Unified analytical evaluation of the two-center coulomb and hybrid integrals over slater-type orbitals

Two-center Coulomb and hybrid integrals are combined into a single expression by use of the formulas given by the author for the expansion of real and complex STO 's about a point displaced from the orbital center. The final results are expressed in terms of the overlap integrals between STO 's. Analytical formulas for the evaluation of these integrals have been established recently by the author.     

Molecular Complexes of Crown Ethers in Crystals and Solutions

A review of the experimental and theoretical studies of the crown ether complexes with polar molecules in their crystals, solutions, and in a gas phase is given. The type of the molecular bonds in the complexes, their stoichiometry, and the change in the macrocycle conformation during complex formation are considered, as well as the effect of the macrocycle structure and the nature of the medium on the efficiency of the molecular bonding. New data are given on the enthalpies of transfer of the crown ethers from tetrachloromethane into solvents capable of forming hydrogen bonds. The enthalpies of specific interactions of macrocycles with the molecules of the solvents in the medium of the same solvents are characterized. The conformations of the crown ethers in the media under study are discussed.     

The antiferromagnetic-ferromagnetic transition in the system Zn1−x CuxCr2S4

The magnetization and paramagnetic susceptibility of the system of compounds Zn_1−x Cu_xCr₂S₄ (0<x⩽1) are investigated at low temperatures. It is shown that as the content of Cu increases the system exhibits a transition from an antiferromagnetic to a ferromagnetic state. Fiz. Tverd. Tela (St. Petersburg) 40, 278–279 (February 1998)     

Phase equilibria in the Tl-TlBr-S system

The polythermal sections TlBr-Tl₂S, TlBr-Tl₄S₃, TlBr-TlS, and Tl₆SBr₄-Tl; the isothermal section at 300 K of the phase diagram; and the projection of the liquidus surface of the Tl-S-Br system have been investigated in the composition region Tl-TlBr-S by DTA, X-ray powder diffraction analysis, and microhardness measurements. The primary crystallization regions, including that of the only ternary compound (Tl₆SBr₄), have been determined, and the types and coordinates of the invariant and univariant equilibria in the phase diagram are determined.     

Synthesis and molecular structure of 3,7-dimethyl-2-[N-(4-methylpyridyl-2)-4-hydroxy-3-methyl-5-oxopyrrolen-3-yl-2]imidazo[1,2-a]pyridine

Heterocyclization of 2-chloroepoxy-1,1-diethoxy-2.3-butane with 2-amino-4-methylpyridine occurred with participation of all three potential electrophilic centers to give 3,7-dimethyl-2-[N-(4-methylpyridyl-2)-4-hydroxy-3-methyl-5-oxopyrrolen-3-yl]imidazo[1,2-a]pyridine, the structure of which was determined by X-ray crystallography. __________ Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 7, 1089–1094, July 2006.     

Determination of an infinite non-self-adjoint Jacobi matrix from its generalized spectral function

Restoration from the generalized spectral function of the equations $$b_0 y_0 + a_0 y_1 = \lambda y_{0,} a_{n - 1} y_{n - 1} + b_n y_n + a_n y_{n + 1} = \lambda y_{n,} n = 1,2,3,...,$$ wherea _n and b_n are arbitrary complex numbers,a _n≠ 0 (n = o, i, 2,...), λ is a complex parameter, and {P _n (λ)} ₀ ^∞ is the required solution, is investigated. Necessary and sufficient conditions for solvability of the inverse problem are obtained, and the restoration procedure is described.     

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.     

On the calculation of arbitrary multielectron molecular integrals over Slater‐type orbitals using recurrence relations for overlap integrals. III. Auxiliary functions \documentclass{article}\pagestyle{empty}\begin{document}$Q_{nn'}^{q}$\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$G_{-nn'}^{q}$\end{document}

The auxiliary functions $Q_{nn'}^{q}(p,pt)$ and $G_{-nn'}^{q}(p_{a},p,pt)$ which are used in our previous paper [Guseinov, I. I.; Mamedov, B. A. Int J Quantum Chem 2001, 81, 117] for the computation of multicenter electron‐repulsion integrals over Slater‐type orbitals (STOs) are discussed in detail, and the method is given for their numerical computation. The present method is suitable for all values of the parameters p_a, p, and pt. Three‐ and four‐center electron‐repulsion integrals are calculated for extremely large quantum numbers using relations for auxiliary functions obtained in this paper. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001