A partial recurrence relation for reduced class coefficients of the symmetric group

An expression for the product of a single-cycle class [(1)^{N - P}(p)]_N and an arbitrary class [(1)^l1(2)^l …? (N)^lN]_N of the symmetric group has recently been conjectured. This expression involves a sum over a relatively small number of reduced class sums, depending on p indices. A further conjecture is formulated and demonstrated, according to which reduced class coefficients (RCCS ) involving cycles whose length is expressed by means of a single index can be related to corresponding coefficients in the product of [(1)^{N - P+1}(p - 1)]_N with an arbitrary class sum. Consequently, the problem of evaluating the general class sum product reduces to that of obtaining a relatively small set of fundamental RCCS containing no single-index cycles. The conjectures mentioned can be used to evaluate the product [(1)^{N - p}(p)]_N · [(1)^{N - q}(q)]_N in terms of fundamental RCCS that can all be obtained from the product [(r)]_r · [(r)]_r, where r = min(p, q). For the latter product, we use a result due to Boccara.     

A Highly Oxidizing and Isolable Oxoruthenium(V) Complex [RuV(N4O)(O)]2+: Electronic Structure,Redox Properties,and Oxidation Reactions Investigated by DFT Calculations

The electronic structure and redox properties of the highly oxidizing, isolable Ru^V?O complex [Ru^V(N₄O)(O)]²⁺, its oxidation reactions with saturated alkanes (cyclohexane and methane) and inorganic substrates (hydrochloric acid and water), and its intermolecular coupling reaction have been examined by DFT calculations. The oxidation reactions with cyclohexane and methane proceed through hydrogen atom transfer in a transition state with a calculated free energy barrier of 10.8 and 23.8 kcal mol^?1, respectively. The overall free energy activation barrier (ΔG^≠=25.5 kcal mol^?1) of oxidation of hydrochloric acid can be decomposed into two parts: the formation of [Ru^III(N₄O)(HOCl)]²⁺ (ΔG=15.0 kcal mol^?1) and the substitution of HOCl by a water molecule (ΔG^≠=10.5 kcal mol^?1). For water oxidation, nucleophilic attack on Ru^V?O by water, leading to O? O bond formation, has a free energy barrier of 24.0 kcal mol^?1, the major component of which comes from the cleavage of the H? OH bond of water. Intermolecular self‐coupling of two molecules of [Ru^V(N₄O)(O)]²⁺ leads to the [(N₄O)Ru^IV? O₂? Ru^III(N₄O)]⁴⁺ complex with a calculated free energy barrier of 12.0 kcal mol^?1.     

Heteronukleare Komplexverbindungen mit Metall—Metall-Bindungen. VIII. Neue heterodinukleare Komplexe mit Bindungen zwischen Kupfer(I) und Mangan(–I), Eisen(–I) oder Cobalt(–I)

Heteronuclear Coordination Compounds with Metal—Metal Bonds. VIII. New Heterodinuclear Complexes with Bonds between Copper(I) and Manganese(?I), Iron(?I), or Cobalt(?I) [(en)Cu? Mn(CO)₅] ( 1a ), [(dien)Cu? Mn(CO)₅] ( 1b ), [(en)Cu? Fe(CO)₃(NO)] ( 2a ), [(dien)Cu? Fe(CO)₃(NO)] ( 2b ), [(en)Cu? Co(CO)₄] ( 3a ), and [(dien)Cu? Co(CO)₄] ( 3b ) are new heterobinuclear metal—metal bonded complexes. The geometry of the [Mn(CO)₅]^?, [Fe(CO)₃(NO)]^?, and [Co(CO)₄]^? ions is distorted only to a less extend in accord with a heteropolar bond to copper.     

Cyanide-bridged FeIII–MnIII bimetallic chain derived from [Fe(bipy)(CN)4]−: synthesis,structure and magnetic characteristics

A chain-like compound of [Mn(salpn)][Fe(bipy)(CN)₄] (1) (salpn = N,N′-propylenebis(salicylideneiminato)dianion; bipy = 2,2′-bipyridine), assembled from building blocks of [Fe(bipy)(CN)₄]^? and [Mn(salpn)]⁺, has been characterized by elemental analyses, ICP, IR, thermoanalysis, single crystal X-ray structure analysis and magnetic measurements. In 1, each [Fe(bipy)(CN)₄]^? anion coordinates with two [Mn^III(salpn)]⁺ cations via two trans-CN^? groups, and each [Mn^III(salpn)]⁺ cation is axially coordinated by two [Fe(bipy)(CN)₄]^? ions, resulting in a straight 1-D chain. The chains stack via aromatic π–π-type interactions. Magnetic studies reveal the presence of weak antiferromagnetic interactions between adjacent Fe^III and Mn^III ions through cyanide-bridges.     

3‐Rhoda‐1,2‐diazacyclopentanes: A Series of Novel Metallacycle Complexes Derived From CN Functionalization of Ethylene

Rh‐containing metallacycles, [(TPA)Rh^III(κ²‐(C,N)‐CH₂CH₂(NR)₂‐]Cl; TPA=N,N,N,N‐tris(2‐pyridylmethyl)amine have been accessed through treatment of the Rh^I ethylene complex, [(TPA)Rh(η²‐CH₂CH₂)]Cl ([ 1 ]Cl) with substituted diazenes. We show this methodology to be tolerant of electron‐deficient azo compounds including azo diesters (RCO₂N?NCO₂R; R=Et [ 3 ]Cl, R=iPr [ 4 ]Cl, R=tBu [ 5 ]Cl, and R=Bn [ 6 ]Cl) and a cyclic azo diamide: 4‐phenyl‐1,2,4‐triazole‐3,5‐dione (PTAD), [ 7 ]Cl. The latter complex features two ortho‐fused ring systems and constitutes the first 3‐rhoda‐1,2‐diazabicyclo[3.3.0]octane. Preliminary evidence suggests that these complexes result from N–N coordination followed by insertion of ethylene into a [Rh]?N bond. In terms of reactivity, [ 3 ]Cl and [ 4 ]Cl successfully undergo ring‐opening using p‐toluenesulfonic acid, affording the Rh chlorides, [(TPA)Rh^III(Cl)(κ¹‐(C)‐CH₂CH₂(NCO₂R)(NHCO₂R)]OTs; [ 13 ]OTs and [ 14 ]OTs. Deprotection of [ 5 ]Cl using trifluoroacetic acid was also found to give an ethyl substituted, end‐on coordinated diazene [(TPA)Rh^III(κ²‐(C,N)‐CH₂CH₂(NH)₂‐]⁺ [ 16 ]Cl, a hitherto unreported motif. Treatment of [ 16 ]Cl with acetyl chloride resulted in the bisacetylated adduct [(TPA)Rh^III(κ²‐(C,N)‐CH₂CH₂(NAc)₂‐]⁺, [ 17 ]Cl. Treatment of [ 1 ]Cl with AcN?NAc did not give the Rh?N insertion product, but instead the N,O‐chelated complex [(TPA)Rh^I ( κ²‐(O,N)‐CH₃(CO)(NH)(N?C(CH₃)(OCH?CH₂))]Cl [ 23 ]Cl, presumably through insertion of ethylene into a [Rh]?O bond.     

The syntheses and magnetic properties of a series of heterospin [LnIIICuII 4] pentanuclear complexes

Twelve oxamide-bridged Ln(III)–Cu(II) heteropentanuclear complexes Ln[Cu(PMoxd)]₄(ClO₄)₃ · 5H₂O (Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Yb, and PMoxd = the N,N′-Bi(α-pyridylmethyl)-oxamide dianion) and 12 oxamide-bridged Ln(III)–Cu(II) heteropentanuclear complexes with the formula of Ln[Cu(PEoxd)]₄(ClO₄)₃ · 5H₂O (PEoxd = the N,N′-Bi(α-pyridylethyl)-oxamide dianion) were synthesized and characterized. The magnetic properties of Gd[Cu(PMoxd)]₄(ClO₄)₃ · 5H₂O (7) and Gd[Cu(PEoxd)]₄(ClO₄)₃ · 2H₂O (19) show that there are ferromagnetic interactions between Gd(III) and Cu(II) in the complexes with J _Cu–Gd = 1.38 cm^?1 and J _Cu–Gd = 1.00 cm^?1, respectively. Fluorescent quenching phenomena for Eu[Cu(PMoxd)]₄(ClO₄)₃ · 5H₂O (6) and Tb[Cu(PMoxd)]₄(ClO₄)₃ · 5H₂O (8) were also observed.     

Diverse structures and magnetism of cobalt(II) and manganese(II) compounds with mixed azido and carboxylato bridges induced by methylpyridinium carboxylates

Herein we present a systematic study of the structures and magnetic properties of six coordination compounds with mixed azide and zwitterionic carboxylate ligands, [M(N₃)₂(2‐mpc)] (2‐mpc=N‐methylpyridinium‐2‐carboxylate; M=Co for 1 and Mn for 2 ), [M(N₃)₂(4‐mpc)] (4‐mpc=N‐methylpyridinium‐4‐carboxylate; M=Co for 3 and Mn for 4 ), [Co₃(N₃)₆(3‐mpc)₂(CH₃OH)₂] ( 5 ), and [Mn₃(N₃)₆(3‐mpc)₂] ( 6 ; 3‐mpc=N‐methylpyridinium‐3‐carboxylate). Compounds 1 – 3 consist of one‐dimensional uniform chains with (μ‐EO‐N₃)₂(μ‐COO) triple bridges (EO=end‐on); 5 is also a chain compound but with alternating [(μ‐EO‐N₃)₂(μ‐COO)] triple and [(EO‐N₃)₂] double bridges; Compound 4 contains two‐dimensional layers with alternating [(μ‐EO‐N₃)₂(μ‐COO)] triple, [(μ‐EO‐N₃)(μ‐COO)] double, and (EE‐N₃) single bridges (EE=end‐to‐end); 6 is a layer compound in which chains similar to those in 5 are cross‐linked by a μ₃‐1,1,3‐N₃ azido group. Magnetically, the three Co^II compounds ( 1 , 3 , and 5 ) all exhibit intrachain ferromagnetic interactions but show distinct bulk properties: 1 displays relaxation dynamics at very low temperature, 3 is an antiferromagnet with field‐induced metamagnetism due to weak antiferromagnetic interchain interactions, and 5 behaves as a noninnocent single‐chain magnet influenced by weak antiferromagnetic interchain interactions. The magnetic differences can be related to the interchain interactions through π–π stacking influenced by different substitution positions in the ligands and/or different magnitudes of intrachain coupling. All of the Mn^II compounds show overall intrachain/intralayer antiferromagnetic interactions. Compound 2 shows the usual one‐dimensional antiferromagnetism, whereas 4 and 6 exhibit different weak ferromagnetism due to spin canting below 13.8 and 4.6 K, respectively.     

Complexes of 3,3′-Oxybis[(diphenylphosphino)methylbenzene] with Ni(II), Pd(II), Pt(II), Rh(I), and Ag(I). How Important is Backbone Rigidity in the Formation of trans-Spanning Bidenatate Chelates??

The bidentate diphosphine ligand, 3,3′-oxybis[(dipenylphosphino)methylbenzene] ( 1 ) forms monomeric, trans-square-planar complexes MX₂( 1 ) (M = Ni, Pd, Pt; X = Cl^?, Br^? I^?, and, in part, N, NCS^?, CN^?, NO) as well as Pt(H)Cl( 1 ), Pt(H)Br( 1 ), and RhCl(CO)( 1 ). Polymeric species have been observed with substitutionally inert metal centres: trans-[PtCl₂( 1 )]₂ and cis-[PtCl₂( 1 )]_n (mean value of n ≈ 4–5) ³¹P-NMR, and selected IR and UV/VIS parameters are reported. Ligand 1 shows a marked preference for trans-spanning and monomeric chelate formation, despite its various degrees of freedom of internal rotation in the lignad backbone. The readily available ligand 1 as well as analogues with other donor atoms, therefore, appear useful in most potential applications of trans-spanning chelate ligands. The crystal structure of AgCl( 1 )·0.5 (CH₃)₂C?O·0.39 C₆H₁₂ (space group C2/c,a = 21.02 Å, b = 14.57 Å, c = 24.79 Å, β = 99.77°, V = 7531.4 ų, Z = 8) confirms the presence of three-coordinate Ag( I ), with a coordination intermediate between a trigonal-planar and a T-shaped geometry (P-Ag-P = 145.61(8)°).     

Metal Complexes with Macrocyclic Ligands. Part XXXIX. Mono- and binuclear copper(II) complexes of a bridging bis[1, 4, 7-triazacyclononane]

The new bis-macrocycle 1, 1′-[(1H-pyrazol-3], 5-diyl)bis(methylene)bis[1, 4, 7-triazacyclononane] ( 1 ) was synthesized and its complexation with Cu²⁺ studied. Potentiometric and spectrophotometric titrations indicate that, in addition to the mononuclear species [Cu(LH₂)]⁴⁺, [Cu(LH)]³⁺, [CuL]²⁺, and [Cu(LH_?1)]⁺, binuclear complexes such as [Cu₂L]⁴⁺, [Cu₂(LH_?1)]³⁺, and [Cu₂(LH_-2)]²⁺ are also formed in solution. The stability constants and spectral properties of these are reported. The binuclear species [Cu₂(LH_?1)]³⁺ specifically reacts with an azide ion to give a ternary complex [Cu₂(LH_?1)(N₃)]²⁺, the stability and structure of which were determined spectrophotometrically and by X-ray diffraction, respectively. The two Cu²⁺ ions are in a square-pyramidal coordination geometry. The axial ligand is one of the N-atoms of the 1, 4, 7-triazacyclononane ring, whereas at the base of the square pyramid, one finds the other two N-atoms of the macrocycle, one N-atom of the pyrazolide and one of the azide, both of which are bridging the two metal centres. In [Cu₂(LH_?1)(N₃)]²⁺, a strong antiferromagnetic coupling is present, thus resulting in a species with a low magnetic moment of 1.36 B.M. at room temperature.     

Tuning the reactivity of mononuclear nonheme manganese(iv)-oxo complexes by triflic acid

Triflic acid (HOTf)-bound nonheme Mn(iv)-oxo complexes, [(L)Mn^IV(O)]²⁺–(HOTf)₂ (L = N4Py and Bn-TPEN; N4Py = N,N-bis(2-pyridylmethyl)-N-bis(2-pyridyl)methylamine and Bn-TPEN = N-benzyl-N,N′,N′-tris(2-pyridylmethyl)ethane-1,2-diamine), were synthesized by adding HOTf to the solutions of the [(L)Mn^IV(O)]²⁺ complexes and were characterized by various spectroscopies. The one-electron reduction potentials of the Mn^IV(O) complexes exhibited a significant positive shift upon binding of HOTf. The driving force dependences of electron transfer (ET) from electron donors to the Mn^IV(O) and Mn^IV(O)–(HOTf)₂ complexes were examined and evaluated in light of the Marcus theory of ET to determine the reorganization energies of ET. The smaller reorganization energies and much more positive reduction potentials of the [(L)Mn^IV(O)]²⁺–(HOTf)₂ complexes resulted in greatly enhanced oxidation capacity towards one-electron reductants and para-X-substituted-thioanisoles. The reactivities of the Mn(iv)-oxo complexes were markedly enhanced by binding of HOTf, such as a 6.4 × 10⁵-fold increase in the oxygen atom transfer (OAT) reaction (i.e., sulfoxidation). Such a remarkable acceleration in the OAT reaction results from the enhancement of ET from para-X-substituted-thioanisoles to the Mn^IV(O) complexes as revealed by the unified ET driving force dependence of the rate constants of OAT and ET reactions of [(L)Mn^IV(O)]²⁺–(HOTf)₂. In contrast, deceleration was observed in the rate of H-atom transfer (HAT) reaction of [(L)Mn^IV(O)]²⁺–(HOTf)₂ complexes with 1,4-cyclohexadiene as compared with those of the [(L)Mn^IV(O)]²⁺ complexes. Thus, the binding of two HOTf molecules to the Mn^IV(O) moiety resulted in remarkable acceleration of the ET rate when the ET is thermodynamically feasible. When the ET reaction is highly endergonic, the rate of the HAT reaction is decelerated due to the steric effect of the counter anion of HOTf.     

Diagonally Related s‐ and p‐Block Metals Join Forces: Synthesis and Characterization of Complexes with Covalent Beryllium–Aluminum Bonds

Additions of beryllium–halide bonds in the simple beryllium dihalide adducts, [BeX₂(tmeda)] (X=Br or I, tmeda=N,N,N′,N′‐tetramethylethylenediamine), across the metal center of a neutral aluminum(I) heterocycle, [:Al(^DipNacnac)] (^DipNacnac=[(DipNCMe)₂CH]^?, Dip=2,6‐diisopropylphenyl), have yielded the first examples of compounds with beryllium–aluminum bonds, [(^DipNacnac)(X)Al‐Be(X)(tmeda)]. For sake of comparison, isostructural Mg–Al and Zn–Al analogues of these complexes, viz. [(^DipNacnac)(X)Al‐M(X)(tmeda)] (M=Mg or Zn, X=I or Br) have been prepared and structurally characterized. DFT calculations reveal all compounds to have high s‐character metal–metal bonds, the polarity of which is consistent with the electronegativities of the metals involved. Preliminary reactivity studies of [(^DipNacnac)(Br)Al‐Be(Br)(tmeda)] are reported.     

Synthesis and magnetic studies of phthalato-bridged oxovanadium(IV) binuclear complexes

Six new μ-phthalato binuclear oxovanadium(IV) complexes, namely [(VO)₂(PHTH)-(L)₂]SO₄ (L denotes 2,2′-bipyridine (bpy); 1,10-phenanthroline (phen); 4,4′-dimethyl-2,2′-bipyridine (Me₂ bpy); 5-nitro-1,10-phenanthroline (NO₂-phen); 5-chloro-1,10-phenanthroline (Cl-phen) and 5-methyl-1,10-phenanthroline (CH₃-phen), where PHTH is the phthalate dianion), have been synthesized and characterized by elemental analyses, IR, electronic spectra, magnetic moments at room temperature and molar conductivity measurements. The temperature dependence of the magnetic susceptibility of complexes [(VO)₂(PHTH)(phen)₂]SO₄ (1) and [(VO)₂(PHTH)(CH₃-phen)₂]SO₄ (2) was measured in 4—300 K range and the observed data were successfully simulated by the equation based on the spin Hamiltonian operator, ?=?2J?₁·?₂, giving the exchange integrals J=?12.8 cm^?1 for 1 and J=?7.9 cm^?l for 2. This indicates an antiferromagnetic spin-exchange interaction between the metal ions within each molecule.     

Synthesis and property of BrCCH- and BrCCBr-coordinated tetrairon clusters

The reaction of (η⁵-C₅H₄Me)₄Fe₄(HCCH)₂ (1) with 1 equiv. of N-bromosuccinimide (NBS) gives the one-electron oxidized form in 83% yield. Further treatment of [1]⁺ with NBS results in the stepwise bromination of four acetylenic protons to give [(η⁵-C₅H₄Me)₄Fe₄(HCCH)(HCCBr)]⁺ ([2]⁺), [(η⁵-C₅H₄Me)₄Fe₄(HCCBr)₂]⁺ ([3a]⁺), [(η⁵-C₅H₄Me)₄Fe₄(HCCBr)(BrCCBr)]⁺ ([4]⁺), and [(η⁵-C₅H₄Me)₄Fe₄(BrCCBr)₂]⁺ ([5]⁺) in moderate yields, with the isomer of [3a]⁺, [(η⁵-C₅H₄Me)₄Fe₄(HCCH)(BrCCBr)]⁺ ([3b]⁺), formed as a minor product. These compounds are characterized by analytical and spectroscopic techniques, and the molecular structures of [2](PF₆), [4](TFPB), and [5](TFPB) are established by X-ray diffraction analysis [TFPB = tetrakis{bis(3,5-trifluoromethyl)phenyl}borate]. The compounds are confirmed to retain the butterfly core of four iron atoms as in [1](TFPB). The bromoacetylene part in [2]⁺ exhibits high reactivity toward various nucleophiles: Cluster[2]⁺ is moisture-sensitive and is converted to a mixture of [(η⁵-C₅H₄Me)₄Fe₄(HCCH)(μ₃-CH)(μ₃-CO)]⁺ ([6]⁺) and [1]⁺. Reactions of [2]⁺ with ZnR₂ (R = Me, Et) give [(η⁵-C₅H₄Me)₄Fe₄(HCCH)(HCC-R)]⁺ in good yields (R = Me ([9]⁺, 88%), Et ([10]⁺, 91%)). Accordingly, treatment of [2]⁺ with HC CMgBr and LiS^pTol leads to the introduction of the ethynyl and thiolate groups to give [(η⁵-C₅H₄Me)₄Fe₄(HCCH)(HCC-CCH)]⁺ ([11]⁺, 95%) and [(η⁵-C₅H₄Me)₄Fe₄(HCCH)(HCC-S^pTol)]⁺ ([12]⁺, 78%), respectively. Substitution of the bromo group in [2]⁺ with pyridine affords [(η⁵-C₅H₄Me)₄Fe₄(HCCH)(HCC-Py)]²⁺ ([13]²⁺) in 90% yield. The reaction with 4,4′-bipyridyl (bpy) requires the severer conditions (70 °C, 2 days), probably due to the relative low basicity of bpy, giving [(η⁵-C₅H₄Me)₄Fe₄(HCCH)(HCC-bpy)]²⁺ ([14]²⁺) in 54% yield. The substitution reaction with 4,4′-bipyridyl is strongly accelerated by treatment with silver salt to give [14]²⁺ in 90% yield. The products derived from [2]⁺ and nucleophiles are unequivocally determined by elemental, spectroscopic, and X-ray diffraction analyses.     

Dinuclear cobalt and nickel complexes of a mercaptoacetic acid substituted 1,2,4‐triazole ligand: syntheses,structures and urease inhibitory studies

Because of its versatile coordination modes and strong coordination ability, the mercaptoacetic acid substituted 1,2,4‐triazole 2‐{[5‐(pyridin‐2‐yl)‐4H‐1,2,4‐triazol‐3‐yl]sulfanyl}acetic acid ( H₂L ) was synthesized and characterized. Treatment of H₂L with cobalt and nickel acetate afforded the dinuclear complexes {μ‐3‐[(carboxylatomethyl)sulfanyl]‐5‐(pyridin‐2‐yl)‐4H‐1,2,4‐triazol‐4‐ido‐κ²N¹,N⁵:N²,O}bis[aqua(methanol‐κO)cobalt(II)] methanol disolvate, [Co₂(C₉H₆N₄O₂S)₂(CH₃OH)₂(H₂O)₂]·2CH₃OH ( 1 ), and {μ‐3‐[(carboxylatomethyl)sulfanyl]‐5‐(pyridin‐2‐yl)‐4H‐1,2,4‐triazol‐4‐ido‐κ²N¹,N⁵:N²,O}bis[diaquanickel(II)] methanol disolvate dihydrate, [Ni₂(C₉H₆N₄O₂S)₂(H₂O)₄]·2CH₃OH·2H₂O ( 2 ), respectively. Complex 1 crystallized in the monoclinic space group P2₁/c, while 2 crystallized in the tetragonal space group I4₁/a. Single‐crystal X‐ray diffraction studies revealed that H₂L is doubly deprotonated and acts as a tetradentate bridging ligand in complexes 1 and 2 . For both of the obtained complexes, extensive hydrogen‐bond interactions contribute to the formation of their three‐dimensional supermolecular structures. Hirshfeld surface analysis was used to illustrate the intermolecular interactions. Additionally, the urease inhibitory activities of 1 , 2 and H₂L were investigated against jack bean urease, where the two complexes revealed strong urease inhibition activities.     

Synthesis,and Structural Characterization of [{CH3(C5H4N)}Ga(SCH2(CO)O)2] −[(4-MepyH)]+, A Novel Ga(III) Five-Coordinate Complex

The synthesis and structural characterization of a novel ionic Ga(III) five-coordinate complex [{CH₃(C₅H₄N)}Ga(SCH₂(CO)O)₂]^?[(4-MepyH)]⁺, (4-Mepy=CH₃(C₅H₅N)) from the reaction between Ga₂Cl₄ with sodium mercapto-acetic acid in 4-methylpyridine is described. Under basic reaction conditions the mercapto ligand is found to behave as a 2e^? bidentate ligand. Single crystal X-ray diffraction studies show the complex to have a distorted square-pyramidal geometry with the [(^?SCH₂(CO)CO^?)] ligands trans. The compound crystallizes in the P2₁/c (No. 14) space group with a=7.7413(6)Å, b=16.744(2)Å, c=14.459(2)Å, V,=1987.1(6)&Aringsup3;, R(F, _o)=0.032 and R_W =0.038.     

Products of class sums of the symmetric group: Rules of partial elimination

Progress in the formulation of a procedure for the combinatorial evaluation of the product of a single-cycle and an arbitrary class sum in the symmetric group algebra is presented. The procedure consists of a “global conjecture” concerning the representation of the product [(p)]_n·[*]_n in terms of a set of operators referred to as reduced class sums, and of an (incomplete) set of rules for the evaluation of the (n-independent!) coefficients of these operators. Two new types of index elimination rules are suggested, and some properties of the formalism are explored. These include useful sum rules as well as a certain “detailed balance” property that sheds some light on a combinatorial aspect of the global conjecture. The present results account for several new types of reduced class coefficients and suggest some feasible further developments. Some outstanding open problems are pointed out. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 961–979, 1997     

Two coordination polymers constructed by 5‐[(4‐carboxyphenoxy)methyl]benzene‐1,3‐dicarboxylic acid and 2,2′‐bipyridine: syntheses,structures and luminescence properties

Coordination polymers (CPs) have attracted increasing interest in recent years. In this work, two new CPs, namely poly[[aquabis(2,2′‐bipyridine‐κ²N,N′){μ₃‐5‐[(4‐carboxylatophenoxy)methyl]benzene‐1,3‐dicarboxylato‐κ⁴O¹,O^1′:O³:O⁵}(μ‐formato‐κ³O:O,O′)dicadmium(II)] monohydrate], {[Cd₂(C₁₆H₉O₇)(HCO₂)(C₁₀H₈N₂)₂(H₂O)]·H₂O}_n ( 1 ), and poly[[(2,2′‐bipyridine‐κ²N,N′){μ₃‐5‐[(4‐carboxylphenoxy)methyl]benzene‐1,3‐dicarboxylato‐κ⁴O¹,O^1′:O³:O⁵}manganese(II)] sesquihydrate], {[Mn(C₁₆H₁₀O₇)(C₁₀H₈N₂)]·1.5H₂O}_n ( 2 ), have been prepared using the tricarboxylic acid 5‐[(4‐carboxyphenoxy)methyl]benzene‐1,3‐dicarboxylic acid and 2,2′‐bipyridine under hydrothermal conditions. CP 1 displays a two‐dimensional layer structure which is further extended into a three‐dimensional (3D) supramolecular structure via intermolecular π–π interactions, while CP 2 shows a different 3D supramolecular structure extended from one‐dimensional ladder chains by intermolecular π–π interactions. In addition, the solid‐state luminescence spectra of 1 and 2 were studied at room temperature.     

Homo- and hetero-bimetallic glycolates and triethanolaminates of niobium

[Nb(OⁱPr)₅] reacts with 2,5-dimethylhexane-2,5-diol (LH₂), 2,3-dimethylbutane-2,3-diol (L¹H₂) and triethanolamine (teaH₃) in different stoichiometric ratios to yield complexes of the types: [Nb(OⁱPr)₃(L)] (1), [Nb(OⁱPr)(L)₂] (2), [Nb(L)₂(LH)] (3), [Nb(L¹)₂(L¹H)] (4) and [Nb(tea)(teaH)] (5). Equimolar reactions of (3), (4) and (5) with Al(OⁱPr)₃, Ti(OⁱPr)₄ and [Ta(OⁱPr)₅] yield novel heterobimetallic isopropoxide-glycolate (6)–(9) and -triethanolaminate (10)–(12) derivatives. Reactions in appropriate molar ratios of (1), (2) and (10) with alkoxyethanols [ROC₂H₄OH; R = Me, Et] and acetylacetone [acacH] give derivatives [(MeOC₂H₄O)₃Nb(L)] (13), [(acac)Nb(L)₂] (14), [Nb(tea)₂{Al(OC₂H₄OMe)₂}] (15), [Nb(tea)₂{Al(OC₂H₄OEt)₂}] (16) and [Nb(tea)₂{Al(acac)₂}] (17). The complexes (6), (8) and (10) on reaction with an excess of t-BuOH give the tert-butoxo analogues (18), (19) and (20), respectively. These new derivatives have been characterized by elemental analyses, spectroscopic studies and molecular weight measurements.     

Facile Synthesis and Versatile Reactivity of an Unusual Cyclometalated Rhodium(I) Pincer Complex

The synthesis of the reactive PN(C^H) ligand 2‐di(tert‐butylphosphanomethyl)‐6‐phenylpyridine ( 1^H ) and its versatile coordination to a Rh^I center is described. Facile C?H activation occurs in the presence of a (internal) base, thus resulting in the new cyclometalated complex [Rh^I(CO)(κ³‐P,N,C‐ 1 )] ( 3 ), which has been structurally characterized. The resulting tridentate ligand framework was experimentally and computationally shown to display dual‐site proton‐responsive reactivity, including reversible cyclometalation. This feature was probed by selective H/D exchange with [D₁]formic acid. The addition of HBF₄ to 3 leads to rapid net protonolysis of the Rh?C bond to produce [Rh^I(CO)(κ³‐P,N,(C?H)‐ 1 )] ( 4 ). This species features a rare aryl C?H agostic interaction in the solid state, as shown by X‐ray diffraction studies. The nature of this interaction was also studied computationally. Reaction of 3 with methyl iodide results in rapid and selective ortho‐methylation of the phenyl ring, thus generating [Rh^I(CO)(κ²‐P,N‐ 1^Me )] ( 5 ). Variable‐temperature NMR spectroscopy indicates the involvement of a Rh^III intermediate through formal oxidative addition to give trans‐[Rh^III(CH₃)(CO)(I)(κ³‐P,N,C‐ 1 )] prior to C?C reductive elimination. The Rh^III–trans‐diiodide complex [Rh^I(CO)(I)₂(κ³‐P,N,C‐ 1 )] ( 6 ) has been structurally characterized as a model compound for this elusive intermediate.