹H, ¹¹B, ¹³C, ¹¹⁹Sn NMR spectroscopy and X-ray diffraction technique. For the preparation of 3, a novel triorganotin(IV) compound Me₂LSnCl (2) has been prepared since the reaction of sterically more demanding Ph₂LSnCl (1) with 1-Me-1,2-C₂B₁₀H₁₀Li did not occur.     

Towards the mechanism of heteroborane isomerisation: 1,2 → 1,2 and 1,2 → 1,7 low-temperature isomerisations from metallations of [5-I-7,8-Ph2-7,8-nido-C2B9H8]

The reaction between [5-I-7,8-Ph₂-7,8-nido-C₂B₉H₈]²⁻ and NiCl₂(dppe) affords 1,2-Ph₂-4,4-dppe-12-I-4,1,2-closo-NiC₂B₉H₈ (1) and 1,8-Ph₂-2,2-dppe-10-I-2,1,8-closo-NiC₂B₉H₈ (2). Reaction between the same carborane ligand and cis-PtCl₂(PMe₂Ph)₂ yields three species, 1,8-Ph₂-2,2-(PMe₂Ph)₂-10-I-2,1,8-closo-PtC₂B₉H₈ (3), 1,8-Ph₂-2,2-(PMe₂Ph)₂-12-I-2,1,8-closo-PtC₂B₉H₈ (4), and 1,8-Ph₂-2,2-(PMe₂Ph)₂-7-I-2,1,8-closo-PtC₂B₉H₈ (5). Compounds 1-5 have been characterised spectroscopically and crystallographically. The 4,1,2-MC₂B₉ architecture of 1 constitutes a “1,2 → 1,2” cage C atom isomerisation, and the 2,1,8-MC₂B₉ architectures of 2-5 a 1,2 → 1,7 cage C atom isomerisation, relative to the presumed first product of the metallations, 1,2-Ph₂-3,3-L₂-9-I-3,1,2-closo-MC₂B₉H₈ [M = Ni, L₂ = dppe; M = Pt, L₂ = (PMe₂Ph)₂]. The location of the (iodide) labelled boron vertex in the products allows speculation as to the mechanism of these isomerisations and the possible involvement of triangle face rotation is discussed.     

Half-sandwich ruthenium thiocarbonate complexes: Structures of CpRu(PPh3)2SCO2Bu, CpRu(dppe)SCO2Bu and CpRu(PPh3)(CO)SCO2Bu

Thiocarbonate ruthenium complexes of the form CpRu(L)(L′)SCO₂R (L = L′ = PPh₃ (1), 1/2 dppe (2), L = PPh₃, L′ = CO (3); R = Et (a), Buⁿ (b), C₆H₅ (c), 4-C₆H₄NO₂ (d)) have been synthesized by the reaction of the corresponding sulfhydryl complexes, CpRu(L)(L′)SH, with chloroformates, ROCOCl, at low temperature. The bis(triphenylphosphine) complexes 1 can be converted to 3 under CO atmosphere. The crystal structures of CpRu(PPh₃)₂SCO₂Buⁿ (1b), CpRu(dppe)SCO₂Buⁿ (2b), and CpRu(PPh₃)(CO)SCO₂Buⁿ (3b) are reported.     

Synthesis, characterization and catalytic evaluation in the Heck coupling reactions of S-P-S pincer complexes of the type [Pd{PhP(C6H4-2-S)2}(PAr3)]

A series of palladium complexes of the type [Pd(phPS₂)(PAr₃)] (phPS₂) = [PhP(C₆H₄-2-S)₂]²⁻ have been synthesized in good yields and their crystal structures determined. Heck coupling reactions were carried out using the [Pd(phPS₂)(PPh₃)] (1), [Pd(phPS₂){P(C₆H₄-4-Cl)₃}] (2), [Pd(phPS₂){P(C₆H₄-4-F)₃}] (3), [Pd(phPS₂){P(C₆H₄-4-CF₃)₃}] (4), [Pd(phPS₂){P(C₆H₄-4-Me)₃}] (5) and [Pd(phPS₂){P(C₆H₄-4-OMe)₃}] (6) complexes as catalyst precursors in order to examine the potential effect of the para-substituted triarylphosphines in the reaction of bromobenzene and styrene.     

New aryl phosphinite ligands avoiding ortho-metallation: Synthesis and molecular structures of trans-[PdCl2(PPh2OR)2] and trans-[Rh(CO)Cl(PPh2OR)2] (R = 2,4,6-Me3C6H2; 2,6-Ph2C6H3)

The new aryl phosphinites PPh₂OR (R = 2,4,6-Me₃C₆H₂, 1; R = 2,6-Ph₂C₆H₃, 2) have been prepared from chlorodiphenylphosphine and the corresponding phenols. In these ligands, the ortho-positions of the aromatic phosphite function are blocked by methyl and phenyl substituents, which allows coordination to metal centres without ortho-metallation. Thus, reaction with [PdCl₂(cod)] leads to the complexes trans-[PdCl₂(PPh₂OR)₂] (R = 2,4,6-Me₃C₆H₂, 3; R = 2,6-Ph₂C₆H₃, 4), while the reaction with [Rh₂(CO)₄Cl₂] gives trans-[Rh(CO)Cl(PPh₂OR)₂] (R = 2,4,6-Me₃C₆H₂, 5; R = 2,6-Ph₂C₆H₃, 6). The single-crystal X-ray structure analyses of 3 and 5 confirm the trans-coordination of the new ligands in these square-planar complexes.     

Complexes of the {ReOX2} (X = Cl, Br) core with single amino acid chelate derivatives

The reactions of 1 equiv. of the ligand 3-(ethoxycarbonylmethyl-pyridin-2-ylmethyl-amino)-propionic acid methyl ester (2) with the Re(V) starting materials [ReOX₃(PPh₃)₂] (X = Cl, Br) in refluxing chloroform yielded the Re(V)-oxo dihalide complexes [ReOX₂{(C₅H₄NCH₂)N(CH₂CO₂)(C₂H₄CO₂CH₃)}] (X = Cl, 3; X = Br, 4). The complexes were characterized by elemental analysis, NMR and IR spectroscopy, cyclic voltammetry and X-ray crystallography. Complex 3 displays distorted octahedral coordination geometry with the tridentate ligand coordinating facially to the Re(V) center. The carboxylate oxygen atom occupies an axial site trans to the ReO bond. The two chlorine atoms consequently adopt a cis configuration.     

Bifunctional chelates with mixed aromatic and aliphatic amine donors for labeling of biomolecules with the {Tc(CO)3} and {Re(CO)3} cores

A series of tridentate ligands consisting of mixed aromatic and aliphatic amine derivatives of single amino acid chelates and phenylpiperazine have been developed, and their reactions with [NEt₄]₂[ReBr₃(CO)₃] have been investigated. The compounds [Re(CO)₃{(NC₅H₄CH₂)NCH₃(C₂H₄)NHCH₃}]Br (4), [Re(CO)₃{(NC₅H₄CH₂)NCH₃(C₂H₄)NCH₃(CH₂)_xCOOC₂H₅}]Br (x = 1, 5; x = 4, 6) [Re(CO)₃{(NC₅H₄CH₂)NH(C₂H₄)N(CH₃)₂}]Br (7), [Re(CO)₃{(NC₅H₄CH₂)N(CH ₂COOC₂H₅)(C₂H₄)N(CH₃)₂}]Br (8) and [Re(CO)₃(NC₅H₄CH₂)(C₂H₄NH₂)N(CH₂)₃-CH₃Ophenpip]Br (9) (phenpip: phenylpiperazine, -C₆H₄-(CH₂CH₂)₂N-) were prepared and characterized by elemental analysis, NMR, IR, HSMS and X-ray crystallography. All complexes exhibit fac-{Re(CO)₃N₃} coordination geometry in the cationic molecular unit. Crystal data for C₁₃H₁₇BrN₃O₃Re (4): orthorhombic, Pbca, a = 13.4510(8) Å, b = 10.5728(6) Å, c = 22.5378(13) Å, V = 3205.2(3) ų, Z = 8; C₁₇H₂₃BrN₃O₅Re (5): orthorhombic, Pcca, a = 16.5907(7) Å,b = 14.8387(6) Å, c = 16.7075(7) Å, V = 4113.1(3) ų, Z = 8; C₁₃H₂₅BrN₃O₇Re (7 · 4H₂O): monoclinic, P2₁/n, a = 14.0698(17) Å, b = 9.6760(12) Å, c = 15.6099 (19) Å, β = 114.930(2)°, V = 1927.1(4) ų, Z = 4; C₁₇H₂₃BrN₃O₅Re (8): monoclinic, P2₁/n, a = 7.5312(5) Å, b = 16.0366(10) Å, c = 16.8741(10) Å, β = 98.9990(10)°, V = 2012.9(2) ų, Z = 4.     

Complexes of N-thiophosphorylthioureas RNHC(S)NHP(S)(OiPr)2 (HL) (R = pyridin-2-yl, pyridin-3-yl, 6-amino-pyridin-2-yl) with copper(I): Crystal structures of Cu(PPh3)nL (n = 1, 2)

Reaction of the potassium salts of N-thiophosphorylated thioureas of common formula RNHC(S)NHP(S)(OiPr)₂ [R = pyridin-2-yl (HL^a), pyridin-3-yl (HL^b), 6-amino-pyridin-2-yl (HL^c)] with Cu(PPh₃)₃I in aqueous EtOH/CH₂Cl₂ leads to mononuclear [Cu(PPh₃)₂L^a,b-S,S′] (1, 2) and [Cu(PPh₃)L^c-S,S′] (3) complexes. Using copper(I) iodide instead of Cu(PPh₃)₃I, polynuclear complexes [Cu_n(L-S,S′)_n] (4-6) were obtained. The structures of these compounds were investigated by IR, ¹H, ³¹P{¹H} NMR spectroscopy, ES-MS and elemental analyses. The crystal structures of Cu(PPh₃)₂L^b (2) and Cu(PPh₃)L^c (3) were determined by single-crystal X-ray diffraction.     

The novel 1D chain and 3D network of mercury carborane-diphenylphosphine complexes constructed by covalent bond or hydrogen bond interactions

The closo- and nido-carborane-diphenylphosphine complexes [Hg₂{1,2-(PPh₂)₂-1,2-C₂B₁₀H₁₀}₂(μ-Cl₂)₂(μ-HgCl₂)₃]·2CH₂Cl₂ (1) and [HgCl(PPh₃){7,8-(PPh₂)₂-7,8-C₂B₉H₁₀}] (2) have been synthesized and characterized by elemental analysis, FT-IR and X-ray structure determination. The X-ray structure analysis for these two complexes showed that the carborane cage ligand was coordinated bidentately to the Hg(II) center through its two phosphorus atoms. The coordination geometry of the mercury atom complexed by P₂Cl₂ unit in complex 1 or P₃Cl unit in complex 2 was a distorted tetrahedron, while the mercury atom in complex 2 coordinated to six Cl atoms was a slightly distorted octahedron. X-ray analysis reveals that the complex 1 forms a 1D chain coordination polymer via bridged Hg-Cl bonds. For complex 2, it displays a 3D network constructed by the C-H···Cl hydrogen bonds and C-H···H-B dihydrogen bonds.     

Quantification of cis and trans influences in [PtX(PPh3)3] complexes. A P NMR study

In [PtX(PPh₃)₃]⁺ complexes (X = F, Cl, Br, I, AcO, NO₃, NO₂, H, Me) the mutual cis and trans influences of the PPh₃ groups can be considered constants in the first place, therefore the one bond Pt-P coupling constants of P_(cis) and P_(trans) reflect the cis and trans influences of X. The compounds [PtBr(PPh₃)₃](BF₄) (2), [PtI(PPh₃)₃](BF₄) (3), [Pt(AcO)(PPh₃)₃](BF₄) (4), [Pt(NO₃)(PPh₃)₃](BF₄) (5), and the two isomers [Pt(NO₂-O)(PPh₃)₃](BF₄) (6a) and [Pt(NO₂-N)(PPh₃)₃](BF₄) (6b) have been newly synthesised and the crystal structures of 2 and 4·CH₂Cl₂·0.25C₃H₆O have been determined. From the ¹J_PtP values of all compounds we have deduced the series: I > Br > Cl > NO₃ > ONO > F > AcO > NO₂ > H > Me (cis influence) and Me > H > NO₂ > AcO > I > ONO > Br > Cl > F > NO₃ (trans influence). These sequences are like those obtained for the (neutral) cis- and trans-[PtClX(PPh₃)₂] derivatives, showing that there is no dependence on the charge of the complexes. On the contrary, the weights of both influences, relative to those of X = Cl, were found to depend on the charge and nature of the complex.     

Synthesis, characterization and luminescence property of heterobimetallic trinuclear Mo(W)-Ag-S clusters containing 1,2-bis(diphenylphosphino)-1,2-dicarba-closo-dodecaborane

Reactions of (NH₄)₂MS₄ or (NH₄)₂MOS₃ (M = Mo, W) with AgSCN and closo carborane diphosphine ligand 1,2-(PPh₂)₂-1,2-C₂B₁₀H₁₀ (L) in CH₂Cl₂ yielded four heterobimetallic trinuclear Mo(W)-Ag-S clusters: [Ag₂MoS₄L₂] (1), [Ag₂WS₄L₂] (2), [Ag₂MoOS₃L₂] (3) and [Ag₂WS₄L₂] (4), respectively. All the new clusters have been characterized by elemental analysis, FT-IR, UV-Vis, ¹H and ¹³C NMR spectroscopy and their molecular structures (except for 3) were further confirmed by single-crystal X-ray diffraction. X-ray crystal structure analysis showed that the closo carborane diphosphine ligand was coordinated bidentately to Ag(I) atom through its two phosphorus atoms, resulting in a stable five-member chelating ring between the diphosphine ligand and the metal. The coordination sphere of the central M atom, as well as all the Ag atoms, was tetrahedron. The skeletons of these clusters could be classified into two types: with (NH₄)₂MS₄, the three metal atoms (two Ag atoms and one M atom) are in a linear conformation, while with (NH₄)₂MOS₃, the conformation of the heterobimetallic trinuclear cluster is butterfly shaped. The luminescence properties of the clusters were investigated in CH₂Cl₂ solution at room temperature and for the first time the butterfly-shaped Ag-W-S cluster containing the Ag₂WS₄ core has been proved to show luminescence property.     

Reactions of the fac-[Re(CO)3] and [ReO] moieties with substituted benzothiazoles

The reaction of 2-(2-aminophenyl)benzothiazole (Habt) with [Re(CO)₅Br] led to the isolation of the rhenium(I) complex fac-[Re(Habt)(CO)₃Br] (1). With trans-[ReOCl₃(PPh₃)₂], the ligand Habt decomposed to form the oxofree rhenium(V) complex [Re(itp)₂Cl(PPh₃)] (2) (itp = 2-amidophenylthiolate). From the reaction of trans-[ReOBr₃(PPh₃)₂] with 2-(2-hydroxyphenyl)benzothiazole (Hhpd) the complex [Re^VOBr₂(hpd)(PPh₃)] (3) was obtained. Complexes 1-3 are stable and lipophilic. ¹H NMR and infrared assignments, as well as the X-ray crystal structures, of the complexes are reported.     

Mapping the pathway of heteroborane isomerisation: Two parallel “1,2 → 1,7” isomerisations of a crowded molybdacarborane and the isolation of isomerisation intermediates

The reaction between [7,8-Ph₂-7,8-nido-C₂B₉H₉]²⁻ and [(η-C₇H₇)Mo(MeCN)₃]⁺ affords five products. Four have been isolated and shown to be structural isomers of (η-C₇H₇)MoPh₂C₂B₉H₉. Compound 1 has a pseudocloso structure. In solution it gives way to the non-icosahedral compound 2 which in turn rearranges into the “1,2 → 1,7” C-atom isomerised compound 5 having a 2,1,8-MoC₂B₉ structure. A further “1,2 → 1,7” C-atom isomerised species, compound 4, is also isolated but has a 1,2,4-MoC₂B₉ architecture. Compound 4 forms via an intermediate 3, which is too unstable to characterise. Structurally the sequence of compounds 1, 2 and 5 maps well onto the sequential diamond-square-diamond isomerisation mechanism of 1,2-closo-C₂B₁₀H₁₂ into 1,7-closo-C₂B₁₀H₁₂ proposed by Wales. An alternative pathway from the notional first product of the metallation, 1,2-Ph₂-3-(η-C₇H₇)-3,1,2-closo-MoC₂B₉H₉, is required to rationalise the intermediate compound 3 and, from it, compound 4.     

Sn-S and Ru-Ru bonds cleavage reactions between [Ph3SnS(CH2)3SSnPh3] and Ru3(CO)12: X-ray crystal structures of [Ph3SnS(CH2)3SSnPh3] and trans-[Ru(CO)4(SnPh3)2]

The organotin complex [Ph₃SnS(CH₂)₃SSnPh₃] (1) was synthesized by PdCl₂ catalyzed reaction between Ph₃SnCl and disodium-1,3-propanedithiolate which in turn was prepared from 1,2-propanedithiol and sodium in refluxing THF. Reaction of 1 with Ru₃(CO)₁₂ in refluxing THF affords the mononuclear complex trans-[Ru(CO)₄(SnPh₃)₂] (2) and the dinuclear complex [Ru₂(CO)₆(μ-κ²-SCH₂CH₂CH₂S)] (3) in 20 and 11% yields, respectively, formed by cleavage of Sn-S bond of the ligand and Ru-Ru bonds of the cluster. Treatment of pymSSnPPh₃ (pymS = pyrimidine-2-thiolate) with Ru₃(CO)₁₂ at 55-60 °C also gives 2 in 38% yield. Both 1 and 2 have been characterized by a combination of spectroscopic data and single crystal X-ray diffraction analysis.     

Bis(O2S2 macrocycle) complexes of palladium(II)

Two isomeric dibenzo-O₂S₂ macrocycles L¹ and L² have been synthesised and their coordination chemistry towards palladium(II) has been investigated. Two-step approaches via reactions of 1:1-type complexes, [cis-Cl₂LPd] (1a: L = L¹, 1b: L = L²), with different O₂S₂ macrocycle systems (L¹ and L²) have led to the isolation of the following bis(O₂S₂ macrocycle) palladium(II) complexes in the solid state: [Pd(L¹)₂](ClO₄)₂ (2a) and a mixture of [Pd(L¹)₂](ClO₄)₂ (2a) + [Pd(L²)₂](ClO₄)₂ (2b).     

Plasticity of the five-membered chelate ring in [PdCl2(1,2-(PR2)2-1,2-C2B10H10)] complexes (R = H or Pr)

Gradient-corrected density functional theory applied to 1,2-diphosphino-1,2-dicarba-closo-dodecaborane, 1,2-(PH₂)₂-1,2-C₂B₁₀H₁₀, and its respective PdCl₂ complex presents a clear picture of the effect of complexation on the P-C_c-C_c-P fragments (C_c = cage carbon C1 or C2) in the structures. The complexation results in clear closing in the P-C_c-C_c angles and shortening of C_c-C_c bond, but only minor changes take place in the P-C_c-C_c-P torsion angle. Furthermore, complexation brings along shortening of the P-C_c bonds with concomitant increase of covalency, as revealed by atoms-in-molecules calculations. Although there is also change in the C_c-C_c distance in the cage, no significant change is involved in the bonding. These findings are compared with the results obtained by single-crystal X-ray study for [PdCl₂(1,2-(PⁱPr₂)₂-1,2-C₂B₁₀H₁₀)] and additional calculations carried out for [PdCl₂(1,2-(PH₂)₂-C₂H₄)].     

Reaction of R(Ph)SnCl2(R=Me, Et) with 2,6-diacetylpyridine bis(thiosemicarbazone) (H2DAPTSC): the crystal structures of [Me(Ph)Sn(HDAPTSC)]Cl · 1.25 MeOH and [Et(Ph)Sn(H2DAPTSC)]Cl2 · MeOH · H2O

The reactions of Me(Ph)SnCl₂ and Et(Ph)SnCl₂ with 2,6-diacetylpyridine bis(thiosemicarbazone) (H₂DAPTSC) afforded the complexes [Me(Ph)Sn(HDAPTSC)]Cl · 1.25MeOH (1) and [Et(Ph)Sn(H₂DAPTSC)]Cl₂ · MeOH · H₂O (2), respectively. Single-crystal X-ray crystallography showed that in both complexes the ligand, monodeprotonated in 1 and neutral in 2, is S(1),S(2),N(3),N(4),N(5)-coordinated, and the coordination geometry around the metal can be described as a distorted pentagonal bipyramid with the aryl and alkyl groups in axial positions. ¹H and ¹¹⁹Sn NMR studies of solution in DMSO suggest that 2 dissociates completely in this solvent, while 1 evolves to the new complex [Me(Ph)Sn(DAPTSC)], with release of H₂DAPTSC and Me(Ph)SnCl₂. These conclusions were also supported by conductivity measurements.     

Synthesis and structural characterization of dinuclear iridium hydrido complex with 3,6-bis(2-pyridyl)tetrazine, [Ir2(H)4(PPh3)4(bptz)](PF6)2 · 4CH2Cl2

Reaction of the precursor Ir complex [Ir(H)₂(PPh₃)₂(Me₂CO)₂]PF₆ with 3,6-bis(2-pyridyl)tetrazine (bptz) in CH₂Cl₂ gave a novel dinuclear Ir hydrido complex [Ir₂(H)₄(PPh₃)₄(bptz)](PF₆)₂ · 4CH₂Cl₂. Crystallographic study described an interesting coordination environment having a π-π interaction and ¹H NMR study showed unique upfield shifts of pyridyl rings that are likely induced by the ring current effect of neighboring PPh₃ ligands.     

Synthesis, crystal structures and, antibacterial and antiproliferative activities in vitro of palladium(II) complexes of triphenylphosphine and thioamides

Palladium(II) complexes with triphenylphosphine (PPh₃) and thioamides of the general formulae, [Pd(L)₂(PPh₃)₂]Cl₂ and [Pd(L)₂(PPh₃)₂] have been prepared and characterized by elemental analysis, IR and NMR (¹H, ¹³C and ³¹P) methods, and two of them (trans-[Pd(PPh₃)₂(Dmtu)₂]Cl₂·(H₂O)(CH₃OH)_0.5 (1) and trans-[Pd(PPh₃)₂(Mpy)₂] (2)) by X-ray crystallography; where L = thiourea (Tu), methylthiourea (Metu), N,N′-dimethylthiourea (Dmtu), tetramethylthiourea (Tmtu), 2-mercaptopyridine (Mpy), 2-mercaptopyrimidine (Mpm) and thionicotinamide (Tna). The spectral data of the complexes are consistent with the sulfur coordination of thioamides to palladium(II). The crystal structures of the complexes show that (1) has ionic character consisting of [Pd(PPh₃)₂(Dmtu)₂]⁺² cations and uncoordinated Cl⁻ ions, while (2) is a neutral complex with Mpy behaving as anionic thiolate ligand. The coordination environment around palladium in (2) is nearly regular square-planar, while in (1) the trans angles show significant distortions from 180°. The complexes were screened for antibacterial effects, brine shrimps lethality bioassay and antitumor activity. These complexes showed significant activities in most of the cases against the tested bacteria as compared to that of a standard drug. Their antitumor activity against prostate cancer cells (PC3) is comparable with doxorubicin, together with no cytotoxic effects in brine shrimps lethality bioassay study.     

1-D coordination chains of Cu(hfac)2 and Mn(hfac)2 bridged by phenyl-nitronylnitroxide derivatives

Two alternating 1-D metal-radical linear [L:Cu(hfac)₂]_n and zig-zag [L:Mn(hfac)₂]_n chains (where L = 4-trimethylsilylethynyl-1-(4,4,5,5-tetramethyl-3-oxylimidazoline-1-oxide)benzene) and hfac = hexafluoroacetylacetonate) are described and characterized by X-ray diffraction of their crystals. Bulk magnetic measurements of L:Cu(hfac)₂ indicated a ferromagnetic interaction with J = 6 cm⁻¹ and L:Mn(hfac)₂ yielded ferrimagnetic interactions with J = −95 cm⁻¹. For the latter, a strong increase of their magnetic moment at lowest temperatures was observed only at very low static magnetic field, while for H_dc > 0.05 T saturation effect led to a downward slope after reaching a maximum.