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    Application of quantum self-frictional nonperturbative theory for the study of atomic anharmonic oscillator potentials and their arbitrary derivatives
    (Springer, 2021) Guseinov, İsrafil İsa; Çopuroglu, E.; Mamedov, B.A.
    The self-frictional (SF) nonperturbative theory, introduced by one of the authors, is used for the evaluation of the V-(pl*()) and V-(alpha*) atomic anharmonic oscillator potentials and their derivatives, where p(l)* = 2l + 2 - alpha* and alpha* represent the integer (alpha* = alpha, -infinity < alpha <= 2) or non-integer (alpha* not equal alpha, -infinity< alpha* < 3) SF quantum numbers. This study is based on the use of complete sets of L-(pl*())and L-(alpha*) SF polynomials. The dependence of the potentials and their derivatives from the nucleus distances is investigated. All of the obtained results are valid for the arbitrary values of quantum numbers, scaling parameters and SF quantum numbers.
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    Calculation of negative ions of B, C, N, O and F using noninteger n Slater type orbitals
    (Chinese Chemical Soc, 2008) Guseinov, İsrafil İsa; Ertürk, Murat; Şahin, Ercan; Aksu, Hüseyin; Bağcı, Ali
    Combined Hartree-Fock-Roothaan calculations have been performed using noninteger n Slater type orbitals for the ground states of the lowest electron configurations 1s(2)2s(2)2p(n) (2 <= n <= 6) for negative ions of B, C, N, O and F. These results are compared with the corresponding results obtained from the use of integer n Slater type orbitals. All of the nonlinear parameters are fully optimized. The results of calculation of coupling-projection coefficients, orbital and total energies and virial ratios are presented. It is shown that the noninteger n Slater type orbitals, in general, improve the orbital energies.
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    Comment on "Electric multipole moments for some first-row diatomic hydride molecules"
    (Int Academic Publ, 2002) Guseinov, İsrafil İsa
    It is demonstrated that the recently presented formulas for the calculation of molecular electric multipole moments (Metin Orbay and Telhat Ozdogan, Commun. Theor. Phys. (Beijing, China) 35 (2001) 585) are not original and they are available in our already published paper (I.I. Guseinov, E. Akin, and A.M. Rzaeva, J. Mol. Struct. (Theochem) 453 (1998) 163). We notice that all the formulas and some of the sentences were also copied from our article.
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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 Hubbell radiation rectangular source integral using binomial coefficients
    (Pergamon-Elsevier Science Ltd, 2004) Guseinov, İsrafil İsa; Öner, F.; Mamedov, B.A.
    Using binomial coefficients a general series expansion formula is established for the integral I-q(a,b) = integral(0)(a) 1/(1 + b(2) + x(2))(q) dx with integer and noninteger values of g appearing in the evaluation of the radiation field generated by a plane isotropic rectangular source (plaque). With the help of this relation the Hubbell radiation rectangular source (HRS) integrals (J. Res. 64C(2) (1960) 121; Appl. Radiat. Isot. 39 (1988) 421) are calculated. The convergence of the series is tested by the concrete cases for values b and a. These formulae are especially useful for the calculation of HRS integrals for small values b and a. (C) 2003 Elsevier Ltd. All rights reserved.
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    On the calculation of arbitrary multielectron molecular integrals over slater-type orbitals using recurrence relations for overlap integrals I. Single-center expansion method
    (John Wiley & Sons Inc, 2000) Guseinov, İsrafil İsa; Mamedov, B.A.
    The multicenter charge-density expansion coefficients [I. I. Guseinov, J Mol Struct (Theochem) 417, 117 (1997)] appearing in the molecular integrals with an arbitrary multielectron operator were calculated for extremely large quantum numbers of Slater-type orbitals (STOs). As an example, using computer programs written for these coefficients, with the help of single-center expansion method, some of two-electron hive-center Coulomb and four-center exchange electron repulsion integrals of Hartree-Fock-Roothaan (HFR) equations for molecules were also calculated. Accuracy of the results is quite high for the quantum numbers, screening constants, and location of STOs. (C) 2000 John Wiley & Sons, Inc.
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    Use of Coulomb-Yukawa like correlated interaction potentials of integer and noninteger indices and one-range addition theorems for Ψα-ETO in evaluation of potential of electric field produced by molecule
    (2009) Guseinov, İsrafil İsa
    Using Coulomb-Yukawa like correlated interaction potentials of integer and noninteger indices the series expansion formulae in terms of multicenter overlap integrals of three complete orthonormal sets of Ψα-exponential type orbitals and linear combination coefficients of molecular orbitals are established for the potential of electrostatic field produced by the charges of molecule, where ? = 1, 0, -1, -2,.... The formulae obtained can be useful for the study of interaction between atomic--molecular systems containing any number of closed and open shells when the ??-exponential type basis functions and Coulomb-Yukawa like correlated interaction potentials are used in the Hartree-Fock-Roothaan and explicitly correlated approximations. The final results are valid for the arbitrary values of parameters of correlated interaction potentials and orbitals. As an example of application, the calculations have been performed for the potential energy of interaction between electron and molecule H2O using combined Hartree-Fock-Roothaan equations suggested by the author.