Yazar "Mamedov, B. A." seçeneğine göre listele

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    A new algorithm for evaluation of the simplified gamma-ray shielding formulas
    (Pergamon-Elsevier Science Ltd, 2006) Guseinov, Israfil Isa; Oner, F.; Mamedov, B. A.
    New analytical formulas for construction of the gamma-ray shielding formulas for a plane, a disk, a cylindrical or a spherical surface (volume) sources are proposed depending on the functional of the binomial coefficients. Numerical stability and optimization of such analytical relations become more important with increasing degree and order. Some numerical results are presented for significant mapping examples and they are briefly discussed. The computation results are compared with those of previously published studies. Using the derived expressions the gamma-ray shielding formulas can be evaluated most efficiently and accurately for mu t = 0, 1, 2. (C) 2006 Elsevier Ltd. All rights reserved.
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    A unified treatment of the lattice Green function, generalized Watson integral and associated logarithmic integral for the d-dimensional hypercubic lattice
    (Taylor & Francis Ltd, 2007) Guseinov, Israfil Isa; Mamedov, B. A.
    Using multinomial expansion theorems, a unified approximation for the lattice Green function, generalized Watson integral and associated logarithmic integral for the d-dimensional hypercubic lattice is presented. The validity of this approximation is tested by other calculation methods. The approximate formulas derived are satisfactory to all other approximations and are a most suitable solution for the study of related physical properties of solids. Some examples of the effectiveness of this methodology are presented.
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    Accurate evaluation of overlap integrals of Slater type orbitals with noninteger principal quantum numbers using complete orthonormal sets of ??-exponential type orbitals
    (Springer, 2008) Guseinov, Israfil Isa; Mamedov, B. A.
    In this paper, by the use of complete orthonormal sets of psi(alpha) exponential-type orbitals (Psi(alpha)-ETOs, alpha = 1, 0, -1,-2,...), the series expansion formulas in line-up coordinate systems are established for the overlap integrals with noninteger n* Slater-type orbitals (NISTOs) in terms of overlap integrals over integer n Slater-type orbitals (ISTOs). The suggested approach guarantees a highly accurate calculation of the noninteger n* overlap integrals with arbitrary values of parameters. The results of computer calculations presented are in a complete agreement with those obtained in the literature using the alternative procedure.
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    Application of combined Hartree-Fock-Roothaan theory to atoms with an arbitrary number of closed and open shells of any symmetry
    (Springer Wien, 2007) Guseinov, Israfil Isa; Mamedov, B. A.; Ertuerk, M.; Aksu, H.; Sahin, E.
    The applicability of a combined open-shell Hartree-Fock theory of atomic-molecular and nuclear systems to the states of a single configuration which has the arbitrary symmetry of open shells is explicitly demonstrated by calculations based on the combined Hartree-Fock-Roothaan equations for atoms. As examples of an application of the combined theory using single-zeta Slater-type basis sets, the calculations have been performed for the lowest states of the lowest and excited electronic configurations of carbon and nitrogen atoms containing one-, two- and three-open shells. For the case of single-open shells for carbon and nitrogen atoms, the double-zeta basis-set calculations are also presented. The results of computer calculations for the orbitals, kinetic and total energies, linear combination coefficients and virial ratios are given.
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    Application of combined open shell Hartree-Fook-Roothaan theory to molecules using symmetrical one-range addition theorems of Slater type orbitals
    (Springer, 2010) Guseinov, Israfil Isa; Mamedov, B. A.; Andic, Z.
    We study the efficiency of symmetrical one-range addition theorems for Slater type orbitals which are used in the calculation of multicenter integrals arising in the combined open shell Hartree-Fook-Roothaan equations for molecules. As an example of application, the calculations are performed for the ground state of electronic configuration of molecules NH3 and CH2 that have the closed and open shells, respectively. The results of computer calculations for the orbital and total energies (in a.u.), and linear combination coefficients for symmetrical molecular orbitals are presented.
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    Calculation of electric multipole transition radial matrix elements, oscillator strengths and Einstein coefficients over nonrelativistic radial wave function using Slater type orbitals
    (Elsevier Science Bv, 2011) Guseinov, Israfil Isa; Mamedov, B. A.
    In this study, a new method is proposed for evaluating electric multipole transition (radial) matrix elements of the generalized type H-nl,nt(k) in hydrogenic atom and ions using the Slater type orbitals (STOs). The formula obtained allows the determination of all multipole transition matrix elements between two different nonrelativistic radial wave functions R-nl and R-nl. A comparative study carried out between the results of analytical computations and other numerical simulations shows that the methods agree well and emphasizing thus the effectiveness and accuracy of the proposed analytical expressions. The simple equation thus obtained has been found to be remarkable accurate and has shown a wide range of applicability. (C) 2011 Elsevier B.V. All rights reserved.
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    Calculation of integer and noninteger n-dimensional debye functions using binomial coefficients and incomplete gamma functions
    (Springer/Plenum Publishers, 2007) Guseinov, Israfil Isa; Mamedov, B. A.
    Recursion and analytical relations for the evaluation of integer and noninteger n-dimensional Debye functions have been derived. Using the binomial expansion theorem, these functions are expressed through the binomial coefficients and familiar incomplete gamma functions. This simplification and the use of the memory of the computer for calculation of binomial coefficients may extend the limits to large arguments for users and result in speedier calculation, should such limits be required in practice. Comparison of numerical results shows that analytical solutions are accurate almost from the beginning of the calculation time. The series expansion relations obtained is sufficiently accurate over the entire range of parameters. The convergence rate of the series is estimated and discussed.
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    Calculation of One-Electron Multicenter Integrals of Slater Type Orbitals and Coulomb-Yukawa Like Correlated Interaction Potentials with Integer and Noninteger Indices Using Unsymmetrical One-Range Addition Theorems
    (Chemical Soc Japan, 2010) Guseinov, Israfil Isa; Mamedov, B. A.
    Using expansion formulae for multicenter charge densities of integer and noninteger a Slater type orbitals (ISTO and NISTO) established by one of the authors with the help of unsymmetrical one-range addition theorems of complete orthonormal sets of Psi(alpha)-exponential type orbitals (Psi(alpha)-ETO), where a is the frictional quantum numbers (a = 1, 0, 1, 2, ... ), we perform the calculations for one-electron multicenter integrals of Slater type orbitals (STO) and Coulomb-Yukawa like correlated interaction potentials (CIP) with integer and noninteger indices (ICIP and NICIP). The convergence of the series is tested by calculating concrete cases for arbitrary values of indices and screening constants of orbitals and potentials. It should be noted that the results for one-electron multicenter integrals presented in this work were not shown in our previous publications. As an example of application, the calculations are performed for the ground state of electronic configuration of molecule BH2 that has the open shell.
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    Computation of molecular integrals over Slater type orbitals - I. Calculations of overlap integrals using recurrence relations (vol 465, pg 1, 1999)
    (Elsevier, 2006) Guseinov, Israfil Isa; Mamedov, B. A.
    [Anstract Not Available]
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    Computation of three-center overlap integrals over noninteger n Slater type orbitals using ??-ETO
    (World Scientific Publ Co Pte Ltd, 2007) Cuseinov, I. I.; Mamedov, B. A.
    Using complete orthonormal sets of Psi(alpha)-exponential type orbitals (Psi alpha-ETO, alpha = 1.0,-1,-2....), the three-center overlap integrals over noninteger n STO (NISTO) appearing in the evaluation of multicenter-multielectron integrals of central and non-central interaction potentials are calculated. The final results are expressed in terms of one- or two-center overlap integrals between NISTO and integer n STO (ISTO). The formulas obtained are valid for arbitrary noninteger principal quantum numbers, screening parameters, and location of NSTO.
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    Construction of One-Range Addition Theorems for Noninteger Slater Functions Using Self-Friction Exponential Type Orbitals and Polynomials
    (Maik Nauka/Interperiodica/Springer, 2020) Guseinov, İsrafil İsa; Mamedov, B. A.; Çopuroğlu, E.
    The addition theorems of Slater type orbitals (STOs) presented in literature are generally complicated to theoretically examine the electronic structure of atoms and molecules. The computational deficiencies in use of these theorems arise from the separation of integral variables. In this work, to eliminate these calculation efforts, a large number of independent one-range addition theorems for chi-noninteger Slater type orbitals (chi-NISTOs) in terms of chi-integer STOs (chi-ISTOs) is presented by using complete orthogonal basis sets of L-(pi*)-self-friction (SF) polynomials (L-(pi*)-SFPs), psi((pi*))-SF exponential type orbitals (psi((pi*))-SFETOs), L-(alpha*)-modified SFPs (L-(alpha*)-MSFPs), and psi((alpha*))-modified SFETOs (psi((alpha*))-MSFETOs) introduced by one of the authors. Here, pl(*) = 2l + 2 - alpha* and alpha* are the integer or noninteger (alpha* = alpha -infinity < alpha <= 2) or noninteger (alpha* not equal alpha, -infinity < 3) SF quantum numbers based on the Lorentz damping theory. The expansion coefficients of series for the one-range addition theorems are expressed through the analytical relations for the overlap integrals of chi-NISTOs with the same screening parameters. As an application, the calculations of overlap integrals with the different screening constants of (chi)-NISTOs are performed.
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    Evaluation of the auxiliary function G-nsq using basic overlap integrals over Slater type orbitals
    (Springer, 2008) Guseinov, Israfil Isa; Mamedov, B. A.
    This paper presents a computationally efficient formula in terms of basic overlap integrals over Slater type orbitals (STOs) for the evaluation of auxiliary function G(-ns)(q) which plays a central role in calculations of multicenter molecular integrals. The basic overlap integrals are calculated with the help of recurrence relations. The resulting simple analytical formula for the auxiliary function G(-ns)(q) (p(a), p, pt) is completely general for p(a) <= 1.2 and arbitrary values of parameters p and pt. The efficiency of calculation of auxiliary function G(-ns)(q) is compared with other method.
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    Evaluation of the Boys function using analytical relations
    (Springer, 2006) Guseinov, Israfil Isa; Mamedov, B. A.
    The analytical relations for Boys function F-m (x) are presented. These relations are useful in the fast and more accurate calculations of multicenter molecular integrals over Gaussian type orbitals (GTOs). The formulas obtained are numerically stable for all values of m and x.
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    Exact analytical expressions and numerical analysis of two-center Franck-Condon factors and matrix elements over displaced harmonic oscillator wave functions
    (Elsevier Science Bv, 2006) Guseinov, Israfil Isa; Mamedov, B. A.; Ekenoglu, A. S.
    A detailed study is undertaken, using various techniques, in deriving analytical formula of Franck-Condon overlap integrals and matrix elements of various functions of power (x(l)), exponential (exp(-2cx)) and Gaussian (exp(-cx(2))) over displaced harmonic oscillator wave functions with arbitrary frequencies. The results suggested by previous experience with various algorithms are presented in mathematically compact form and consist of generalization. The relationships obtained are valid for the arbitrary values of parameters and the computation results are in good agreement with the literature. The numerical results illustrate clearly a further reduction in calculation times.
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    Generalized flow rate functions arising in study of effects of processing on shear rate of yoghurt
    (Elsevier Sci Ltd, 2009) Guseinov, Israfil Isa; Mamedov, B. A.
    In this work, the generalized now rate functions arising in file Study of flow problems are introduced. The efficient and accurate formulas through the hypergeometrical and incomplete beta functions are established. It is shown that the now rate functions C(m) and D(m,epsilon) describing the effects of processing on shear rate of yoghurt are Special Cases of generalized now rate functions. Comparative numerical examples are presented to demonstrate the efficiency of the proposed approaches. (C) 2008 Elsevier Ltd. All rights reserved.
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    On the evaluation of generalized exponential integral functions
    (Pergamon-Elsevier Science Ltd, 2006) Guseinov, Israfil Isa; Mamedov, B. A.
    This paper deals with generalized exponential integral (GEI) functions arising in the study of anisotropic scattering in a multidimensional media. These functions are represented as finite linear combinations of basic GEIs introduced in this work. The recurrence relations are derived for the linear combination coefficients and basic GEIs. Numerical results are also given. The extensive test calculations show that the work proposed in this algorithm is the most efficient practical computations of GEI functions. (C) 2006 Elsevier Ltd. All rights reserved.
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    Studies of quantum self-frictional atomic potentials and nuclear attraction forces in standard convention
    (Elsevier, 2015) Guseinov, Israfil Isa; Mamedov, B. A.
    This paper is devoted to examine a physical nature of quantum self-frictional atomic potentials and nuclear attraction forces. Using analytical formulas for the L-l((p)*())-generalized Laguerre polynomials (L-l((p)*())-GLPs) and psi((p)(l)*())-generalized exponential type orbitals (psi((p)(l)*())-GETOs) in standard convention, the self-frictional atomic potentials and nuclear attraction forces are investigated, where p(l)* = 2l + 2 - alpha* and alpha* is the integer (alpha* = alpha, -infinity < alpha <= 2) or noninteger (alpha* not equal alpha, -infinity < alpha* < 3) self-frictional quantum number. We notice that the L-l((p)*())-GLPs, the origin of which is the quantum self-frictional fields, are the radial parts of the psi((p)(l)*())-GETOs. The dependence of the quantum self-frictional potentials and nuclear attraction forces as a function of the distance from nucleus is analyzed. The relationships presented are valid for the arbitrary values of quantum numbers and scaling parameters. (C) 2014 Elsevier B.V. All rights reserved.
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    The use of unsymmetrical one-range addition theorems of Slater type orbitals for the calculation of intermolecular Coulomb interaction energy
    (Elsevier Science Bv, 2011) Guseinov, Israfil Isa; Mamedov, B. A.
    The formulae at Hartree-Fock level are derived for the energy of Coulomb interaction between molecules containing any number of closed and open shells. These formulae are expressed in terms of linear combination coefficients of molecular orbitals and multicenter integrals of Slater type orbitals and interaction potentials produced by the charges of the molecules. As an example of application, by the use of unsymmetrical one-range addition theorems of Slater type orbitals the Hartree-Fock-Roothaan calculations have been performed for the energy of interaction produced by the ground states of two molecules H(2)O. (C) 2010 Elsevier B.V. All rights reserved.