An average fock operator technique of approximate open-shell LCAO-MO-SCF calculation

The exchange part of the usual Hartree-Fock potential in the unrestricted Hartree-Fock (UHF) theory is suitablyaveraged to construct an, average one-electron model Hamiltonian which generates a set of spin-restricted one-electron orbitals in a self-consistent manner. These orbitals are then used to calculate the electronic energy of the open-shell system by using the proper functional form for the energy which handles the exchange terms correctly. The eigenvalues ofF ^av can be used for calculating either the spin-polarised or spin-averaged ionisation potentials of different orbitals at theKoopmans’ theorem level of approximation. Comparison ofE ^ac with the UHF-energy shows thatE _UHF<E ^ac in each case revealing some kind of an upper bound nature ofE ^ac. An approximate variational argument is given. Relationship of our model with the hyper-Hartree-Fock theory of slater is explored and the general problem of eliminating ‘self-interaction’ terms in average Fock-operator based theories is discussed.     

Crystal structure of barium bis [N-(2-hydroxyethyl)iminodiacetato]cobaltate(III) hydrocarbonate dihydrate Ba(μ4-HCO3)[ trans (N)-Co(heida)2]·2H2O

Ba[Co(heida)₂](HCO₃)·2H₂O crystals were grown (orthorhombic, a = 9.4491(5) Å, b = 10.9719(5) Å, c = 19.6077(9) Å, Z = 4, space group Pca2₁), and their structure was solved by X-ray diffraction. The Co atoms in the complex anion were coordinated by two N-(2-hydroxyethyl)iminodiacetate (heida) ligands via the N atom and two O atoms of each ligand. The Ba atoms and the complex anions form “honeycomb” layers linked via three O atoms. The “honeycombs” are additionally linked by their Ba atoms with the O atoms of the hydroxyethyl groups. The Ba atoms are aligned within a layer and linked via the bridging HCO₃ hydrocarbonate groups. The c.n. of Ba atoms is 10 (one water molecule; five O atoms of the complex anions, one from each of the nearest neighbors; and four O atoms of the hydrocarbonate ions). Original Russian Text Copyright ? 2008 by M. Zabel, A. L. Poznyak, and V. I. Pavlovskii __________ Translated from Zhurnal Strukturnoi Khimii, Vol. 49, No. 3, pp. 594–597, May–June, 2008.     

Probability of fluctuations in the number of the nearest neighbours in a hard-sphere liquid: Probabilities of large deviations

The paper analyzes the physical implications of the result obtained in the work [1] that a random variable — the number of the nearest neighbors M _λ in a fluid consisting of N hard spheres in the Gibbs canonical ensemble — can be expressed as a sum of N independent and similarly distributed random variables. The mean value of a functional of this random variable determines the free Helmholtz energy of a fluid with the SW interaction potential (hard sphere plus square well). The paper shows that the said property of the random variable M _λ allows one to average this functional using the general methods of the probability theory (the Cramer theorem or the method of large deviations) without expanding it in a perturbation theory series. All the mathematical variables introduced in the proof of the Cramer theorem have a simple physical meaning and are determined by the thermodynamic characteristics of the SW fluid. The conditions of the Cramer theorem are shown to hold in the entire region of the fluid existence except the critical point area.     

Paradoxes and paradigms: influence of the power of z on the estimation of entropies of formation of aqueous anions using simple parameters

We continue our use of “simple” energetic patterns, where simple means the use of parameters derived only from the stoichiometry of these species in our studies of the entropy of formation (TΔ_f S ^o) of aqueous anions. Relationships between the entropy of formation and different parameters such as the number of oxygen atoms, the natural logarithm of the molecular weight and the total number of atoms are explored. The charge of the species, z− continues to be explicitly considered where we now explore various choices of p and use of z ^p as a parameter.     

Heat capacities of a series of terminal linear alkyldiamides determined by DSC

Molar heat capacities of twelve linear alkane-α,ω-diamides H₂NOC-(CH₂)_(n-2)-CONH₂, (n=2 to 12 and n=14) were measured by differential scanning calorimetry at T=183 to 323 K. Heat flow rate calibration of the Mettler DSC 30 calorimeter was carried out by using benzoic acid as reference material. The calibration was checked by determining the molar heat capacity of urea in the same temperature range as that of measurements. The molar heat capacities of alkane-α,ω-diamides increased in function of temperature and fitted into linear equations. Smoothed values of C _p,m at 298.15 K displayed a linear increase with the number of carbon atoms. The C _p,m contribution of CH₂ group was (22.6±0.4) J K⁻¹ mol⁻¹, in agreement with our previous results concerning linear alkane-a,ω-diols and primary alkylamides as well as the literature data on various series of linear alkyl compounds. On leave from the Faculty of Chemistry, University of Craiova, Calea Bucureşti 165, Craiova 1100, Romania     

X-ray photoelectron study of the state of Ba atoms in YBa2Cu3O7−δ doped with Co and Zn atoms

Investigating changes in the charged state of atoms upon superconductivity-suppressing substitutions is one of the methods to examine a relationship between the electronic structure of HTSC materials and the transition temperature to the superconducting state. In this paper, we measured E_bnd of the inner levels of Ba atoms in Co- and Zn-doped YBa₂Cu₃O_7−δ by X-ray photoelectron spectroscopy. Upon copper substitution by Co and Zn atoms, E_bnd of the inner levels diminishes for Ba atoms but remains the same for Cu and O atoms. The change of E_bnd of the inner levels of Ba atoms is attributed to the change of the Fermi level position in the “anionic” sublattice of (Cu₃O_7−δ)⁷⁻. Institute of Inorganic Chemistry, Siberian Branch, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 35, No. 4, pp. 91–95, July–August, 1994. Translated by L. Smolina     

Geometry and orientation of molecules in a graphite fluoride matrix

Polarization dependences of the EXAFS and XANES spectra of graphite fluoride intercalation compounds C₂F_x·yA (x ≈ 1, A=Br₂, Fe(AA)₃, FeCl₃, SnCl₄; AA=acetylacetonate) synthesized by diffusion from solution were measured. The measurements were carried out in the FeK-, BrK-, and SnK-edge of absorption spectral regions using synchrotron radiation of the VEPP-3 storage ring (Institute of Nuclear Physics, Siberian Branch, Russian Academy of Sciences). The polarization dependences of effective coordination numbers and edge σ-resonance intensity are analyzed, and parameters of the local surroundings of atoms (coordination numbers, interatomic distances, Debye-Waller factors σ²) are determined. For the Br₂ intercalates, the orientation angle with respect to the matrix layers is 64±1.5°, and the interatomic distances are close to those in the gas phase. The FeCl₃ molecule forms dimers in the matrix as it does in the gas phase, and the iron atoms have tetrahedral surroundings. For the Fe(AA)₃ molecules intercalated into the matrix, the iron atoms have significantly distorted octahedral environments. For the SnCl₄ intercalates, the lowering of temperature does not cause additional coordination of Sn atoms, and structural disorder of SnCl₄ makes the major contribution to σ². Institute of Inorganic Chemistry, Siberian Branch, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 37, No. 6, pp. 1081–1088, November–December, 1996 Translated by L. Smolina     

Radial electron-pair densities in momentum space and shell structure of atoms

 The radial electron-pair intracule (relative motion) H(u) and extracule (center-of-mass motion) D(R) densities in position space were known to reveal four types of maxima which are related to the four inner electron shells, K, L, M, and N, of atoms. The corresponding radial electron-pair intracule Hˉ(v) and extracule Dˉ(P) densities in momentum space are studied for the 102 atoms from He (atomic number Z=2) to Lr (Z=103). The densities Hˉ(v) and Dˉ(P) are found to have either one maximum or two maxima, and the numbers of maxima in Hˉ(v) and Dˉ(P) are the same for 98 atoms. For these atoms, the locations υ _max and P _max and the heights Hˉ _max and Dˉ _max of the corresponding maxima satisfy the approximate relations υ _max ≅ 2P _max and Hˉ _max ≅Dˉ _max /2. On the basis of their Z-dependence, the maxima in Hˉ(v) and Dˉ(P) of the 102 atoms are classified into five types. Shell-pair decompositions of the radial densities show that these maxima reflect five outer electron shells of atoms. Received: 24 January 2001 / Accepted: 12 March 2001 / Published online: 13 June 2001     

Oxygen desorption from polycrystalline palladium: Thermal desorption of O<Subscript>2</Subscript> from a chemisorbed layer of O<Subscript>ads</Subscript> in the course of the decomposition of PdO surface oxide and in the release of oxygen from the bulk of palladium

The desorption of oxygen from polycrystalline palladium (Pd(poly)) was studied using temperature-programmed desorption (TPD) at 500–1300 K and the amounts of oxygen absorbed by palladium (n) from 0.05 to 50 monolayers. It was found that the desorption of O₂ from Pd(poly), which occurred from a chemisorbed oxygen layer (O_ads), in the release of oxygen from a near-surface metal layer in the course of the decomposition of PdO surface oxide, and in the release of oxygen from the bulk of palladium (O_abs), was governed by repulsive interactions between O_ads atoms and the formation and decomposition of O_ads-Pd*-O_abs structures (Pd* is a surface palladium atom). At θ ≤ 0.5, the repulsive interactions between O_ads atoms (ɛ_aa = 10 kJ/mol) resulted in the desorption of O₂ from Pd(poly) at 650–950 K. At 0.5 ≤ n ≤ 1.0, the release of inserted oxygen from a near-surface palladium layer occurred during TPD in the course of the migration of O_abs atoms to the surface and the formation-decomposition of O_ads-Pd*-O_abs structures. As a result, the desorption of O₂ occurred in accordance with a first-order reaction with a thermal desorption (TD) peak at T _max ∼ 700 K. At 1.0 ≤ n ≤ 2.0, the decomposition of PdO surface oxide occurred at a constant surface cover-age with oxygen during TPD in the course of the formation-decomposition of O_ads-Pd*-O_abs structures. Because of this, the desorption of O₂ occurred in accordance with a zero-order reaction at low temperatures with a TD peak at T _max ∼ 675 K. At 1.0 ≤ n ≤ 50, oxygen atoms diffused from deep palladium layers in the course of TPD and arrived at the surface at high temperatures. As a result, O₂ was desorbed with a high-temperature TD peak at T > 750 K.     

Influence of the effective mass on the relative neutron density distribution inside a large sample in prompt-gamma neutron activation analysis

A Monte Carlo study was carried out to determine the influence of the effective scattering mass (M _e) of the atoms on the neutron density profile inside and outside the sample illuminated by a thermal neutron beam as in large-sample prompt-gamma neutron activation analysis (LS-PGNAA). From theory it is known that the spatial neutron density distribution (n(r)) inside a large sample is not the same for atoms with the same macroscopic scattering and absorption cross-section (Σ _s and Σ _a) but different M _e, due to anisotropic scattering at low M _e. The probability of neutron absorption in the sample was found to be the same for materials with equal Σ _s and Σ _a but different M _e, even though the neutron density distribution in the sample was found to change slightly. In view of typical sample, collimator and detector dimensions, it is concluded that M _e does not need to be taken into account in a correction method for neutron self-shielding in LS-PGNAA.     

Estimation of the upper limit of carbon concentration in boron carbide crystals

The existence of a boron carbide phase with ∼25 at % carbon was proven experimentally. To evaluate the maximum possible concentration of C atoms in boron carbide (B_{12 − x} C _x )(BC₂) crystals, we performed quantum-chemical calculations of (B_{12 − x} C _x )(BH₂)₆(CH₃)₆ model compounds (x = 0–4; the goal of calculations was to determine the upper limiting number of C atoms in the B_{12 − x} C _x icosahedron) by the density functional theory method (B3LYP, 6-31G** basis set, full geometry optimization). A comparison of the experimental and calculated data showed that the calculations of the model compounds reproduced the experimental dependences of the structural parameters of the icosahedron (mean bond length and volume) on the number of C atoms in it. The icosahedra were found to be stable at x ≤ 3. According to the results of the quantum-chemical calculations, the maximum carbon concentration in boron carbide was 33 at %, which corresponded to the composition B₁₀C₅ and the structural formula (B₉C₃)(BC₂).     

Indium-containing heterofullerenes and their η5-π-complexes

The molecular and electronic structure of hypothetical metallofullerenes In₅C₅₅ (1a) and In₁₀C₆₀ (2a) were simulated by the MNDO/PM3 method. Formally, heterofullerene1a is obtained from the C₆₀ cluster by replacement of the carbon atoms at α-positions relative to one of the pentagons by In atoms, and cluster2a is obtained from the C₇₀ cluster by replacement of the carbon atoms framing the polar pentagons of this fullerene by In atoms. Along with clusters1a and2a, their η⁵-π-complexes ln(η⁵-1a (1b) and ln₂(2η⁵-2a) (2b) with one (1b) and two (2b) exohedral In atoms coordinated to the pentagons (pent ^*) isolated by In atoms were also studied. The energies of the In—pent ^* bonds in1b and2b are approximately equal to 104 kcal mol⁻¹. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 880–883, May, 1998.     

The reaction mechanisms of boron amidinate and small molecules: a density function theory study

Density functional theory calculations have been carried out to explore the reaction mechanisms for the reactions of “frustrated Lewis pairs” (FLPs) with small molecules. Four reactions were studied in the present investigation. A new N-heterocyclic carbene borane, boron amidinate compound HC(iPrN)₂B(C₆F₅)₂ (1), classified as FLPs, was chosen as the common reactant of these reactions. It was used to react with CO₂, CO, and two terminal alkynes, methylacetylene and phenylacetylene. The reactions of 1 with CO₂ and CO can both be regarded as the concerted addition mechanisms. In these reactions, the formations of the C2–N2 and B–O1 bonds take place simultaneously. For the reactions of 1 and methylacetylene or phenylacetylene, our calculations indicated that a deprotonation pathway and the connection between B atoms and terminal alkyne C atoms occur by a concerted manner simultaneously, together with the connection between N2 and hydrogen atoms. We also investigated the reaction mechanisms according to the frontier molecular orbital (FMO) theory and carried out electric charge analyses, finding that the two results were consistent with each other perfectly. Electric charges transfer from HOMO of 1_OPEN to LUMO of CO₂ or CO. In contrast, electric charges transfer from HOMO of methylacetylene or phenylacetylene to LUMO of 1_OPEN.     

Determination of steryl sulphates in invertebrate tissue by liquid chromatography–tandem mass spectrometry

A method for the identification and quantification of underivatised steryl sulphates in invertebrates by liquid chromatography (LC) coupled with tandem mass spectrometry (MS) involving a single cleanup step has been developed. Negative electrospray ionisation and positive and negative atmospheric-pressure chemical ionisation (APCI) spectra of steryl sulphate showed pseudomolecular ions ([M+H–H₂SO₄]⁺or [M–H]⁻). Collision-induced dissociation (CID) was efficient only in positive APCI. LC-MS in negative APCI was least susceptible to interference and possible differences in response factors. The detection limits (signal-to-noise ratio of 3) based on cholest-5-enyl-3-sulphate in positive and negative APCI modes are 3.66 and 0.73 pmol μL⁻¹, respectively. Calibration plots and response factors for cholest-5-enyl-3-sulphate relative to the internal standard, cholecalciferyl-3-sulphate, in both positive and negative polarities, were linear in the concentration range from 1.22 to 16.4 pmol μL⁻¹ with good coefficients of determination (R ²>0.98). It is suggested that the structure elucidation of steryl sulphates is best achieved in CID positive APCI mode, whereas their quantification should be carried out using negative APCI.     

Crystal structure of the reaction product of copper(II) nitrate with α-(3,3-Dimethyl-3,4-dihydro-1-isoquinolyl)hydroxy-iminoacetonitrile [Cu3(μ3-OH)(μ-L)3(NO3)2(H2O)] · 2H2O

The coordination compound [Cu₃(μ₃-OH)(μ-L)₃(NO₃)₂(H₂O)] · 2H₂O (I), where L is the α-(3,3-dimethyl-3,4-dihydro-1-isoquinolyl)hydroxyiminoacetonitrile anion, has been synthesized. The crystal and molecular structure of I was determined by X-ray diffraction (Enraf-Nonius CAD4, MoK _α radiation, graphite monochromator, ω-scan mode, 2θ_max = 49.96°, 7673 unique reflections, a = 12.745(3) ?, b = 13.726(3) ?, c = 28.835(6) ?, β = 93.44(3)°, V = 5035.2(17) ?³, Z = 4, space group P2₁/c). In the trimer complex I, the copper atoms are combined by a bridging hydroxy group. The copper atoms are additionally linked pairswise by three tridentate chelating bridging organic anions coordinated to the Cu(II) atoms by the N and O atoms of the deprotonated oxime group and by the N atom of the dihydroisoquinoline moiety. Original Russian Text ? V.I. Sokol, V.V. Davydov, N. Yu. Merkur’eva, E.I. Polyakova, Yu.V. Shklyaev, V.S. Sergienko, 2007, published in Zhurnal Neorganicheskoi Khimii, 2007, Vol. 52, No. 10, pp. 1643–1652.     

Optical Study of Radicals (OH, O, H, N) in a Needle-plate Negative Pulsed Streamer Corona Discharge

Optical emission spectroscopy has been applied to study the OH radicals and O, H, and N active atoms produced by a high-voltage negative pulsed streamer corona discharge of N₂ and H₂O mixture gas in a needle-plate reactor at one atmosphere. The relative vibrational populations and the vibrational temperature of N₂(C, v′) were determined. The effects of pulsed peak voltage, pulsed repetition rate, and the addition of O₂ on the relative populations of OH(A²Σ) radicals, O(3p⁵P), H_α (3P), and N(3p⁴P) active atoms were investigated. It was found that the relative populations of those radicals increase with increasing pulsed peak voltage and pulsed repetition rate. The relative population of OH(A²Σ) radicals decreases with increasing O₂ flow rate, while the relative populations of O (3p⁵P), H_α (3P), and N (3p⁴P) active atoms exhibit a maximum over the studied range of the O₂ flow rate. The involved physicochemical processes have also been discussed.     

Structure and coordination of organometallic groups on a chemically modified SiO2 surface

The structural, electronic, and energy parameters of the metal-containing clusters (H₃SiO)₃Si−O−XMe _n (X=H, B, Al, or Zn;n=0, 1, or 2), which model organometallic groups on a SiO₂ surface modified with B-, Al-, and Zn-containing alkyls, have been studied by quantum-chemical methods. Full geometry optimization for these clusters was carried out by the SCF MO LCAO method taking into account the electron correlation within the frameworks of the MP2 and B3LYP schemes using the 6-31G(d) (6-311G(d) for Zn) basis set. The effect of the crystal environment was taken into account in calculations of siliconoxygen clusters containing 10 and 30 silicon atoms using theab initio SCF/6-31G(d) and semiempirical MNDO-PM3 methods. Various modes of coordination and interactions of organometallic groups with oxygen atoms of surface groups were studied. For the organoaluminum group on the surface, two stable conformations were found, namely, the three-coordinate structure with the chain −O−AlMe₂ ligand and the four-coordinate (quasicyclic) structure with the Al atom that forms two nonequivalent bonds with the O atoms at the same Si atom. The four-coordinate structure is energetically more favorable. No stable structures were found for the organoboron and organozinc fragments. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1296–1303, July, 1998.     

Rare Earth-Rich Indides <Emphasis Type="Italic">RE</Emphasis><Subscript>5</Subscript>Pt<Subscript>2</Subscript>In<Subscript>4</Subscript> (<Emphasis Type="Italic">RE</Emphasis> = Sc,Y, La–Nd,Sm, Gd–Tm,Lu)

Summary. The isotypic indides RE ₅Pt₂In₄ (RE = Sc, Y, La–Nd, Sm, Gd–Tm, Lu) were synthesized by arc-melting of the elements and subsequent annealing. They were investigated via X-ray powder diffraction. Small single crystals of Gd₅Pt₂In₄ were grown via slow cooling and the structure was refined from X-ray single crystal diffractometer data: Pbam, a = 1819.2(9), b = 803.2(3), c = 367.6(2) pm, wR ² = 0.089, 893 F ² values and 36 parameters. The structure is an intergrowth variant of distorted trigonal and square prismatic slabs of compositions GdPt and GdIn. Together the platinum and indium atoms build up one-dimensional [Pt₂In₄] networks (292–333 pm Pt–In and 328–368 pm In–In) in an AA stacking sequence along the c axis. The gadolinium atoms fill distorted square and pentagonal prismatic cages between these networks with strong bonding to the platinum atoms.     

M?ssbauer spectra of iron doped CuCrS2

M?ssbauer spectroscopy is used to study the state of iron atoms in samples with a composition of CuCr_1−x Fe _x S₂ (x = 0.01–0.30). It is shown that at x ≤ 0.02 samples are solid solutions in which iron atoms have an oxidation number of 3+ and replace chromium atoms in octahedral sites. When the iron concentration increases, the second phase — chalcopyrite CuFeS₂ — forms along with the solid solution. The relative iron concentration in this phase increases from 11% at x = 0.03 to 52% at x = 0.30. Original Russian Text Copyright ? 2009 by V. A. Varnek, V. V. Sokolov, I. Yu. Filatova, and S. A. Petrov __________ Translated from Zhurnal Strukturnoi Khimii, Vol. 50, No. 2, pp. 365–368, March–April, 2009.     

Rare Earth-Rich Indides RE 5Pt2In4 ( RE = Sc, Y, La–Nd, Sm, Gd–Tm, Lu)

The isotypic indides RE ₅Pt₂In₄ (RE = Sc, Y, La–Nd, Sm, Gd–Tm, Lu) were synthesized by arc-melting of the elements and subsequent annealing. They were investigated via X-ray powder diffraction. Small single crystals of Gd₅Pt₂In₄ were grown via slow cooling and the structure was refined from X-ray single crystal diffractometer data: Pbam, a = 1819.2(9), b = 803.2(3), c = 367.6(2) pm, wR ² = 0.089, 893 F ² values and 36 parameters. The structure is an intergrowth variant of distorted trigonal and square prismatic slabs of compositions GdPt and GdIn. Together the platinum and indium atoms build up one-dimensional [Pt₂In₄] networks (292–333 pm Pt–In and 328–368 pm In–In) in an AA stacking sequence along the c axis. The gadolinium atoms fill distorted square and pentagonal prismatic cages between these networks with strong bonding to the platinum atoms.