Evaluation of two‐center,three‐ and four‐electron integrals over Slater‐type orbitals in elliptical coordinates

An algorithm for evaluation of two‐center, three‐electron integrals with the correlation factors of the type rr and rrr as well as four‐electron integrals with the correlation factors rrr and rrr in the Slater basis is presented. This problem has been solved here in elliptical coordinates, using the generalized and modified form of the Neumann expansion of the interelectronic distance function r for k ≥ ?1. Some numerical results are also included. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Monitoring cascade processes using VSI EWMA control charts

The paper considers the variables process control scheme for cascade process. We construct variable sampling interval (VSI) EWMA and EWMA control charts to effectively monitor the input variable and the output variable produced by a cascade process. Numerical analysis results demonstrate that the performance of the VSI control charts is much better than the fixed sampling interval (FSI) control charts in detecting small and median shifts. Copyright © 2009 John Wiley & Sons, Ltd.     

The role of d orbitals in tetrahedral hybrid orbitals of oxy-ions

The hybrid orbitals of tetrahedral oxy-ions containing some d character have been calculated by maximum overlap method. The d characters of hybrid orbitals increase in the order of SiO, PO, SO, ClO, and decrease in order of GeO, AsO, SeO, BrO. The bond strengths are also obtained for these ions. The hybrid Orbital of VO, CrO, and MnO are of the type d³s as the result of calculation.     

Laser ablation of AgSbS2 and cluster analysis by time‐of‐flight mass spectrometry

Thin films of AgSbS₂ are important for phase‐change memory applications. This solid is deposited by various techniques, such as metal organic chemical vapour deposition or laser ablation deposition, and the structure of AgSbS₂(s), as either amorphous or crystalline, is already well characterized. The pulsed laser ablation deposition (PLD) of solid AgSbS₂ is also used as a manufacturing process. However, the processes in plasma have not been well studied. We have studied the laser ablation of synthesized AgSbS₂(s) using a nitrogen laser of 337 nm and the clusters formed in the laser plume were identified. The ablation leads to the formation of various single charged ternary Ag_pSb_qS_r clusters. Negatively charged AgSbS, AgSb₂S, AgSb₂S, AgSb₂S and positively charged ternary AgSbS⁺, AgSb₂S⁺, AgSb₂S, AgSb₂S clusters were identified. The formation of several singly charged Ag⁺, Ag, Ag, Sb, Sb, S ions and binary Ag_pS_r clusters such as AgSb, Ag₃S^?, SbS (r = 1–5), Sb₂S^?, Sb₂S, Sb₃S (r = 1–4) and AgS, SbS⁺, SbS, Sb₂S⁺, Sb₂S, Sb₃S (r = 1–4), AgSb was also observed. The stoichiometry of the clusters was determined via isotopic envelope analysis and computer modeling. The relation of the composition of the clusters to the crystal structure of AgSbS₂ is discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Correlated n1,3S states for coulomb three‐body systems

n^1,3S (n = 1 ? 4) states for atomic three‐body systems are studied with the Angular Correlated Configuration Interaction method. A recently proposed angularly correlated basis set is used to construct, simultaneously and with a single diagonalization, ground and excited states wave functions which: (i) satisfy exactly Kato cusp conditions at the two‐body coalescence points; (ii) involve only linear parameters; (iii) show a fast convergency rate for the energy; and (iv) form an orthogonal set. The efficiency of the method is illustrated by the study a variety of three‐body atomic systems [m m m] with two negatively charged light particles, with diverse masses m and m, and a heavy positively charged nucleus m. The calculated ground 1¹S and excited n^1,3S (n = 2 ? 4) state energies are compared with those given in the literature, when available. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Ab initio studies of negative ion-molecule(s) clusters present in the atmosphere. II. OH−(H2O)n for n = 0, 2, 3, 4

Ab initio calculations are performed with 6–31G basis set to study the geometry and binding of the H₃O, H₅O, H₇O, and H₉O complexes. The H₃O complex is also investigated with the 6–31 G* basis set and MP 2 (Moller–Plesset perturbation theory of second order).     

Finding Y‐relevant part of X by use of PCR and PLSR model reduction methods

The paper is considering the following question: using principal component regression (PCR) or partial least squares regression (PLSR), how much data can be removed from X while retaining the original ability to predict Y ? Two model reduction methods using similarity transformations are discussed, one giving projections of original loadings onto the column space of the fitted response matrix (essentially the orthogonal signal correction (OSC) methods), and one giving projections of original scores onto the column space of the coefficient matrix (essentially the net analyte signal (NAS) methods). The loading projection method gives model residuals that are orthogonal to Y and , which is valuable in certain applications. The score projection method, on the other hand, gives model residuals that are orthogonal to , which is essential in other applications. It is shown that the reduced matrix X from the score projection method is a subset of the reduced matrix X from the loading projection method. It therefore has the smallest Frobenius norm, and thus the smallest total column variance, assuming centered data. Copyright © 2007 John Wiley & Sons, Ltd.     

Convergence accelerator approach for the evaluation of some three‐electron integrals containing explicit rij factors

A simplified analysis is presented for the evaluation of the three‐electron one‐center integrals of the form ∫rrrrrred r ₁d r ₂d r ₃, for the cases i, j, k, ≥−2, l=−2, m≥−1, n≥−1. These integrals arise in the calculation of lower bounds for energy levels and certain relativistic corrections to the energy when Hylleraas‐type basis sets are employed. Convergence accelerator techniques are employed to obtain a reasonable number of digits of precision, without excessive CPU requirements. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 93–99, 1999     

SCF and MC–SCF Study of CO2 with bond angle variation

Multiconfiguration (MC ) SCF calculations are reported for CO₂ for bond angles between 60° and 180°. The ground state configuration is found to be …?5a4b∣b∣a for small bending angles and …?6a3b∣b∣a for large bending angles, the change in ground state character occurring at a bond angle of about 100°. The force constant for bending obtained from the MC –SCF function is about 8.0% lower than the corresponding SCF value, and in considerably better agreement with experiment.     

Characteristic operators and unitarily invariant decomposition of hermitian operators

A set of characteristic operators {F} is proposed for performing the decomposition of p-particle Hermitian operators {D^p} to constitute irreducible components {D} of the unitary group D = FD^p, q = 0,1,2,…,p. For a deeper expolration of the properties of the characteristic operators, a few theorems are presented. As an illustration, the expected values for symmetric p-particle Hermitian operators are obtained as a number of terms having invariant group-theoretical meaning.     

Darstellung,Schwingungsspektrum und Kristallstruktur von (n‐Bu4N)2[(W6Cl)F] · 2 CH2Cl2 und 19F‐NMR‐spektroskopischer Nachweis der gemischten Clusteranionen [(W6Cl)FCl]2–, n = 1–6

Synthesis, Vibrational Spectra, and Crystal Structure of ( n ‐Bu₄N)₂[(W₆Cl )F ] · 2 CH₂Cl₂ and ¹⁹F NMR Spectroscopic Evidence of the Mixed Cluster Anions [(W₆Cl )F Cl ]^2–, n = 1–6 The reaction of (n‐Bu₄N)₂[(W₆Cl)Cl] with CF₃COOH in dichloromethane gives intermediately a mixture of the cluster anions [(W₆Cl)(CF₃COO)Cl]^2–, n = 1–6. By treatment with NH₄F the outer sphere coordinated trifluoracetato ligands are easily substituted and the components of the series [(W₆Cl)FCl], n = 1–6 are formed and characterized by their distinct ¹⁹F NMR chemical shifts. An X‐ray structure determination has been performed on a single crystal of (n‐Bu₄N)₂[(W₆Cl)F] · 2 CH₂Cl₂ (orthorhombic, space group Pbca, a = 15.628(4), b = 17.656(3), c = 20.687(4) Å, Z = 4). The low temperatur IR (60 K) and Raman (20 K) spectra are assigned by normal coordinate analysis based on the molecular parameters of the X‐ray determination. The valence force constants are f_d(WW) = 1.89, f_d(WF) = 2.43 and f_d(WCl) = 0.93 mdyn/Å.     

Atomic integrals containing rrr with λ, μ, ν ≥ −2

In this paper, the efficient evaluation of the atomic integrals I =∫rrrrrre^{?αr1?βr2?γr3}dτ with one or two factors r is described. These integrals are necessary for a lower-bound calculation for Li-like systems using the method of variance minimization or Temple's formula. © 1993 John Wiley & Sons, Inc.     

A Fluorescence Ratiometric Protein Assay Using Light‐Harvesting Conjugated Polymers

Summary: A highly selective protein assay was created which combines the fluorescent ratiometric technique based on FRET with the light‐harvesting properties of conjugated polymers. The cationic poly[(9,9‐bis(6′‐N,N,N‐trimethylammonium)‐hexyl)‐fluorene phenylene] bromide (PFP‐NMe) and the negatively charged biotinylated fluorescein probe (Fl‐B) were used to detect the target protein streptavidin optically. The strong electrostatic interactions between PFP‐NMe and fluorescein result in efficient FRET from PFP‐NMe to fluorescein. In the presence of streptavidin, however, the biotin moiety of Fl‐B specifically associates with streptavidin and the fluorescein molecule is buried deeply in the adjacent vacant binding sites. This separates the fluorescein spatially from the PFP‐NMe moiety, resulting in inefficient FRET from PFP‐NMe to fluorescein. Although a nonspecific protein, such as BSA, shows nonspecific interactions with PFP‐NMe, it does not affect the fluorescent ratio value of PFP‐NMe to fluorescein. Hence, the charged neutral complex of two oppositely charged conjugated polymers can eliminate the nonspecific interactions, and thus optimize their application in protein assays.

A schematic representation of the protein assay operation.     

Rigid backbone polymers. XI. Solution phase-viscosity relationship

Using combined results of isothermal viscosity measurements and cross-polarized light microscopy on four polyisocyanate/solvent systems, the following were demonstrated: (a) an anisotropic phase appears, associated with a shoulder in the viscosity curve, at a concentration v lower than the peak viscosity at v; (b) the inversion from anisotropic inclusions in an isotropic matrix to isotropic inclusions in an anisotropic matrix, occurs at concentrations v > v and (c) the attainment of a single phase, microscopically anisotropic, occurs at v > v; where the viscosity is decreasing but has not yet reached its minimum. When the experiments were repeated with changes in temperature, the following were observed: (a) within each single phase the viscosity drops with increased temperature; (b) in the biphasic range, the total viscosity η⁰ remains about constant in the concentration range ≤ and increases with temperature in the range v > v; (c) in the interval v > v of the biphasic range, at constant temperature an increase in concentration decreases η⁰, and at constant concentration, a decrease in temperature lowers η⁰. Qualitative explanations of the observations are proposed.     

Aromaticity of ionic structures: Investigation and application of NICS value and 4n + 2 rule

At DFT/B3LYP/6‐31G** theoretical level, C₆H and C (n = 0, ?2, and +2), C₆H and C (n = 0, ±2, ±4, and ±6), C₆H (n = 0–6), as well as C₆H₆‐A and C₆‐A (A = Be, B, N, O, Mg, Al, Si, S, and Fe) structures were investigated. Comparing NICS values of C₆H and C (n = 0, ?2, and +2), we discovered that C₆H, C₆H were antiaromatic, and C₆H₆, C₆, C, C had aromaticity with negative NICS values. According to research of C₆H and C (n = 0, ±2, ±4, ±6), C₆H (n = 0–6), we sustained that their σ and π orbit were different and the locations of electrons were difficult to confirm in ionic structures. Thus, neither 4n + 2 rule nor NICS values can precisely estimate the aromaticity of ionic structures. Besides, through WBI (NBO) research of C₆H₆‐A and C₆‐A (A = Be, B, N, O, Mg, Al, Si, S, and Fe) structures, we found that C₆H₆ was easy to accept electrons, contrarily, C₆ was prone to bestowing electrons. Moreover, C₆H₆ took the symmetrical carbon atoms form feeble interaction or bond, and C₆ used all carbon atoms to impact with other atom. C₆H₆ generated two contrapuntal single bonds with oxygen, sulfur, and nitrogen atoms, whereas C₆ molecule formed double bond with oxygen and nitrogen atoms, two conjoint single bonds with sulfur atom. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Experimental and theoretical investigation on binary semiconductor clusters of B/Si and Al/Si

ASi (A = B and Al; n = 1–6) binary cluster anions were generated by laser ablation of samples composed of mixtures of Si and A (A = B and Al), and studied in the gas phase by tandem time‐of‐flight mass spectrometry. Some abundant ions are present in the mass spectrum, indicating that the clusters with these ions have stable structures. The structures of ASi clusters were investigated theoretically by the density functional theory (DFT) method and the energetically lowest‐lying structures were obtained. The binary clusters BSi and AlSi, with the same number of n, share different geometric structures except for ASi with n = 1 and 6, which have the same geometric structures in the ground state. For all the anionic clusters ASi, the lower spin state is lower in energy than the higher spin state in their optimized structures except for the linear ASi^? anions, for which the triplet state is lower in energy than the singlet. Calculations of the bonding energy (BE), energy gain (Δ) and HOMO‐LUMO energy gaps confirm that the cluster ASi has a very stable structure, which agrees well with the experimental results. Copyright © 2007 John Wiley & Sons, Ltd.     

Ab initio MO calculations on the stability of the CF,PF, SF,and MoF ions with the F1s core hole

For the CF, PF, SF, and MoF ions appearing after the F1s photoionization, the possibility of dissociation has been shown by the ab initio MO LCAO method within the Z + 1 core equivalent model. According to the calculations, the decay channel AF → AF + F(1s¹2p⁶) is energetically open for the ions. So the interpretation of the gas-phase emission FKα spectra, in which the bands are assigned to the discrete transition energies, can be unacceptable for these ions. The conditions and signs of such failure are discussed.     

Structure and stability of B6, B,and B clusters

We investigated various isomers of B₆, B, and B clusters with ab initio [Hartree–Fock (HF), MP2)] and density functional theory (DFT) methods. Ten B₆ isomers, 6 B isomers, and 6 B isomers are determined to be local minima on their potential energy hypersurfaces by the HF, B3LYP, B3PW91, and MP2 methods. Fourteen of these structures are first reported. The most stable neutral B₆ cluster is the capped pentagonal pyramid (C_5v), in agreement with the results reported previously. Hexagon B (C_2h) isomer and fan‐shaped B (C_2v) isomer are found to be the most stable on the cationic and anionic energy hypersurfaces, respectively. Natural bond orbital analysis suggests that there are three‐centered bonds in the most stable B₆ neutral and ionic clusters. The multicentered bonds are responsible for the special stability of the lowest‐energy isomer. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 269–278, 2003     

Effects of nitrate and water on the oxygen isotopic analysis of barium sulfate precipitated from water samples

BaSO₄ precipitated from mixed salt solutions by common techniques for SO isotopic analysis may contain quantities of H₂O and NO that introduce errors in O isotope measurements. Experiments with synthetic solutions indicate that δ¹⁸O values of CO produced by decomposition of precipitated BaSO₄ in a carbon reactor may be either too low or too high, depending on the relative concentrations of SO and NO and the δ¹⁸O values of the H₂O, NO, and SO. Typical δ¹⁸O errors are of the order of 0.5 to 1‰ in many sample types, and can be larger in samples containing atmospheric NO, which can cause similar errors in δ¹⁷O and Δ¹⁷O. These errors can be reduced by (1) ion chromatographic separation of SO from NO, (2) increasing the salinity of the solutions before precipitating BaSO₄ to minimize incorporation of H₂O, (3) heating BaSO₄ under vacuum to remove H₂O, (4) preparing isotopic reference materials as aqueous samples to mimic the conditions of the samples, and (5) adjusting measured δ¹⁸O values based on amounts and isotopic compositions of coexisting H₂O and NO. These procedures are demonstrated for SO isotopic reference materials, synthetic solutions with isotopically known reagents, atmospheric deposition from Shenandoah National Park, Virginia, USA, and sulfate salt deposits from the Atacama Desert, Chile, and Mojave Desert, California, USA. These results have implications for the calibration and use of O isotope data in studies of SO sources and reaction mechanisms. Published in 2008 by John Wiley & Sons, Ltd.     

Assembly of Chiral Two- and Three-dimensional Copper(I) Pseudohalide Based Coordination Polymers with Asymmetrically Substituted Pyrazine and Pyrimidine Ligands

The coordination polymers [(CuCN)₂(μ-2 Mepyz)], [CuCN(μ-2 Mepyz)] and [CuCN(μ-4 Mepym)] ( 1 – 3 ) (2 Mepyz = 2-methylpyrazine; 4 Mepym = 4-methylpyrimidine) may be prepared by self-assembly in acetonitrile solution at 100 °C ( 1 , 3 ) or without solvent at 20 °C ( 2 ). All three contain [CuCN] chains that are bridged by the bidentate aromatic ligands into sheets in 1 and 3 D frameworks in 2 and 3 . Reaction of CuSCN with these heterocyclic diazines at 100 °C leads to formation of the lamellar coordination polymers [(CuSCN)(μ-2 Mepyz)] ( 4 ) and [CuSCN · (4 Mepym-κN1)] ( 5 ), which contain respectively [CuSCN] chains and trans-trans fused [CuSCN] sheets as substructures. The presence of an asymmetric substitution pattern in 2 Mepyz and 4 Mepym induces the adoption of a chiral structure by 2 and 5 (space groups P2₁2₁2₁ and P1).