N-Representability conditions generated by a one-particle grassmann factor of an antisymmetric function

N-representability conditions for a two-particle density operator implied by positive-semidefiniteness of the projection operator P^N+1(?¹ Λ Ψ^N) are derived and discussed. The operator P^N+1(?¹ Λ Ψ^N) projects onto an (N + 1)-particle antisymmetric function ?¹ Λ Ψ^N, the Grassmann product of a one-particle factor ?¹ and an N-particle factor Ψ^N. The polar subcone ??²_N(g, q) to the set of N-representable two-particle density operators ??²_N which corresponds to these conditions is found. It is shown that its extreme rays belong to two orbits for the action of the unitary group of transformations in one-particle Hilbert space. The facial structure of the convex set ??²_N exposed by elements of ??²_N(g, q) is analyzed. An example of the operator that changes the structure of its bottom eigenspace when the number of fermions N surpasses a certain value is noted. A new approach to the diagonal conditions for N-representability is found. It consists of the decomposition of the N-particle antisymmetric identity operator onto the mutually orthogonal projection operators.     

Density functional theory for open-shell systems using a local-scaling transformation scheme. II. Euler-Lagrange equation for f(r) versus that for ρ(r)

Following the previous article (Part I), we express the total nonrelativistic energy for spin manifolds of open-shell multielectronic systems, within an orbit θ^N induced by a model wave function (MWF) _Ψ using a single local-scaling transformation (LST) as an exact functional of the single-particle density ρ( r ) or, alternatively, of the LST scalar function f( r ). We derive the corresponding Euler–Lagrange variational equations: one implicit in ρ( r ), which can be solved iteratively through steps involving f( r ), and one explicit in f( r ), derived from the total energy as a functional of f( r ). Both equations fulfill the space and spin symmetries characterizing the system. The problems arising from the specificities of these two highly nonlinear integrodifferential equations are discussed. The optimal charge density ρ( r ) derived from these equations is N- and v-representable and determines the optimal spin density σ( r ) as well. Accurate optimal values of all observables can be derived from this scheme using standard procedures. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 257–268, 1997     

Synthesis,crystal structures,thermal properties,and DNA-binding studies of transition metal complexes with imidazole ligands

A new series of complexes of transition metal (Cu, Zn, Ni) perchlorate with imidazole have been synthesized and characterized by elemental analysis, infrared (IR), UV-Vis spectroscopy, and single-crystal X-ray diffraction. Based on elemental and spectral data, the complexes are M(C₃H₄N₂) _x (ClO₄)₂ (M?=?Cu, Zn, x?=?4; M?=?Ni, x?=?6; C₃H₄N₂?=?imidazole). The crystal structures of Cu(C₃H₄N₂)₄(ClO₄)₂ (1) and Zn(C₃H₄N₂)₄(ClO₄)₂ (2) show metals surrounded by four nitrogens of imidazole, while the nickel complex Ni(C₃H₄N₂)₆(ClO₄)₂ (3) has six nitrogens of imidazole. Intra- and inter-molecular hydrogen bonds exist between hydrogen of imidazole and oxygen of perchlorate. The thermal stabilities of 1, 2, and 3 at different heating rates (β?=?5°C?min^?1, 10°C?min^?1, and 15°C?min^?1) show that all the complexes exhibit two thermal decomposition stages; the sequence of thermal stability is 2?>?1?>?3. 1, 2, 3, and imidazole display DNA binding ability, ascertained by UV-Vis titration.     

The use of chebyshev polynomials orthogonal on a finite arbitrary system of points for interpolating changes in nematic-isotropic liquid phase transition temperatures in homologous series

Chebyshev polynomials Ψ _q (x) orthogonal on a finite arbitrary system of points x _i (i = 1−N) are used to interpolate changes in nematic-isotropic liquid phase transition temperatures t _c(x) in homologous series of liquid crystals (x = 1/n, where n is the number of the homologue). The expansion of the t _c(x) function into a series in Ψ _q (x) polynomials was found to be very effective. Already at q ≤ 3, this series describes the known types of the t _c(x) dependences with high accuracy and very small root-mean-square deviations for mesogenic molecules of various chemical structures and dimensions. The dependence of the limiting t _l = t _c(0) value on the form of X-shaped molecules and linear dimensions of N-mers with N rigid aromatic fragments linked with each other by flexible spacer chains was studied.

     

Darstellung,Kristallstrukturen und Schwingungsspektren von trans‐[Pt(N3)4(ECN)2]2–, E = S,Se

Synthesis, Crystal Structures, and Vibrational Spectra of trans ‐[Pt(N₃)₄(ECN)₂]^2–, E = S, Se By oxidative addition to (n‐Bu₄N)₂[Pt(N₃)₄] with dirhodane in dichloromethane trans‐(n‐Bu₄N)₂[Pt(N₃)₄(SCN)₂] and by ligand exchange of trans(n‐Bu₄N)₂[Pt(N₃)₄I₂] with Pb(SeCN)₂ trans‐(n‐Bu₄N)₂[Pt(N₃)₄(SeCN)₂] are formed. X‐ray structure determinations on single crystals of trans‐(Ph₄P)₂[Pt(N₃)₄(SCN)₂] (triclinic, space group P 1, a = 10.309(3), b = 11.228(2), c = 11.967(2) Å, α = 87.267(13), β = 75.809(16), γ = 65.312(17)°, Z = 1) and trans‐(Ph₄P)₂[Pt(N₃)₄(SeCN)₂] (triclinic, space group P 1, a = 9.1620(10), b = 10.8520(10), c = 12.455(2) Å, α = 90.817(10), β = 102.172(10), γ = 92.994(9)°, Z = 1) reveal, that the compounds crystallize isotypically with octahedral centrosymmetric complex anions. The bond lengths are Pt–S = 2.337, Pt–Se = 2.490 and Pt–N = 2.083 (S), 2.053 Å (Se). The approximate linear Azidoligands with N^α–N^β–N^γ‐angles = 172,1–175,0° are bonded with Pt–N^α–N^β‐angles = 116,7–120,5°. In the vibrational spectra the platinum chalcogen stretching vibrations of trans‐(n‐Bu₄N)₂[Pt(N₃)₄(ECN)₂] are observed at 296 (E = S) and in the range of 186–203 cm^–1 (Se). The platinum azide stretching modes of the complex salts are in the range of 402–425 cm^–1. Based on the molecular parameters of the X‐ray determinations the IR and Raman spectra are assigned by normal coordinate analysis. The valence force constants are f_d(PtS) = 1.64, f_d(PtSe) = 1.36, f_d(PtN^α) = 2.33 (S), 2.40 (Se) and f_d(N^αN^β, N^βN^γ) = 12.43 (S), 12.40 mdyn/Å (Se).     

Charge densities for singlet and triplet electron pairs

Analytic properties of charge densities associated with singlet and triplet electron pairs, ρ₀( r ) and ρ₁( r ), are presented. In an N‐electron system with total spin S, distributions ρ₀( r ) and ρ₁( r ) are independent of the spin projection quantum number M (spin rotation invariance), as opposed to the usual spin‐up and spin‐down electron densities, ρ_α( r ) and ρ_β( r ). We derive equations showing that in the case of a wave function which is a spin‐eigenfunction, ρ₀( r ) and ρ₁( r ) are linear combinations of the total charge density ρ( r ) and the uncompensated spin density ρ_s( r )=[ρ_α( r )−ρ_β( r )]/2M. For a wave function which is not an eigenfunction of $\mathcal{S}^{2}$, no such relationship exists. In a related discussion, a definition of the high‐spin solution corresponding to a given spin‐unrestricted Hartree–Fock wave function is proposed, and a notion of effectively unpaired electrons is introduced. The distributions ρ₀( r ) and ρ₁( r ) are shown not to be invariant under spin coupling between isolated systems. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 651–660, 2000     

Synthesis,characterization and acceptor behavior of n-butyltin(IV)-2,4-dimethylphenoxides

The n-butyltin(IV) complexes, n-BuSnCl_3?x(OC₆H₃(CH₃)₂-2,4) _x (where x?=?1–3), have been synthesized in quantitative yields by employing the reaction of n-BuSnCl₃ with 2,4-dimethylphenol and sodium acetate in methanol and benzene solvents at room temperature. The complexes have been characterized by elemental analysis, molar conductivity, and FT-IR, ¹H- and ¹³C-NMR, and mass spectral studies. Thermal behavior has been studied by TG–DTA techniques. Lewis acid character of n-BuSn(OC₆H₃(CH₃)₂-2,4)₃ has been investigated by reacting it with bases such as 2,2′-bipyridine and 1,10-phenanthroline (B), Ph₃PO and Ph₃AsO (LO) and phosphorus and arsenic donors Ph₃P, Ph₃As, and As(SPh)₃ (L). The formation of 1?:?1 and 1?:?2 (metal?:?base) coordination compounds [n-BuSn(OC₆H₃(CH₃)₂-2,4)₃·B] and n-[BuSn(OC₆H₃(CH₃)₂-2,4)₃·2LO/2L] has been authenticated by physicochemical and IR spectral studies. In order to infer the biological relevance of newly synthesized complexes, the antibacterial activity has been assayed against six bacterial strains Klebsiella pneumoniae, Staphylococcus epidermidis, Staphylococcus aureus, Salmonella typhi, Salmonella paratyphi, and Escherichia coli. In this study, n-BuSnCl₂(OC₆H₃(CH₃)₂-2,4) and n-BuSnCl(OC₆H₃(CH₃)₂-2,4)₂ showed better activity than precursor and ligand, while n-BuSn(OC₆H₃(CH₃)₂-2,4)₃ did not exhibit improved activity.     

A novel two‐dimensional MnII coordination polymer with 1,2‐bis­(imidazol‐1‐yl)­ethane

In the crystal structure of the title complex, poly­[[di­azido­manganese(II)]‐di‐μ‐1,2‐bis­(imidazol‐1‐yl)­ethane‐κ⁴N³:N^3′], [Mn(N₃)₂(C₈H₁₀N₄)₂]_n or [Mn(N₃)₂(bim)₂]_n, where bim is 1,2‐­bis(imidazol‐1‐yl)­ethane, each Mn^II atom is six‐coordinated in a distorted octahedral coordination environment to four N atoms from four bim ligands and two N atoms from two azide ligands. The Mn^II atoms, which lie on inversion centres, are bridged by four bim ligands to form a two‐dimensional (4,4)‐network. The azide ligands are monodentate (terminal).     

Fluorescence quenching of para-substitutedstyrenes by tetramethylethylene. Correlationanalysis of the quenching coefficient KSV and thequenching rate constant k_q by the dual-parameter equation with polar and spin-delocalization substituent constants

The fluorescence quenching coefficient (Ksv) and the quenching rate constant kq of ten para-substituted styrenes (1-Ys) have been measured and correlation-analyzed by both the dual-parameter equation (Eq. 1) with (ρxσx+ρ'σ') and the single-parameter equation (Eq. 2) with ρxσx. Ex-cellent results have been obtained for the correlation of KSV against (ρxσmb+ρ'σ'JJ) or (ρxσ+ +ρ'σ'JJ). Our results suggest that, possibly, there might be no need to use excited-state substituent constant for the fluorecence quenching process of excited states of styrenes.     

Computation of auxiliary functions in STO molecular integrals up to arbitrary accuracy. I. evaluation of incomplete gamma function En(x) by forward recursion

A new inequality and an approximate relation of incomplete Gamma function E_n(x) are derived in this paper. Applying both to simplify the error analysis on the recursive algorithm of E_n(x), we analytically derived a criterion about relative error. The criterion decides whether the forward recursive relation can be used to compute {E_n(x), n = 0, 1, ?, N} with an acceptable loss of significant figures. Further analytical exploration leads to another criterion that decides whether the group of E_n(x) can be evaluated with an acceptable absolute error by the same methods. Both criteria are not only superior to those given in previous work by other authors, but also strongly supported by our numerical experiments. A strategy is illustrated to explain how to apply both criteria to evaluate molecular integral over Slater-type orbitals. © 1993 John Wiley & Sons, Inc.     

Thermal decomposition of lighter lanthanide selenate hydrates and their solid solutions

The thermal dehydration-decomposition of Ln₂(SeO₄)₃·nH₂O (wheren=12 forLn=Pr, Nd andn=8 forLn=Sm) and Pr_xLn_2−x(SeO₄)₃·nH₂O (wheren=12 forx=1.0 andLn=Nd;n=8 forx=0.2 and 1.0 in case ofLn=Sm) have been reported.

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Zusammenfassung Die thermische Dehydratation-Zersetzung von Ln₂(SeO₄)₃·nH₂O (mitn=12 fürLn=Pr, Nd undn=8 fürLn=Sm) und Pr_xLn_2−x(SeO₄)₃·nH₂O (mitn=12 fürx=1.0 undLn=Nd;n=8 fürx=0.2 und 1.0 in Falle vonLn=Sm) wurde beschrieben.

     

Ruthenium-Catalyzed Cross-Metathesis of Trisubstituted Vinylsilanes with Light Alkenes

In the cross-metathesis reaction of tri(methyl, ethoxy)vinylsilanes with propene and/or 1-butene catalyzed by RuCl₂(PPh₃)₃ activated in benzene at 115–130 °C, a series of l-alkenylsilanes of general formula CH₃(CH₂)_mCH = CHSiMe_3−n(OEt)_n, where m=0, 1, and n=0–3 (1-silyl-1-alkenes), as well as of formula CH₂=C(Me)SiMe_3−n(OEt)_n, where n=1, 2 (2-silyl-1-alkenes), were obtained. Additional products determined were allysilanes of general formula CH₂=CHCH₂SiMe_3−n(OEt)_n and CH₃CH= CHCH₂SiMe_3−n(OEt)_n, where n=1–3. © 1997 John Wiley & Sons, Ltd.     

Darstellung,Kristallstrukturen und Schwingungsspektren von [Pt(N3)6]2– und [Pt(N3)Cl5]2–, 195Pt‐ und 15N‐NMR‐Spektren von [Pt(N3)nCl6–n]2– und [Pt(15NN2)n(N215N)6–n]2–, n = 0–6

Synthesis, Crystal Structures, and Vibrational Spectra of [Pt(N₃)₆]^2– and [Pt(N₃)Cl₅]^2–, ¹⁹⁵Pt and ¹⁵N NMR Spectra of [Pt(N₃)_nCl_6–n]^2– and [Pt(¹⁵NN₂)_n(N₂¹⁵N)_6–n]^2–, n = 0–6 By ligand exchange of [PtCl₆]^2– with sodium azide mixed complexes of the series [Pt(N₃)_nCl_6–n]^2– and with ¹⁵N‐labelled sodium azide (Na¹⁵NN₂) mixtures of the isotopomeres [Pt(¹⁵NN₂)_n(N₂¹⁵N)_6–n]^2–, n = 0–6 and the pair [Pt(¹⁵NN₂)Cl₅]^2–/[Pt(N₂¹⁵N)Cl₅]^2– are formed. X‐ray structure determinations on single crystals of (Ph₄P)₂[Pt(N₃)₆] ( 1 ) (triclinic, space group P1, a = 10.175(1), b = 10.516(1), c = 12.380(2) Å, α = 87.822(9), β = 73.822(9), γ = 67.987(8)°, Z = 1) and (Ph₄As)₂[Pt(N₃)Cl₅] · HCON(CH₃)₂ ( 2 ) (triclinic, space group P1, a = 10.068(2), b = 11.001(2), c = 23.658(5) Å, α = 101.196(14), β = 93.977(15), γ = 101.484(13)°, Z = 2) have been performed. The bond lengths are Pt–N = 2.088 ( 1 ), 2.105 ( 2 ) and Pt–Cl = 2.318 Å ( 2 ). The approximate linear azido ligands with N^α–N^β–N^γ‐angles = 173.5–174.6° are bonded with Pt–N^α–N^β‐angles = 116.4–121.0°. In the vibrational spectra the PtCl stretching vibrations of (n‐Bu₄N)₂[Pt(N₃)Cl₅] are observed at 318–345, the PtN stretching modes of (n‐Bu₄N)₂[Pt(N₃)₆] at 401–428 and of (n‐Bu₄N)₂[Pt(N₃)Cl₅] at 408–413 cm^–1. The mixtures (n‐Bu₄N)₂[Pt(¹⁵NN₂)_n(N₂¹⁵N)_6–n], n = 0–6 and (n‐Bu₄N)₂[Pt(¹⁵NN₂)Cl₅]/(n‐Bu₄N)₂[Pt(N₂¹⁵N)Cl₅] exhibit ¹⁵N‐isotopic shifts up to 20 cm^–1. Based on the molecular parameters of the X‐ray determinations the vibrational spectra are assigned by normal coordinate analysis. The average valence force constants are f_d(PtCl) = 1.93, f_d(PtN^α) = 2.38 and f_d(N^αN^β, N^βN^γ) = 12.39 mdyn/Å. In the ¹⁹⁵Pt NMR spectrum of [Pt(N₃)_nCl_6–n]^2–, n = 0–6 downfield shifts with the increasing number of azido ligands are observed in the range 4766–5067 ppm. The ¹⁵N NMR spectrum of (n‐Bu₄N)₂[Pt(¹⁵NN₂)_n(N₂¹⁵N)_6–n], n = 0–6 exhibits by ¹⁵N–¹⁹⁵Pt coupling a pseudotriplett at –307.5 ppm. Due to the isotopomeres n = 0–5 for terminal ¹⁵N six well‐resolved signals with distances of 0.03 ppm are observed in the low field region at –201 to –199 ppm.     

Red and yellow solvates of chloro­(2,2′:6′,2′′‐terpyridine)platinum(II) chloride and Pt⋯Pt inter­actions

Crystallization of chloro­(2,2′:6′,2′′‐terpyridine)platinum(II) chloride from dimethyl sulfoxide yields a red polymorph, [PtCl(C₁₅H₁₁N₃)]Cl·C₂H₆OS, (I), which exhibits stacking along the a axis through pairs of Pt⋯Pt(−x, −y, −z) inter­actions of 3.3155 (8) Å. The cations are further associated through close Pt⋯Pt(1 − x, −y, −z) distances of 3.4360 (8) Å. Recrystallization from water gives a mero­hedrally twinned yellow–orange dihydrate form, [PtCl(C₁₅H₁₁N₃)]Cl·2H₂O, (II), with pairwise short Pt⋯Pt(1 − x, 2 − y, −z) contacts of 3.3903 (5) Å but no long‐range stacking through the crystals. Inter­pair Pt⋯Pt(−x, 2 − y, −z) distances between cation pairs in the hydrate are 4.3269 (5) Å.     

Ladder operators for the Kratzer oscillator and the Morse potential

Taking a close look at the Infeld–Hull ladder operators for the Kratzer oscillator system, V(x) = [x² + β(β ? 1)x^?2]/2, we deduce and explicitly construct energy‐raising and ‐lowering operators for the generalized Morse potential system V(z) = (Ae^?4αz ? Be^?2αz)/2, through a canonical transformation that exists between the two systems. For the Morse potential system, we obtain a system of raising and lowering operators P_±(n) (n = 0, 1, 2, 3, … , n_max) with the specific property that P_±(n)Φ_n = c_±(n)Φ_n±1, where Φ_n denotes the nth energy eigenfunction. While P_?(0) annihilates the ground‐state Φ₀, the operator P₊(n_max), instead of annihilating the highest bound‐state Φ, actually knocks it out of the L₂ space spanned by the discrete bound states and becomes inadmissible. Yet, raising and lowering operators _± with proper end‐of‐spectrum behavior (i.e., _?|0〉 = 0 and ₊|n_max〉 = 0) can be constructed in a straightforward way in the energy representation. We show that the operators ₊, _?, and ₀ (where ₀ ≡ (1/2)[ ₊, _?]) form a su(2) algebra only if we restrict them to the (N ? 1)‐dimensional subspace spanned by the lowest (N ? 1) basis vectors, but not in the full (N + 1)‐dimensional space spanned by the discrete bound states [N ≡ n_max ≡ integral part of (1/2)(B/(2α ) ? 1)]. Realization of this su(2) algebra in the position representation (when restricted to the (N ? 1)‐dimensional subspace) is also given. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Synthesis,electrochemical and antimicrobial studies of mono and binuclear iron(III) and oxovanadium(IV) complexes of [ONO] donor tridentate Schiff-base ligands

Tridentate Schiff bases (H₂L¹ or H₂L²) were derived from condensation of acetylacetone and 2-aminophenol or 2-aminobenzoic acid. Binuclear square pyramidal complexes of the type [M₂(L¹)₂]?·?nH₂O (M?=?Fe–Cl, n?=?0; M?=?VO, n?=?1) were accessed from interaction of H₂L¹ with anhydrous FeCl₃ and VOSO₄?·?5H₂O, respectively. A similar reaction with H₂L², however, produced mononuclear complexes [ML²(H₂O) _x ]?·?nH₂O (M=Fe–Cl, x?=?0, n?=?0; M=VO, x?=?1, n?=?1). The compounds were characterized using elemental analysis, FT-IR, UV-Vis, and NMR (for ligand only), and mass spectroscopies and solution electrical conductivity studies. Magnetic susceptibility measurements suggest antiferromagnetic exchange in binuclear Fe(III) and VO(IV) complexes. Thermo gravimetric analysis (TGA) provided unambiguous evidence for the presence of coordinated as well as lattice water in [VOL²(H₂O)]?·?H₂O. Cyclic voltammetric studies showed well-defined redox processes corresponding to Fe(III)/Fe(II) and VO(V)/VO(IV). In vitro antimicrobial activities of the compounds were investigated against Klebsiella pneumoniae, Staphylococcus aureus, Pseudomonas aeroginosa, Escherichia coli, Bacillus subtilis, and Proteus vulgaris. H₂L¹ and its binuclear complexes exhibited pronounced activity against all the microorganisms tested.     

Synthesis,crystal structures and characterization of two Cu(II) complexes with asymmetric sulfonamide Schiff-base ligands

Reaction of the N-tosyl-1,2-diaminopropane or N-tosyl-1,2-diaminobenzene with salicylaldehyde forms two new asymmetric sulfonamide Schiff bases, N-[2-(2-hydroxybenzylideneamino)propyl]-4-methylbenzenesulfonamide (H₂L¹ ) and N-[2-(2-hydroxybenzylideneamino)phenyl]-4-methylbenzenesulfonamide (H₂L² ). Two new complexes [CuL ^x (H₂O)] (x = 1 for 1, x = 2 for 2) constructed from H₂L ^x have been prepared and characterized via X-ray single-crystal diffraction, elemental analysis, FT-IR, UV-Vis, TGA, quantum chemical calculations, and photoluminescence measurements. Weak C–H ··· π, hydrogen bonds, π–π, and Cu ··· O weak interactions lead to 3-D supramolecular architecture, 1, and 1-D double chain, 2.     

Novel metal cluster complexes synthesized by matrix deposition of mass-selected clusters

Metal complexes produced by depositing size selected Fe and Ag cluster cations in N₂ and O₂ matrices respectively are studied by infrared spectroscopy. Unknown species such as Fe(N₂)x, Fe₃ (N₂)x and Ag₃(O₂)x are observed. The IR spectra of Ag⁺, Ag ₂ ⁺ and Ag ₉ ⁺ in excess O₂ indicate that no complexes involving molecular oxygen are formed. However, the strong silver cluster UV-visible absorptions detected in Ar matrices disappear in the oxygen matrices, suggesting that silver-oxygen complexes are formed with dissociated oxygen.     

Synthesis,structures, and spectroscopic properties of Hg(II) complexes of bidentate NN and tridentate NNO Schiff-base ligands

Reactions of HgX₂ (X?=?Cl, N₃, NO₃) with (E)-2-methoxy-N-(pyridin-2-ylmethylene)aniline (L¹) and (E)-4-methoxy-N-(pyridin-2-ylmethylene)aniline (L²) in ethanol gave two monomers, [HgL¹(Cl)₂] (1) and [HgL²(NO₃)₂(DMSO)] (5), and three coordination polymers, {[HgL¹(N₃)₂]₂·Hg(N₃)₂}_n (2), [HgL²(Cl)₂]_n (3), and [HgL²(NO₃)₂]_n·nCH₃CN (4). Compounds 1–5 were characterized by elemental analysis, IR, NMR spectroscopy, and single-crystal X-ray diffraction. The common feature of monomeric 1 and 5 is the presence of intra- and intermolecular Hg–O bonds. In the absence of these, polymeric structures arise as a result of azide, chloride, and nitrate bridging in 2, 3, and 4, respectively. Fluorescent properties of 1–5 were also investigated.