Calculation of molecular electric and magnetic multipole moment integrals of integer and noninteger n Slater orbitals using overlap integrals

Closed formulas are established for the magnetic multipole moment integrals of integer and noninteger n Slater‐type orbitals (ISTOs and NISTOs) in terms of electric multipole moment integrals for which the analytic expressions through the overlap integrals with ISTOs and NISTOs are derived. The overlap integrals are evaluated by the use of auxiliary functions. Using the derived expressions the multipole moment integrals, and therefore the electric and magnetic properties of molecules, can be evaluated most efficiently and accurately. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Evaluation of two‐center overlap and nuclear attraction integrals over Slater‐type orbitals with integer and noninteger principal quantum numbers

A general formula has been established for the expansion of the product of two normalized associated Legendre functions centered on the nuclei a and b. This formula has been utilized for the evaluation of two‐center overlap and nuclear attraction integrals over Slater‐type orbitals (STOs) with integer and noninteger principal quantum numbers. The formulas given in this study for the evaluation of two‐center overlap and nuclear attraction integrals show good rate of convergence and great numerical stability under wide range of quantum numbers, orbital exponents, and internuclear distances. © 2001 Wiley Periodicals, Inc. Int J Quantum Chem, 2001     

Unified treatment for the evaluation of arbitrary multielectron multicenter molecular integrals over Slater‐type orbitals with noninteger principal quantum numbers

The expansion formula has been presented for Slater‐type orbitals with noninteger principal quantum numbers (noninteger n‐STOs), which involves conventional STOs (integer n‐STOs) with the same center. By the use of this expansion formula, arbitrary multielectron multicenter molecular integrals over noninteger n‐STOs are expressed in terms of counterpart integrals over integer n‐STOs with a combined infinite series formula. The convergence of the method is tested for two‐center overlap, nuclear attraction, and two‐electron one‐center integrals, due to the scarcity of the literature, and fair uniform convergence and great numerical stability under wide changes in molecular parameters is achieved. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Evaluation of Multicenter Electronic Attraction, Electric Field and Electric Field Gradient Integrals with Screened and Nonscreened Coulomb Potentials over Integer and Noninteger n Slater Orbitals

By the use of complete orthonormal sets of -exponential-type orbitals, where ( = 1, 0, –1, –2,...) the multicenter electronic attraction (EA), electric field (EF) and electric field gradient (EFG) integrals of nonscreened and Yukawa-like screened Coulomb potentials are expressed through the two-center overlap integrals with the same screening constants and the auxiliary functions introduced in our previous paper (I.I. Guseinov, J. Phys. B, 3 (1970) 1399). The recurrence relations for auxiliary functions are useful for the calculation of multicenter EA, EF and EFG integrals for arbitrary integer and noninteger values of principal quantum numbers, screening constants, and location of slater-type orbitals. The convergence of the series is tested by calculating concrete cases.     

Expansion Formulae for Two-center Integer and Noninteger <Emphasis Type="Italic">n</Emphasis> STO Charge Densities and their Use in Evaluation of Multi-center Integrals

Using complete orthonormal sets of Ψ^α-exponential type orbitals (Ψ^α-ETOs, α =1, 0, −1, −2, ...) introduced by the author, the series expansion formulae are derived for the two-center integer and noninteger n STO (ISTO and NISTO) charge densities in terms of integer n STOs at a third center. The expansion coefficients occurring in these relations are presented through the two-center overlap integrals between STOs with integer and noninteger principal quantum numbers. The general formulae obtained for the STO charge densities are utilized for the evaluation of two-center Coulomb and hybrid integrals of NISTOs appearing in the Hartee–Fock–Roothaan approximation. The final results are expressed in terms of both the overlap integrals and the one-center basic integrals over integer n STOs. It should be noted that the result for the multi-center multielectron integrals with two-center noninteger n STO charge densities presented in this paper were not appeared in our past publications.     

Calculation of Two-Center Nuclear Attraction Integrals over Integer and Noninteger n-Slater Type Orbitals in Nonlined-Up Coordinate Systems

Two-center nuclear attraction integrals over Slater type orbitals with integer and noninteger principal quantum numbers in nonlined up coordinate systems have been calculated by means of formulas in our previous work (T. Özdoan and M. Orbay, Int. J. Quant. Chem. 87 (2002) 15). The computer results for integer case are in best agreement with the prior literature. On the other hand, the results for noninteger case are not compared with the literature due to the scarcity of the literature, but also compared with the limit of integer case and good agreements are obtained. The proposed algorithm for the calculation of two-center nuclear attraction integrals over Slater type orbitals with noninteger principal quantum numbers in nonlined-up coordinate systems permits to avoid the interpolation procedure used to overcome the difficulty introduced by the presence of noninteger principal quantum numbers. Finally, numerical aspects of the presented formulae are analyzed under wide range of quantum numbers, orbital exponents and internuclear distances.     

Use of addition theorems in evaluation of multicenter nuclear-attraction and electron-repulsion integrals with integer and noninteger n Slater-type orbitals

Multicenter integrals appearing in the Hartree–Fock–Roothaan equations for molecules are calculated using different kinds of series expansion formulas obtained from the expansions of integer and noninteger n Slater-type orbitals, in terms of Ψ ^α -exponential-type orbitals (where α=1, 0, –1, –2,...) at a displaced center, that form complete orthonormal sets and are represented by linear combinations of integer n Slater-type orbitals. The convergence of these series is tested by calculating concrete cases. The accuracy of the results is quite high for quantum numbers, screening constants, and location of orbitals. Received: 13 February 2002 / Accepted: 11 March 2002 / Published online: 4 July 2002     

Calculation of the viscosity of <Emphasis Type="Italic">n</Emphasis>-heptane-methanol solutions at low <Emphasis Type="Italic">n</Emphasis>-heptane concentrations

The molar heat capacity C _p of the methanol-n-heptane system was measured at low concentrations of n-heptane and 298.15 K. The dynamic viscosity η of the system at 298.15 K was calculated from data on the molar heat capacity of methanol-n-heptane solutions within the framework of the Flory theory and the theory of free volume with regard to the molecular association. Based on the experimental data and calculation results, it was concluded that the viscosity of the methanol-n-heptane system exhibits an anomalous behavior.     

Calculation of the anisotropy of molecular polarizability of liquid <Emphasis Type="Italic">n</Emphasis>-alkanes and <Emphasis Type="Italic">n</Emphasis>-alcohols

Light scattering from liquid n-alkanes and n-alcohols in a strong electric field is measured by a photoelectric colorimeter at various wavelengths. The anisotropy of molecular polarizability of the substances is calculated by the Rayleigh formula.     

Use of Recursion and Analytical Relations in Evaluation of Hypergeometric Functions Arising in Multicenter Integrals with Noninteger <Emphasis Type="Italic">n</Emphasis> Slater Type Orbitals

In this work we present the new recursion and analytical relations for the calculation of hypergeometric functions F(1,b;c;z) occurring in multicenter integrals of noninteger n Slater type orbitals. The formulas obtained are numerically stable for 0 < z < 1 and all integer and noninteger values of parameters b and c The Author cordially congratulates Prof. I.I. Guseinov on his 70th birthday     

Isothermal solubility of individual light fullerenes in the homologous series of <Emphasis Type="Italic">n</Emphasis>-alkanes, <Emphasis Type="Italic">n</Emphasis>-alkanols, <Emphasis Type="Italic">n</Emphasis>-alkylcarboxylic acids,and arenes

Available published data on isothermal solubility (at 20°C) of individual light fullerenes in a homologous series of n-alkanes, n-alkanols, n-alkylcarboxylic acids, and arenas were systematized. A correlation between the parameter of Hildebrand’s cohesion and the logarithm of the mole fraction of the fullerene in the saturated solution was revealed.     

Speciation studies of nitric acid and U(VI) third phases in <Emphasis Type="Italic">n</Emphasis>,<Emphasis Type="Italic">n</Emphasis>-dialkyl amides/<Emphasis Type="Italic">n</Emphasis>-dodecane systems

Conventionally composition of the actinide-extractant solvate is assumed to be the same in the unpartitioned organic phase and the formed third phase. For example, if a m:n solvate has formed during extraction, the solvate is expected to be in the same state even during the third phase condition. However contemporary analysis, based on the spectroscopy measurements and empirical observations, has indicated the presence of an extended solvate. In this article, the proposed speciation in nitric acid and U(VI) third phase formation in n–n dialkyl amide/dodecane-nitric acid systems has been modeled with empirical correlations.     

The smallest Hosoya index in (<Emphasis Type="Italic">n</Emphasis>, <Emphasis Type="Italic">n</Emphasis> + 1)-graphs

A (n, n + 1)-graph G is a connected simple graph with n vertices and n + 1 edges. In this paper, we determine the lower bound for the Hosoya index in (n, n + 1)-graphs in terms of the order n, and characterize the (n, n + 1)-graph with the smallest Hosoya index.     

Radiothermoluminescence of <Emphasis Type="Italic">n</Emphasis>-eicosane mixtures with <Emphasis Type="Italic">n</Emphasis>-tetracosane: Effect of mixture composition

Radiothermoluminescence (RTL) curves of mixtures of C20 and C24 n-alkanes have been deconvoluted into the curves of crystalline and disordered regions, and their change depending on the mixture composition has been analyzed. The shape of the total RTL curve of the mixture regardless of the its composition is fundamentally different from that shape of the sum of the curves of the individual components taken in the relevant ratios. The difference becomes noticeable at as low a C20 amount in the mixture as 2% and is manifested in the disappearance of the intense RTL peaks of the individual components and appearance of new intense peaks in temperature intervals other than those of the RTL peaks of the components. It has been shown that these changes correlate with changes of the crystalline structure of the mixture: a new crystalline structure other than the structure of any of the individual components emerges and the mixture becomes amorphous. High selectivity of charge trapping in disordered regions of the mixture has been revealed: the contribution of RTL of the disordered regions to the total curve is many times higher than their volume fraction in the mixture. This selectivity might be due to an increase in concentration of defects in the unordered regions of the mixture in comparison with their concentration in the pure alkanes. These defects are traps for electrons that are accessible to acceptors introduced into the mixture.     

Quantum-chemical investigation of structure and stability of [<Emphasis Type="Italic">n</Emphasis>]-prismanes and [<Emphasis Type="Italic">n</Emphasis>]-asteranes

The study by DFT [B3LYP/6-311G(2df,p)] method of structural and energy characteristics peculiar to [n]-prismanes and [n]-asteranes demonstrated that prismanes of n = 3–10 and asteranes of n = 3–7 possessed a stable structure of D_nh-symmetry; the D_nh-geometry was distorted in the subsequent terms of the series.     

Kinetics of <Emphasis Type="Italic">n</Emphasis>-hexane isomerization over supported palladium catalysts

The steady- and unsteady-state kinetics of n-hexane isomerization over Ni- or Co-promoted Pd/HZSM-5 catalysts in the presence of hydrogen has been investigated. The kinetics of the reaction is described by similar fractional rational rate equations differing in the values of their constants. Hydrogen exerts a favorable effect on the isomerization rate. The catalysts have been characterized by the BET-N₂ method, X-ray diffraction, transmission electron microscopy, H₂-TPR, and NH₃-TPD. The introduction of a promoter (Ni or Со) strengthens the adsorption of the reactants and increases the amount of reactants adsorbed.     

Skeletal Isomerization of <Emphasis Type="Italic">n</Emphasis>-butenes over Solid Acid Catalysts

Conversion reactions of n-butenes over zeolites and amorphous catalysts have been investigated to deduce the factor that determines the selectivity for the skeletal isomerization producing isobutene. The effects of pore structure and acid site concentration on the selectivity for the skeletal isomerization are discussed on various catalysts. The pore structures of FER and CLI zeolites induce the distant locations of butene molecules, accelerating monomolecular skeletal isomerization. On the other hand, acid site concentration determines the preferred reaction path of n-butenes on amorphous catalysts. Oligomerization followed by cracking that produces various hydrocarbons is suppressed on the catalyst with low acid site concentration, resulting in high selectivity for isobutene. The feasibility of monomolecular skeletal isomerization on zeolites and amorphous catalysts is confirmed by its reversibility with high selectivity.     

A new stilbene glycoside from the <Emphasis Type="Italic">n</Emphasis>-butanol fraction of <Emphasis Type="Italic">Veratrum dahuricum</Emphasis>

A new stilbene glycoside, 5-methylresveratrol-3,4′-O-β-D-diglucopyranoside (1), was isolated from the n-butanol fraction of the rhizomes of Veratrum dahuricum, together with five known stilbenoids: resveratrol-3-O-β-D-glycoside (2), 4′-methylresveratrol-3-O-β-D-glycoside (3), oxyresveratrol-4′-O-β-D-glycoside (4), oxyresveratrol-3-O-β-D-glycoside (5), and oxyresveratrol-3,4′-O-β-D-diglycoside (6), and found for the first time in the investigated plant. The structures of six isolates were identified on the basis of 1D and 2D NMR data. Compounds 1–6 showed platelet aggregation inhibition, and compound 1 had an IC₅₀ value of 383.6 μM against platelet aggregation induced by AA. Published in Khimiya Prirodnykh Soedinenii, No. 3, pp. 279–282, May–June, 2009.