Synthesis and X-ray crystal structures of amine bis(phenolate) lanthanide complexes containing alkali metal cation

Three lanthanide “ate” complexes L₂YbM(THF)_n supported by amine bis(phenolate) ligand [L=Me₂NCH₂CH₂N{CH₂-(2-O-C₆H₂-Bu^t₂-2,4)}₂; M=Li, n=2 (1); M=Na, n=2 (2); M=K, n=3 (3)] were synthesized by the metathesis reactions of LM₂ with anhydrous YbCl₃ in 2:1 molar ratio in high yield. All the complexes were characterized by elemental analysis, IR spectroscopy and single-crystal X-ray diffraction. The influence of the alkali metal ions on the molecular structure of these lanthanide complexes has been elucidated.     

Synthesis, characterization and reactivity of heteroleptic rare earth metal bis(phenolate) complexes

The synthesis, characterization and reactivity of heteroleptic rare earth metal complexes supported by the carbon-bridged bis(phenolate) ligand 2,2'-methylene-bis(6-tert-butyl-4-methyl-phenoxo) (MBMP(2-)) are described. Reaction of (C(5)H(5))(3)Ln(THF) with MBMPH(2) in a 1 : 1.5 molar ratio in THF at 50 degrees C produced the heteroleptic rare earth metal bis(phenolate) complexes (C(5)H(5))Ln(MBMP)(THF)(n) (Ln = La, n = 3 (); Ln = Yb (), Y (), n = 2) in nearly quantitative yields. The residual C(5)H(5)(-) groups in complexes to can be substituted by the bridged bis(phenolate) ligands at elevated temperature to give the neutral rare earth metal bis(phenolate) complexes, and the ionic radii have a profound effect on the structures of the final products. Complex reacted with MBMPH(2) in a 1 : 0.5 molar ratio in toluene at 80 degrees C to produce a dinuclear complex (MBMP)La(THF)(mu-MBMP)(2)La(THF)(2) () in good isolated yield; whereas complexes and reacted with MBMPH(2) under the same conditions to give (MBMP)Ln(MBMPH)(THF)(2) (Ln = Yb (), Y ()) as the final products, in which one hydroxyl group of the phenol is coordinated to the rare earth metal in a neutral fashion. The reactivity of complexes and with some metal alkyls was explored. Reaction of complex with 1 equiv. of AlEt(3) in toluene at room temperature afforded unexpected ligand redistributed products, and a discrete ion pair ytterbium complex [(MBMP)Yb(THF)(2)(DME)][(MBMP)(2)Yb(THF)(2)] () was isolated in moderate yield. Furthermore, reaction of complex with 1 equiv. of ZnEt(2) in toluene gave a ligand redistributed complex [(mu-MBMP)Zn(THF)](2) () in reasonable isolated yield. Similar reaction of complex with ZnEt(2) also afforded complex ; whereas the reaction of complex with 1 equiv. of n-BuLi in THF afforded the heterodimetallic complex [(THF)Yb(MBMP)(2)Li(THF)(2)] (). All of these complexes were well characterized by elemental analyses, IR spectra, and single-crystal structure determination, in the cases of complexes , and -.     

Thermochemical and structural investigations on alkali metal chlorides-iron(III)-chloride systems

The pseudobinary systems ACl?FeCl₃ (A=Na, K, Rb, Cs) were reinvestigated by means of differential thermal analysis and X-ray powder diffraction. The existence of the compounds AFeCl₄ (A=Na?Cs) and Cs₃Fe₂Cl₉ could be confirmed; Cs₃Fe₂Cl₉ is a stable compound which decomposes to CsCl and CsFeCl₄ above 270°C. Additionally, two Rb-compounds—Rb₃FeCl₆ and Rb₃Fe₂Cl₉—were found, which decompose, when heated, in the solid state. Rb₃Fe₂Cl₉ is isotypic with the analogous Cs-compound; Rb₃FeCl₆ has the Cs₃BiCl₆ structure. Cs₃FeCl₆ is isotypic with Cs₃CrCl₆, a recently found orthorhombic variant of the elpasolite type.     

Synthetic, structural, and theoretical investigations of alkali metal germanium hydrides--contact molecules and separated ions

The preparation of a series of crown ether ligated alkali metal (M=K, Rb, Cs) germyl derivatives M(crown ether)_nGeH₃ through the hydrolysis of the respective tris(trimethylsilyl)germanides is reported. Depending on the alkali metal and the crown ether diameter, the hydrides display either contact molecules or separated ions in the solid state, providing a unique structural insight into the geometry of the obscure GeH₃^? ion. Germyl derivatives displaying M? Ge bonds in the solid state are of the general formula [M([18]crown‐6)(thf)GeH₃] with M=K ( 1 ) and M=Rb ( 4 ). The compounds display an unexpected geometry with two of the GeH₃ hydrogen atoms closely approaching the metal center, resulting in a partially inverted structure. Interestingly, the lone pair at germanium is not pointed towards the alkali metal, rather two of the three hydrides are approaching the alkali metal center to display M? H interactions. Separated ions display alkali metal cations bound to two crown ethers in a sandwich‐type arrangement and non‐coordinated GeH₃^? ions to afford complexes of the type [M(crown ether)₂][GeH₃] with M=K, crown ether=[15]crown‐5 ( 2 ); M=K, crown ether=[12]crown‐4 ( 3 ); and M=Cs, crown ether=[18]crown‐6 ( 5 ). The highly reactive germyl derivatives were characterized by using X‐ray crystallography, ¹H and ¹³C NMR, and IR spectroscopy. Density functional theory (DFT) and second‐order Møller–Plesset perturbation theory (MP2) calculations were performed to analyze the geometry of the GeH₃^? ion in the contact molecules 1 and 4 .     

Synthesis and structural chemistry of alkali metal tris(HMDS) magnesiates containing chiral diamine donor ligands

Six alkali metal tris(HMDS) magnesiate complexes (HMDS, 1,1,1,3,3,3,-hexamethyldisilazide) containing chiral diamine ligands have been prepared and characterised in both the solid- and solution-state. Four of the complexes have a solvent-separated ion pair composition of the form [{M·(chiral diamine)(2)}(+){Mg(HMDS)(3)}(-)] [M = Li for 1 and 3, Na for 2 and 4; chiral diamine = (-)-sparteine for 1 and 2, (R,R)-TMCDA for 3 and 4, (where (R,R)-TMCDA is N,N,N',N'-(1R,2R)-tetramethylcyclohexane-1,2-diamine)] and two have a contacted ion pair composition of the form [{K·chiral diamine}(+){Mg(HMDS)(3)}(-)](n) [chiral diamine = (-)-sparteine for 5 and (R,R)-TMCDA for 6]. In the solid-state, complexes 1-4 are essentially isostructural, with the lithium or sodium cation sequestered by the respective chiral diamine and the previously reported anion consisting of three HMDS ligands coordinated to a magnesium centre. As such, complexes 1-4 are the first structurally characterised complexes in which the alkali metal is sequestered by two molecules of either of the chiral diamines (-)-sparteine (1 and 2) or (R,R)-TMCDA (3 and 4). In addition, complex 4 is a rare (R,R)-TMCDA adduct of sodium. In the solid state, complexes 5 and 6 exist as polymeric arrays of dimeric [{K·chiral diamine}(+){Mg(HMDS)(3)}(-)](2) subunits, with 5 adopting a two-dimensional net arrangement and 6 a linear arrangement. As such, complexes 5 and 6 appear to be the only structurally characterised complexes in which the chiral diamines (-)-sparteine (5) or (R,R)-TMCDA (6) have been incorporated within a polymeric framework. In addition, prior to this work, no (-)-sparteine or (R,R)-TMCDA adducts of potassium had been reported.     

Pulse radiolysis and voltammetry of bis(diamine)dioxorhenium(V) complexes

The Re(V) complexes [Re(L)₂O₂]⁺ [L = en (1,2-diaminoethane) or pn (1,3-diaminopropane)] are reduced irreversibly near −1.5 V (SCE) in a neutral or basic aqueous solution, but protonation causes a significant anodic shift of ≈ + 1 V. No oxidation is observed in aqueous solution before the solvent limit (≈ + 1 V) at solid electrodes but oxidation of [Re(en)₂O₂]⁺ with OH in pulse radiolysis experiments generates a Re(VI) intermediate which decays by first-order kinetics (k_d 2.5 × 10⁴ s⁻¹), apparently by rate-determining ligand loss. Reduction with e⁻_aq likewise forms transient d³-Re(IV) complexes which show first-order decay (6 × 10³ s⁻¹ for en, 9 × 10³ s⁻ for pn), ultimately to ReO₂. Transient intermediates were characterized by their electronic spectra, which for d³-Re(IV) complexes are qualitatively similar to Cr(III) and known octahedral Re(IV) complexes with different donor ligands.     

Titanium complexes with sulfur‐linked bis(phenolate) ligands

High‐quality crystals of two bis(phenolate)titanium complexes, namely dichlorido{4,4′‐dimethyl‐2,2′‐[cyclohexane‐1,2‐diylbis(sulfanediyl)]diphenolato}titanium(IV), [Ti(C₂₀H₂₂O₂S₂)Cl₂], (I), and dichlorido{2,2′‐[cyclohexane‐1,2‐diylbis(sulfanediyl)]diphenolato}titanium(IV), [Ti(C₁₈H₁₈O₂S₂)Cl₂], (II), were obtained by reactive crystallization. Depending on the solvent, compound (II) was obtained as unsolvated (IIa) or as the toluene hemisolvate, [Ti(C₁₈H₁₈O₂S₂)Cl₂]·0.5C₇H₈, (IIb). These systems without bulky substituents on the aromatic phenolate rings serve as ideal model compounds for precatalysts. The excellent X‐ray diffraction data will help clarify the nature of the mismatched interactions between the soft S atoms within the ligand and the hard titanium center. Molecule (I) has crystallographic C₂ symmetry.     

Synthesis, characterization, and lactide polymerization activity of group 4 metal complexes containing two bis(phenolate) ligands

A series of group 4 metal complexes Zr-(1)(2), Zr-(2)(2), Zr-(3)(2), Zr-(4)(2), Zr-(5)(2), Hf-(1)(2), and Hf-(4)(2) containing two bridged bis(phenolate) ligands of the (OSSO)-type were prepared by the reaction of the corresponding bis(phenol) and group 4 metal precursor MX(4) (X = O(i)Pr, CH(2)Ph) and isolated as robust, colorless crystals. NMR spectra indicate D(2) symmetry, in agreement with the solid state structure determined by single crystal X-ray diffraction study of the complexes Zr-(1)(2), Hf-(1)(2), Zr-(3)(2), Zr-(4)(2), and Zr-(5)(2). The complexes with the 1,4-dithiabutanediyl bridged ligands exhibit a highly symmetric coordination around the metal center. The introduction of the rigid trans-1,2-cyclohexanediyl bridged ligands led to a distorted coordination around the metal center in Zr-(4)(2) and Zr-(5)(2) when the ortho substituent is tert-butyl and the para substituent is larger than methyl. The complexes Zr-(1)(2), Zr-(2)(2), Zr-(3)(2), Zr-(4)(2) as well as Hf-(1)(2) and Hf-(4)(2) initiated the ring-opening polymerization of meso-lactide at 100 °C to give heterotactic polylactide with pronounced heterotacticity (>70%) and varying polydispersity (1.05 < M(w)/M(n) < 1.61). As shown by kinetic studies, zirconium complex Zr-(1)(2) polymerized meso-lactide faster than the homologous hafnium complex Hf-(1)(2).     

Aerobic oxidation reactions catalyzed by vanadium complexes of bis(phenolate) ligands

Vanadium(V) complexes of the tridentate bis(phenolate)pyridine ligand H(2)BPP (H(2)BPP = 2,6-(HOC(6)H(2)-2,4-(t)Bu(2))(2)NC(5)H(3)) and the bis(phenolate)amine ligand H(2)BPA (H(2)BPA = N,N-bis(2-hydroxy-4,5-dimethylbenzyl)propylamine) have been synthesized and characterized. The ability of the complexes to mediate the oxidative C-C bond cleavage of pinacol was tested. Reaction of the complex (BPP)V(V)(O)(O(i)Pr) (4) with pinacol afforded the monomeric vanadium(IV) product (BPP)V(IV)(O)(HO(i)Pr) (6) and acetone. Vanadium(IV) complex 6 was oxidized rapidly by air at room temperature in the presence of NEt(3), yielding the vanadium(V) cis-dioxo complex [(BPP)V(V)(O)(2)]HNEt(3). Complex (BPA)V(V)(O)(O(i)Pr) (5) reacted with pinacol at room temperature, to afford acetone and the vanadium(IV) dimer [(BPA)V(IV)(O)(HO(i)Pr)](2). Complexes 4 and 5 were evaluated as catalysts for the aerobic oxidation of 4-methoxybenzyl alcohol and arylglycerol β-aryl ether lignin model compounds. Although both 4 and 5 catalyzed the aerobic oxidation of 4-methoxybenzyl alcohol, complex 4 was found to be a more active and robust catalyst for oxidation of the lignin model compounds. The catalytic activities and selectivities of the bis(phenolate) complexes are compared to previously reported catalysts.     

Synthesis and structural characterisation of novel linked bis(beta-diketiminato) rare earth metal complexes

Rare earth metal complexes based on novel linked bis(beta-diketiminato) ligands have been prepared via amine elimination and their structural characterisation revealed that the linker unit has significant influence on the geometry and coordination mode of the ancillary ligand.     

Synthesis and structural characterization of novel mixed-valent samarium and divalent ytterbium and europium complexes supported by amine bis(phenolate) ligands

The amine-elimination reactions of Ln[N(SiMe3)2]2(THF)2(Ln=Sm, Yb and Eu) with amine bis(phenol)s (L1H2=[BunN(CH(2)-2-OC6H(2)-3,5-But2)2]H2; L2H2=[Me2NCH2CH2N(CH(2)-2-OC6H(2)-3,5-But2)2]H2) were investigated. It was found that the number of heteroatom(s) in the ligands has a profound effect on the reaction outcome for the samarium systems. Reaction of the tetradentate diamino-bis(phenol)s L2H2 with Sm[N(SiMe3)2]2(THF)2 afforded a yellow solution, which indicated the complete oxidation of the SmII species, yellow being the characteristic color of SmIII species, while the same reaction with Eu[N(SiMe3)2]2(THF)2 gave a divalent complex with a dimeric structure (EuL2)2. Using the tridentate amine bis(phenol)s L1H2 as the reagent, the novel mixed-valent samarium complex SmIII2SmIIL1(4) was prepared by the same reaction. Both reactions of L1H2 with Yb[N(SiMe3)2]2(THF)2 and Eu[N(SiMe3)2]2(THF)2 yielded the normal divalent lanthanide complexes: monomeric complex for YbII, YbL1(THF)3 and dimeric complex for EuII, (EuL1)2. All of the complexes are well characterized with elemental analyses, IR and 1H NMR spectra for , and , as well as X-ray crystal structure determination in the cases of complexes , , and .     

Structural diversity of indium complexes containing a tetradentate (OSSO)-type bis(phenolate) ligand

Indium bis(phenolato) complexes [{In(CH₃)₂(THF)}₂(L)] (L = 1,4-dithiabutanediylbis(4,6-di-tert-butylphenolato) (etbbp), 2) and [In(cytp)(CH₃)]₂ (L = (1,2-cyclohexanediyldithio)-2,2′-diphenolato (rac-cytp), 3) were prepared from [In(CH₃)₃] and the tetradentate 1,2-dithiaalkanediyl-bridged bis(phenol) LH₂. The nature of the ligand bridging two indium centers was shown by X-ray diffraction studies of the complex [{In(CH₃)₂(THF)}₂(etbbp)] (2) that was synthesized from complex [In(etbbp)(CH₃)(THF)_n] (1) by reaction with a second equivalent of [In(CH₃)₃]. A related ligand without bulky substituents on the aromatic rings leads to the dimeric compound [In(cytp)(CH₃)]₂ (3) with distorted octahedral configuration in the solid state. It was converted into the cation [In(cytp)]⁺ by methyl abstraction with [B(C₆F₅)₃].     

Synthesis of mono- and geminal dimetalated carbanions of bis(phenylsulfonyl)methane using alkali metal bases and structural comparisons with lithiated bis(phenylsulfonyl)imides

The alpha,alpha'-stabilized carbanion complexes [(PhSO2)2CHLi.THF]1, [(PhSO2)2CHNa.THF]2 and [(PhSO2)2CHK]3 were prepared by the direct deprotonation of bis(phenylsulfonyl)methane I in THF with one molar equivalent of MeLi, BuNa and BnK respectively. The geminal dianionic complexes [(PhSO2)2CLi2.THF]4, [(PhSO2)2CNa2.0.55THF]5 and [(PhSO2)2CK2]6 were similarly prepared by the reaction of I with two molar equivalents of MeLi, BuNa and BnK respectively in THF. NMR and MS solution studies of 1-3 are consistent with the formation of charge-separated species in DMSO media. Solutions studies of 4-6, in conjunction with trapping experiments, indicate that the dianions deprotonate DMSO and regenerate the monoanions 1-3. Crystallographic analysis of 1 revealed a 1D chain polymer in which the metal centers are chelated by the bis(sulfonyl) ligands and connect to neighboring units through Li-O(S) interactions. An unexpected feature of 1 is that the polymeric chains are homochiral, since the chelating ligands of the backbone adopt the same relative configuration. Also, the phenyl substituents of each chelate in 1 are oriented in a cisoid manner. The sodium derivative 2 adopts a related solid-state structure, where enantiomeric pairs of chains combine to give a 1D ribbon motif. The lithium bis(phenylsulfonyl)imides [(PhSO2)2NLi.THF]9 and [(PhSO2)2NLi.Pyr2]10 were also prepared and structurally characterized. In the solid state 9 has a similar connectivity to that found for 1 but with heterochiral chains. In comparison, the more highly solvated complex 10 forms a 1D polymeric arrangement without chelation of the ligands and with the phenyl substituents oriented in a transoid fashion.     

Zwitterionic bis(phenolate)amine lanthanide complexes for the ring-opening polymerisation of cyclic esters

The reaction of Sm{N(SiMe3)2}3 with the bis(phenol)amines H2O2N(R) (H2O2N(R) = RCH2CH2N(2-HO-3,5-C6H2(t)Bu2)2; R = OMe, NMe2 or Me) gave exclusively zwitterions Sm(O2N(R))(HO2N(R)). For R = OMe or NMe2 these were efficient catalysts for the ring-opening polymerisation of epsilon-caprolactone and D,L-lactide with a tendency to form cyclic esters; in contrast, no polymerisation was observed for R = Me.     

Optical investigations of alkali metal thiomanganates(II) containing isolated complexes as well as chain and planar compounds

Tetracoordinated Mn(II) complexes providing different molecular structures were investigated using various spectroscopical procedures. Na(6)MnS(4) contains separate pseudotetrahedral Mn-S complex units, K(2)MnS(2) has chains of edge-shared tetrahedra, and Cs(2)Mn(3)S(4) crystallizes in corresponding layers. Also doped materials, i.e., Cs(2)(Mn(x)Zn(1-x))(3)S(4) with 0.0 < x < 1.0, are considered. Absorption spectra recorded from samples incorporated in polyethylene pellets and excitation spectra taken from pure materials at 15-20 K temperature are assigned on the basis of energy level calculations obtained from the angular overlap model. All compounds exhibit intensive emission in the red, some of them also in the yellow region, which both are investigated in the temperature range from 12.5 to 250 K, in some cases varying the excitation power and excitation wavelength. Decay measurements supply lifetimes and activation energies evaluated from Arrhenius plots. The results support an assignment of both types of emissions to MnS(4) complex entities for all compounds, the red emission from the lowest excited level (Kasha luminescence) and the yellow emission, observed for some of the compounds with increasing intensity at lower temperature, from higher electronic levels.     

Electrochemical and spectroscopic effects of mixed substituents in bis(phenolate)-copper(II) galactose oxidase model complexes

Nonsymmetric substitution of salen (1(R(1),R(2))) and reduced salen (2(R(1),R(2))) Cu(II)-phenoxyl complexes with a combination of -(t)Bu, -S(i)Pr, and -OMe substituents leads to dramatic differences in their redox and spectroscopic properties, providing insight into the influence of the cysteine-modified tyrosine cofactor in the enzyme galactose oxidase (GO). Using a modified Marcus-Hush analysis, the oxidized copper complexes are characterized as Class II mixed-valent due to the electronic differentiation between the two substituted phenolates. Sulfur K-edge X-ray absorption spectroscopy (XAS) assesses the degree of radical delocalization onto the single sulfur atom of nonsymmetric [1((t)Bu,SMe)](+) at 7%, consistent with other spectroscopic and electrochemical results that suggest preferential oxidation of the -SMe bearing phenolate. Estimates of the thermodynamic free-energy difference between the two localized states (ΔG(o)) and reorganizational energies (λ(R(1)R(2))) of [1(R(1),R(2))](+) and [2(R(1),R(2))](+) lead to accurate predictions of the spectroscopically observed IVCT transition energies. Application of the modified Marcus-Hush analysis to GO using parameters determined for [2(R(1),R(2))](+) predicts a ν(max) of ～13600 cm(-1), well within the energy range of the broad Vis-NIR band displayed by the enzyme.     

Transition metal complexes of bis(diphenylphosphine oxide)methane

Complexes of bis(diphenylphosphine oxide)methane with Fe(III), Ni(II), Co(II), Cu(II) and Zn(II) have been prepared and characterized. Experimental data are in support of chelation by the ligand to give 6-coordinate metal ions. The properties of the complexes are similar to those for the corresponding complexes of octamethylpyrophosphoramide.     

Coordination chemistry of amine bis(phenolate) cobalt(II), nickel(II), and copper(II) complexes

Cobalt(II), nickel(II), and copper(II) (1, 2, and 3) complexes of the dianionic form of the bis(phenolate) ligand N,N-bis(3,4-dimethyl-2-hydroxybenzyl)-N',N'-dimethylethylenediamine (H2L) have been synthesized by electrochemical oxidation of the appropriate metal in an acetonitrile solution of the ligand. When copper is used as the anode, the addition of 1,10-phenanthroline to the electrolytic phase gave rise to a different compound [CuL]2.2CH3CN (4). The compounds [CoL]2.2CH3CN (1), [Ni2L2(H2O)].H2O (2), [CuL]2.3H2O (3), and [CuL]2.2CH3CN (4) were characterized by microanalysis, IR, electronic spectroscopy, FAB mass spectrometry, magnetic measurements and by single-crystal X-ray diffraction. The crystal structures show that the complexes have a dinuclear structure. In compounds 1, 3, and 4, two metal ions are coordinated by the two amine nitrogens and the two phenol oxygen atoms of a deprotonated pendant phenol ligand, with one phenolic oxygen atom from ligand acting as a bridge. In compounds 1 and 3, each metal center has a geometry that is closest to trigonal bipyramidal. Magnetic susceptibility data for both compounds show an antiferromagnetic coupling with 2J = -15 cm(-1) for the cobalt(II) complex and a strong antiferromagnetic coupling with 2J = -654 cm(-1) for the copper(II) complex. However, in 4 the geometry around the metal is closer to square pyramidal and the compound shows a lower antiferromagnetic coupling (2J = -90 cm(-1)) than in 3. The nickel atoms in the dimeric compound 2 are hexacoordinate. The NiN2O4 chromophore has a highly distorted octahedral geometry. In this structure, a dianionic ligand binds to one nickel through the two amine nitrogen atoms and the two oxygen atoms and to an adjacent nickel via one of these oxygen atoms. The nickel atoms are linked through a triple oxygen bridge involving two phenolic oxygens, each from a different ligand, and an oxygen atom from a water molecule. The two nickel ions in 2 are ferromagnetically coupled with 2J = 19.8 cm(-1).     

Infrared spectra of bis(aniline) and bis (p-toluidine) metal(II) isothiocyanate complexes

The infrared spectra of eight complexes of general formula [ML₂(NCS)₂] (M = Co, Ni, Cu, Zn; L = aniline or p-toluidine) have been determined over the range 4000–4150 cm^?1. Colour, magnetic moments and IR spectra are consistent with polymeric octahedral coordination in the Co(II) and Ni(II) complexes and polymeric tetragonal coordination in the Cu(II) complexes, while the Zn(II) complexes are assigned polymeric octahedral (L = aniline) and tetrahedral (L = p-toluidine) structure on the basis of their IR spectra. Independent ¹⁵N-labelling of the nitrogen atoms of the amino and isothiocyanate groups yields assignments for the internal vibrations of both groups and enables the metal-amine and metal—isothiocyanate stretching vibrations (vM-NH₂ and vM-NCS) to be distinguished. Both vM-NH₂ and vM-NCS are metal ion dependent in the Irving-Williams sequence (Co < Ni < Cu > Zn) expected from their proposed structures while the vN-H and vN-CS vibrations are inversely related to the masses of the coordinated metal ions.