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    Accurate and Fast Evaluation of Three-Center Nuclear Attraction Integrals of Coulomb-Yukawa Like Correlated Interaction Potentials and Slater Type Orbitals
    (Chemical Soc Japan, 2013) Guseinov, Israfil I.; Gorgun, Nursen Seckin
    With the use of one-range addition theorems of Slater type orbitals (STOs) introduced by one of the authors, three-center nuclear attraction integrals containing Coulomb-Yukawa like correlated interaction potentials (C-CIPs and Y-CIPs) appearing in the Hartree-Fock-Roothaan (HFR) equations for molecules are evaluated. These integrals are expressed through the overlap integrals which depend on the frictional quantum number alpha, where -infinity < alpha <= 2. The convergence of the series is tested by calculating three-center nuclear attraction integrals of C-ClPs, Y-CIPs, and STOs for the arbitrary values of potential parameters and locations of orbitals. For rapid calculations of these integrals, we use the partial summations of some indices corresponding to progressively increasing upper limits appearing in the series expansion relations. Additionally, the binomial coefficients arising in the series are stored in the memory of the computer using their recurrence relation. The fast and accurate computation approach suggested in this work is demonstrated.
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    Algebraic Treatment of Scattering via the Manning-Rosen Potential Related to the SO(2, 1) Group
    (Tubitak Scientific & Technological Research Council Turkey, 2007) Gorgun, Nursen Seckin; Isik, Fikret
    In this study, we consider SO(2,1) superset of SO(1,1) subgroup reduction from one dimensional scattering systems related to SO( 2,1). As an analytical application, we show via algebraic approach the Manning Rosen potential belongs to the class of potentials corresponding to the reduction SO(2,1) superset of SO(1,1). The wave function and the scattering matrix of the system with this potential were determined.
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    Calculation of multicenter electric field gradient integrals over Slater-type orbitals using unsymmetrical one-range addition theorems
    (Springer, 2011) Guseinov, Israfil I.; Gorgun, Nursen Seckin
    The electric field induced within a molecule by its electrons determines a whole series of important physical properties of the molecule. In particular, the values of the gradient of this field at the nuclei determine the interaction of their quadrupole moments with the electrons. Using unsymmetrical one-range addition theorems introduced by one of the authors, the sets of series expansion relations for multicenter electric field gradient integrals over Slater-type orbitals in terms of multicenter charge density expansion coefficients and two-center basic integrals are presented. The convergence of the series is tested by calculating concrete cases for different values of quantum numbers, parameters and locations of orbitals.
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    On the fast evaluation of three-center nuclear attraction integrals using one-range addition theorems for Slater functions
    (Iop Publishing Ltd, 2013) Gorgun, Nursen Seckin
    Using one-range addition theorems, the three-center nuclear attraction integrals are expressed through the overlap integrals containing chi- and chi(alpha)-Slater-type orbitals (chi-STOs and chi(alpha)-STOs), where -infinity < alpha <= 2 and chi(alpha)(nlm) (zeta, (r) over right arrow) = 1/(2 zeta r)(alpha)chi(nlm) (zeta, (r) over right arrow). For the fast calculation, the partial summation is utilized for some indices of series expansion relations which correspond to progressively increasing upper limits. The binomial coefficients are stored in the memory of the computer. The convergence and accuracy of series are tested by calculating concrete cases. The best values are obtained for alpha = 0.
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    Use of lined-up auxiliary functions in the evaluation of overlap integrals over integer and non-integer n Slater type orbitals
    (Elsevier, 2019) Guseinov, Israfil I.; Andic, Zekayi; Mamedov, Bahtiyar A.; Gorgun, Nursen Seckin
    A combined theory for the overlap integrals of integer and non-integer n chi-Slater type orbitals (chi-ISTO and chi-NISTO) is presented. This approach is based on the use of lined-up auxiliary functions introduced by one of the authors. The suggested theory guarantees a highly accurate calculation of the overlap integrals for the arbitrary values of quantum numbers and locations of orbitals.
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    The use of quantum damping self-frictional theory in a study of hydrogen-like atomic energies and forces
    (Elsevier Science Bv, 2018) Gorgun, Nursen Seckin; Guseinov, Israfil I.; Aydin, Ramazan
    By the use of complete orthogonal sets of psi((delta*))-damping self-frictional (DSF) exponential type orbitals (psi((delta*))-DSFETO) introduced by one of the authors, the quantum DSF study of hydrogen-like atomic energies and forces are suggested. Here, (delta*) = (alpha*) or (delta*) = (p(l)*), P-l* = 2l +2-alpha* and alpha* = alpha(-)(nl)*(Z)* are the integer and noninteger DSF quantum numbers which depend on quantities n, l and z, where z=H, He+, Li++, Be+++, B++++, C+++++, N++++++, O+++++++, F++++++++, Ne+++++++++. The average values of potentials, kinetic and total energies and forces of the hydrogen-like atomic systems are calculated. The given values are compared with the results obtained in the non-DSF (NDSF) theory.