Structural analysis of certain linear operators representing chemical network systems via the existence and uniqueness theorems of spectral resolution. VI*

The present Part VI of this series of articles provides a mathematical and methodical link between (i) fundamental methodology in the repeat space theory (RST), which is referred to as the approach via the aspect of form and general topology and which has universal unifying power to handle additivity problems of molecules that have many identical moieties, and (ii) frontier electron theory of reactivity indices. Using theoretical tools required to link (i) and (ii), we establish a theorem from which the Generalized Alpha Existence Theorem (a theorem essential in the RST and proved in the previous Part V) directly follows. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 84: 389–400, 2001     

Normalized irreducible tensorial matrices and the Wigner–Eckart theorem for unitary groups: A superposition hamiltonian constructed from octahedral NITM

The concepts of normalized irreducible tensorial matrices (NITM ) are extended to all finite and compact unitary groups by a development that clarifies their relationship to group theory and matrix algebra. NITM for a unitary group G are shown to be elements of a basis obtained by symmetry adapting to G the matrix basis of a matrix space M (α₁ × α₂). Elements [X] ∈ M (α₁ α₂) transform under G_a ∈ G according to [G_a] [X][G^?1_a], where [G_a] and [G^?1_a] belong to irreducible representations of G . The usual properties of NITM and the Wigner–Eckart theorem follow from these results, which are valid for both finite and compact unitary groups. The NITM span M (α₁ × α₂) are orthonormal under the trace and transform irreducibly with respect to G . This NITM basis of M (α₁ × α₂) is said to be simple. A compound NITM basis of a matrix space results when the space is partitioned into two or more subspaces, each spanned by a simple NITM basis. NITM determined from Griffith's V coefficients for the octahedral group are tabulated and used to construct a six-coordinate superposition Hamiltonian.     

Addition of Ethylene or Hydrogen to a Main‐Group Metal Cluster under Mild Conditions

Reaction of the tin cluster Sn₈(Ar)₄ (Ar=C₆H₂‐2,6‐(C₆H₃‐2,4,6‐Me₃)₂) with excess ethylene or dihydrogen at 25 °C/1 atmosphere yielded two new clusters that incorporated ethylene or hydrogen. The reaction with ethylene yielded Sn₄(Ar)₄(C₂H₂)₅ that contained five ethylene moieties bridging four aryl substituted tin atoms and one tin–tin bond. Reaction with H₂ produced a cyclic tin species of formula (Sn(H)Ar)₄, which could also be synthesized by the reaction of {(Ar)Sn(μ‐Cl)}₂ with DIBAL‐H. These reactions represent the first instances of direct reactions of isolable main‐group clusters with ethylene or hydrogen under mild conditions. The products were characterized in the solid state by X‐ray diffraction and IR spectroscopy and in solution by multinuclear NMR and UV/Vis spectroscopies. Density functional theory calculations were performed to explain the reactivity of the cluster.     

Aldehyde‐Assisted Hydrogen Transfer during the Formation of Hydride–Iridafurans from Alkynes and Aldehydes

The bis(ethylene) Ir^I complex [TpIr(C₂H₄)₂] ( 1 ; Tp=hydrotris(3,5‐dimethylpyrazolyl)borate) reacts with two equivalents of aromatic or aliphatic aldehydes in the presence of one equivalent of dimethyl acetylenedicarboxylate (DMAD) with ultimate formation of hydride iridafurans of the formula [TpIr(H){C(R¹)?C(R²)C(R³)O }] (R¹=R²=CO₂Me; R³=alkyl, aryl; 3 ). Several intermediates have been observed in the course of the reaction. It is proposed that the key step of metallacycle formation is a C? C coupling process in the undetected Ir^I species [TpIr{η¹‐O‐R³C(?O)H}(DMAD)] ( A ) to give the trigonal‐bipyramidal 16 e^? Ir^III intermediates [TpIr{C(CO₂Me)?C(CO₂Me)C(R³)(H)O }] ( C ), which have been trapped by NCMe to afford the adducts 11 (R³=Ar). If a second aldehyde acts as the trapping reagent for these species, this ligand acts as a shuttle in transfering a hydrogen atom from the γ‐ to the α‐carbon atom of the iridacycle through the formation of an alkoxide group. Methyl propiolate (MP) can be used instead of DMAD to regioselectively afford the related iridafurans. These reactions have also been studied by DFT calculations.     

One‐range Addition Theorems for Complete Sets of Modified Exponential Type Orbitals and Noninteger n Slater Functions in Standard Convention

Using the L ‐generalized Laguerre polynomials L ‐GLPs) and φ ‐generalized exponential type orbitals φ ‐GETOs) introduced by the author in standard convention, the one‐ and two‐center onerange addition theorems are established for the complete sets of Ψ^(α*) ‐modified exponential type orbitals (Ψ^(α*) ‐METOs) and noninteger n χ‐Slater type orbitals (χ‐NISTOs), where p_l* = 2l + 2 ‐ α* and α* is the integer (α* = α, ?∞ < α ≤2) or noninteger (α* ≠ α, ?∞ < α* < 3) self‐frictional quantum number. It should be noted that the origin of the L ‐GLPs, φ ‐GETOs and Ψ^(α*) ‐METOs, therefore, of the one‐range addition theorems presented in this work is the Lorentz damping or self‐frictional field produced by the particle itself.     

The Functional Delta Existence Theorem and the Reduction of a Proof of the Fukui Conjecture to That of the Special Functional Asymptotic Linearity Theorem

This article establishes a fundamental existence theorem, called the Functional Delta Existence Theorem (DET), which is significant for a new development in the repeat space theory (RST) and also for elucidating an empirical asymptotic principle from experimental chemistry. By using the Functional DET, we reduce a proof of the Fukui conjecture to that of a special and simpler version of the Asymptotic Linearity Theorem (ALT). This reduction provides a basis for the forthcoming series of articles entitled “Proof of the Fukui conjecture via resolution of singularities and related methods”. A proof of the Functional DET is given here in a unifying manner so that an investigative link is formed among: (i) fundamental methodology in the RST, which is referred to as the approach via the aspect of form and general topology, (ii) frontier electron theory of reactivity indices, and (iii) the Shingu–Fujimoto empirical asymptotic principle for long chain molecules.     

On the ν1/2 ν2 Resonance in the Complex of Carbon Dioxide with Dimethyl Ether

Infrared and Raman spectra of solutions in liquid argon and krypton containing dimethyl ether or its fully deuterated isotopomer and ¹²CO₂ or ¹³CO₂ are investigated. The spectra lead to new data on the ν₁/2 ν₂ resonances appearing in the complex of CO₂ with the ether. The experimental data, and their interpretation, is supported by MP2/6‐311++G(2d,2p) calculations of the cubic and quartic force constants and of the first and higher order dipole moment derivatives required for the modelling of the Fermi and Darling‐Dennison resonances observed.     

Subgroup‐chain symmetry‐adapted irreducible matrices and CG coefficients of point groups

The irreducible matrices and Clebsch–Gordan coefficients of any crystallographic point group adapted to all possible canonical subgroup chains are calculated ab initio for both single‐valued and double‐valued representations and tabulated with exact values in the form of or and with components labeled by the irrep labels of the group chain in Koster notation. The phases and ordering of the components of irreducible bases for the cubic point groups are properly chosen so that irreducible matrices for all subgroup chains of G=T_d, O, O_h obey the associated relations D(G)=D(G)D(G), i=4, 6, and the complex conjugation relation for the group T, D(T)=D(T)*. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 67–80, 1999     

Shape‐Selective Interception by Hydrocarbons of the O2‐Derived Oxidant of a Biomimetic Nonheme Iron Complex

Picky ferryl : The complex [Fe(Tp)(BF)] (Tp=hydrotris(3,5‐diphenylpyrazolyl)borate; BF=benzoylformate) reacts with O₂ to generate an oxidant (see picture; O red, pink; Fe yellow; N blue; C gray; H white) that oxidizes added hydrocarbons shape‐selectively. Discrimination derives from a cleft formed by two phenyl groups of the Tp ligand, favoring oblate spheroidal substrates.

     

New RuII(arene) Complexes with Halogen‐Substituted Bis‐ and Tris(pyrazol‐1‐yl)borate Ligands

[RuCl(arene)(μ‐Cl)]₂ dimers were treated in a 1:2 molar ratio with sodium or thallium salts of bis‐ and tris(pyrazolyl)borate ligands [Na(Bp)], [Tl(Tp)], and [Tl(Tp^{iPr, 4Br})]. Mononuclear neutral complexes [RuCl(arene)(κ²‐Bp)] ( 1 : arene=p‐cymene (cym); 2 : arene=hexamethylbenzene (hmb); 3 : arene=benzene (bz)), [RuCl(arene)(κ²‐Tp)] ( 4 : arene=cym; 6 : arene=bz), and [RuCl(arene)(κ²‐Tp^{iPr, 4Br})] ( 7 : arene=cym, 8 : arene=hmb, 9 : arene=bz) have been always obtained with the exception of the ionic [Ru₂(hmb)₂(μ‐Cl)₃][Tp] ( 5′ ), which formed independently of the ratio of reactants and reaction conditions employed. The ionic [Ru(CH₃OH)(cym)(κ²‐Bp)][X] ( 10 : X=PF₆, 12 : X=O₃SCF₃) and the neutral [Ru(O₂CCF₃)(cym)(κ²‐Bp)] ( 11 ) have been obtained by a metathesis reaction with corresponding silver salts. All complexes 1 – 12 have been characterized by analytical and spectroscopic data (IR, ESI‐MS, ¹H and ¹³C NMR spectroscopy). The structures of the thallium and calcium derivatives of ligand Tp, [Tl(Tp)] and [Ca(dmso)₆][Tp]₂ ? 2 DMSO, of the complexes 1 , 4 , 5′ , 6 , 11 , and of the decomposition product [RuCl(cym)(Hpz^{iPr, 4Br})₂][Cl] ( 7′ ) have been confirmed by using single‐crystal X‐ray diffraction. Electrochemical studies showed that 1 – 9 and 11 undergo a single‐electron Ru^II→Ru^III oxidation at a potential, measured by cyclic voltammetry, which allows comparison of the electron‐donor characters of the bis‐ and tris(pyrazol‐1‐yl)borate and arene ligands, and to estimate, for the first time, the values of the Lever E_L ligand parameter for Bp, Tp, and Tp^{iPr, 4Br}. Theoretical calculations at the DFT level indicated that both oxidation and reduction of the Ru complexes under study are mostly metal‐centered with some involvement of the chloride ligand in the former case, and also demonstrated that the experimental isolation of the μ³‐binuclear complex 5′ (instead of the mononuclear 5 ) is accounted for by the low thermodynamic stability of the latter species due to steric reasons.     

Kinetics of the reaction O(3P) + SO2 + M → SO3 + M over the temperature range of 299°–440°K

Rate constants for the reaction O(³P) + SO₂ + M have been determined over the temperature range of 299°–440°K, using a flash photolysis–NO₂ chemiluminescence technique. For M?Ar, the Arrhenius expression was obtained. At room temperature k₂^Ar = (1.05 ± 0.21) × 10^?33 cm⁶/molec²·sec. In addition, the rate constants k₂ = (1.37 + 0.27) × 10^?33 cm⁶/molec²·sec, k₂ = (9.5 ± 3.0) ± 10^?33 cm⁶/molec²·sec, k₃ = (1.1 ± 0.2) ± 10^?31 cm⁶/molec²·sec, and k₃ = (2.6 ? 0.9) ± 10^?31 cm⁶/molec²·sec were obtained at room temperature where k₃^M is the rate constant for the reaction O + NO + M → NO₂ + M. The rate data are compared and discussed with literature values.     

1H, 13C and 15N nuclear magnetic resonance coordination shifts in Au(III), Pd(II) and Pt(II) chloride complexes with phenylpyridines

¹H, ¹³C and ¹⁵N nuclear magnetic resonance studies of gold(III), palladium(II) and platinum(II) chloride complexes with phenylpyridines (PPY: 4‐phenylpyridine, 4ppy; 3‐phenylpyridine, 3ppy; and 2‐phenylpyridine, 2ppy) having the general formulae [Au(PPY)Cl₃], trans‐/cis‐[Pd(PPY)₂Cl₂] and trans‐/cis‐[Pt(PPY)₂Cl₂] were performed and the respective chemical shifts (δ, δ and δ) reported. ¹H, ¹³C and ¹⁵N coordination shifts (i.e. differences between chemical shifts of the same atom in the complex and ligand molecules: , , ) were discussed in relation to the type of the central atom (Au(III), Pd(II) and Pt(II)), geometry (trans‐/cis‐) and the position of a phenyl group in the pyridine ring system. Copyright © 2009 John Wiley & Sons, Ltd.     

Pyrazolato Ligands towards Gold(I) Derivatives with Aurophilic Interactions: X‐Ray Structure of Bis[3,5‐(dibutoxyphenyl)‐1H‐pyrazolato‐κN1]bis(triphenylphosphine)digold(Au⋅⋅⋅Au)([Au(pz)(PPh3)]2; RC4H9?O?C6H4)

A crossed ‘torch' structure and a short Au⋅⋅⋅Au contact was established by X‐ray analysis for the dimeric complex [Au(pz)(PPh₃)]₂ (pz=3,5‐disubstituted pyrazolato, RC_nH_2n+1 O C₆H₄, n=4; 1 ). The complex is a representative member of a new well‐characterized family of derivatives containing the pyrazolato ligand in an uncommon monodentate coordination form. In addition, 1 is luminescent in the solid state at 77 K.     

Reversible nonlinear conduction behavior for high‐density polyethylene/graphite powder composites near the percolation threshold

The reversible nonlinear conduction (RNC) behavior of high‐density polyethylene/graphite powder composites with various graphite powder volume concentrations slightly above the threshold has been studied. The relationships between the current density (J) and electric field (E) of the composites, as shown in J(E) curves, can be well described by the scaling functions of J/J_c ～ (E/E_c) when E < E_c and J/J_c ～ (E/E_c) when E > E_c, where J_c is the crossover current density and E_c is the crossover electric field. The results indicate that J_c scales with the linear conductivity σ₀ as J_c ～ σ. It is believed that the macroscopic RNC is a combined result of the microscopic conduction processes, involving electronic transporting along carbon chains and tunneling or hopping across thin polymer bridges. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2833–2842, 2001     

Activation parameters and kinetic isotope effect in the system tropaeolin O-OH−

The kinetics of the deprotonation of tropaeolin O by OH^? ions was investigated between 9° and 30°C, and by OD^? ions at 24.7°C. The pH range was 10.7–12.5, and the ionic strength 0.1M throughout. All results were obtained by the temperature jump method. On the basis of a mechanism suggested earlier, rate constants k₃₁ for the reaction between OL^? and the internally bonded weak acid and k₃₂ for the opening of the internal hydrogen bond were evaluated. The activation energies in ordinary water were found to be ΔH≠₃₁ = 3.6 kcal/mol, ΔS≠₃₁ = –19 eu, and ΔH≠₃₂ = 27 kcal/mol, ΔS≠₃₂ = 46 eu. The kinetic isotope effect was k₃₁/k₃₁ ～ 1.5 and k₃₂/k₃₂ ～ 0.9. The unusual results for reaction path are discussed in terms of solvent participation.     

Reduction of CO2 by Pyridine Monoimine Molybdenum Carbonyl Complexes: Cooperative Metal–Ligand Binding of CO2

[(^ArPMI)Mo(CO)₄] complexes (PMI=pyridine monoimine; Ar=Ph, 2,6‐di‐iso‐propylphenyl) were synthesized and their electrochemical properties were probed with cyclic voltammetry and infrared spectroelectrochemistry (IR‐SEC). The complexes undergo a reduction at more positive potentials than the related [(bipyridine)Mo(CO)₄] complex, which is ligand based according to IR‐SEC and DFT data. To probe the reaction product in more detail, stoichiometric chemical reduction and subsequent treatment with CO₂ resulted in the formation of a new product that is assigned as a ligand‐bound carboxylate, [(PMI)Mo(CO)₃(CO₂)]^2?, by NMR spectroscopic methods. The CO₂ adduct [(PMI)Mo(CO)₃(CO₂)]^2? could not be isolated and fully characterized. However, the C?C coupling between the CO₂ molecule and the PDI ligand was confirmed by X‐ray crystallographic characterization of one of the decomposition products of [(PMI)Mo(CO)₃(CO₂)]^2?.     

Heterolytic Cleavage of Hydrogen by an Iron Hydrogenase Model: An Fe‐H⋅⋅⋅H‐N Dihydrogen Bond Characterized by Neutron Diffraction

Hydrogenase enzymes in nature use hydrogen as a fuel, but the heterolytic cleavage of H? H bonds cannot be readily observed in enzymes. Here we show that an iron complex with pendant amines in the diphosphine ligand cleaves hydrogen heterolytically. The product has a strong Fe‐H???H‐N dihydrogen bond. The structure was determined by single‐crystal neutron diffraction, and has a remarkably short H???H distance of 1.489(10) Å between the protic N‐H^δ+ and hydridic Fe‐H^δ? part. The structural data for [CpFe H (P^tBu₂N^tBu₂ H )]⁺ provide a glimpse of how the H? H bond is oxidized or generated in hydrogenase enzymes. These results now provide a full picture for the first time, illustrating structures and reactivity of the dihydrogen complex and the product of the heterolytic cleavage of H₂ in a functional model of the active site of the [FeFe] hydrogenase enzyme.     

Use of noninteger n‐generalized exponential type orbitals with hyperbolic cosine in atomic calculations

The efficiency of noninteger n‐generalized exponential type orbitals (NGETO) r^n*?1 e with hyperbolic cosine (HC) cosh (βr^μ) as radial basis functions in atomic ground state total energy calculations is studied. By the use of these functions, the combined Hartree‐Fock‐Roothaan calculations have been performed for some closed and open shell neutral atoms and their anions and cations with Z ≤ 21. The performance of new basis functions within the minimal basis framework has been compared with numerical Hartree‐Fock (NHF) results. Our total energy values are significantly close to NHF results. The presented minimal basis total energies obtained from the noninteger NGETO with HC are notably better than minimal basis functions total energies previously reported in the literature. It is found that the accuracy of new noninteger NGETO with HC almost correspond to the accuracy of the conventional double‐zeta functions. All the nonlinear parameters are fully optimized. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Kinetics of cerium(IV) oxidation of macrocyclic complexes of chromium(III) and fate of chromium(IV) intermediates

Kinetics and mechanism of the cerium(IV) oxidation of Cr(III) complexes of a series of macrocyclic (or pseudomacrocyclic) ligands with [14]-membered intraligand ring-sizes have now been investigated at I = 1.0 M (LiClO₄) Temp. 30°C. The complexes of the formulation Cr(macrocycle)(X)(H₂O) where X = CHCl₂ and H₂O, n = 0 or 1 undergo oxidation to Cr(VI) with the formation of chromium(IV) intermediates. The observed kinetic parameters for the Ce(IV) oxidation of Cr(III) macrocyclic complexes have been discussed in terms of changes brought about by the macrocyclic ligands on the Cr(III)—Cr(IV) redox potentials and in specific rates for Cr(IV)—Cr(V) conversion. On the basis of this study, it has been suggested that the trapping of Cr(IV) is easier when a macrocyclic ligand having a symmetrical intra-ligand ring size and unsaturation in the cyclic structure is coordinated equatorially. Cyclic voltammetric studies indicate the formation of Cr(IV) transient in the case of electrochemical oxidation of trans-Cr(Me₄[14]tetraene)(H₂O).