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Öğe Calculation of Rotation Coefficients for Overlap Integrals Over Arbitrary Atomic Orbitals(1997) Guseinov, I. I.; Atav, Ü.; Özmen, A.; Yüksel, H.; Aliyeva, T. H.Rotation coefficients for overlap integrals over arbitrary atomic orbitals are calculated by two methods. In the first method, using binomial coefficients, directly calculated Clebsch-Gordan coefficients and normalized associated Legendre functions were used to obtain the rotation coefficients. Whereas in the second method recursively calculated Clebsch-Gordan coefficients and normalized associated Legendre functions were used. The methods are compared with respect to cpu time requirement and accuracy. It was concluded that it is appropriate to use the first method for angular momentum quantum numbers up to 40 and for larger quantum numbers the second method is more advantageous.Öğe Computation of Overlap Integrals Over Slater-Type Orbitals Using Auxiliary Functions(JOHN WILEY & SONS INC, 1998) Guseinov, I. I.; Özmen, A.; Atav, U.; Yüksel, H.Analytical expressions through the binomial coefficients and recursive relations are derived for the expansion coefficients of overlap integrals in terms of a product of well-known auxiliary functions A(k) and B-k. These formulas are especially useful for the calculation of overlap integrals for large quantum numbers. Accuracy of the computer results is satisfactory for the values of quantum numbers up to 50 and for the arbitrary values of screening constants of atomic orbitals and internuclear distances.Öğe Evaluation of Molecular Electric Multipole Moments Using Slater-Type Orbitals(ELSEVIER SCIENCE BV, 1998) Guseinov, I. I.; Akın, Emre; Rzaeva, A. M.A general formula in terms of overlap integrals has been established for the 2(nu)-pole electric moments of a molecule by the Hartree-Fock-Roothaan method involving the use of real or complex Slater-type orbitals (STOs). Using this formula we have calculated the monopole, dipole, quadrupole, and octupole moments of the ground states for a series of diatomic molecules. By the use of the derived expressions the electric multipole moment integrals, therefore, the electric properties of molecules can be evaluated most efficiently and accurately.Öğe On the Evaluation of Multielectron Molecular Integrals Over Slater-Type Orbitals Using Binomial Coefficients(ELSEVIER SCIENCE BV, 1995) Guseinov, I. I.In the formulas given by the author for the multicenter molecular integrals with an arbitrary s-electron operator F-(s)(s = 1, 2,...) all the expansion coefficients are expressed through the binomial coefficients. The final results are of a simple structure and are, therefore, especially useful for the calculation of these coefficients for large quantum numbers. By the use of the derived expressions in terms of binomial coefficients multielectron molecular integrals over Slater-type orbitals can be evaluated most efficiently and accurately from the series expansion formulas.Öğe On the Evaluation of Overlap Integrals with the Same Screening Parameters of Slater-Type Orbitals Using Binomial Coefficients(John Wiley & Sons Inc, 1996) Guseinov, I. I.; İlik, Aslan; Allahverdiyev, S. I.A general formula has been established for the overlap integrals with the same screening parameters of Slater-type orbitals in terms of bionomial coefficients. The final results are especially useful for the calculation of these integrals for large quantum numbers, which occur in the multicenter integrals.Öğe On the Evaluation of Rotation Coefficients for Spherical Harmonics Using Binomial Coefficients(Elsevier Science Bv, 1996) Guseinov, I. I.The rotation coefficients for spherical harmonics (SH) are expressed through the binomial coefficients. The final results are especially useful for the machine computations of rotation coefficients for large quantum numbers. The derived expressions, in terms of binomial coefficients, are of considerable importance in the evaluation of multi-electron molecular integrals over Slater-type orbitals (STO's) from the series expansion formulas which have recently been established by the author.Öğe Spherically Symmetrical Properties of 2-Center Overlap Integrals Over Arbitrary Atomic Orbitals and Translation Coefficients for Slater-Type Orbitals(ELSEVIER SCIENCE BV, 1995) Guseinov, I. I.The orthogonality relations are derived for the rotation coefficients of two-center overlap integrals over arbitrary atomic orbitals (AAOs) and expansion coefficients for translation of Slater-type orbitals (STOs). Using these formulas, a very interesting theorem regarding the angular dependence is established. If we add the products of all the overlap integrals or all the translation coefficients with the same n and l values, but different m values, the result is independent of orientation. The final results are of a simple structure and are, therefore, especially useful for machine computations of multielectron multicenter molecular integrals by expanding one- and two-center electron charge density over STOs in terms of STOs about a new center.Öğe Spherically Symmetrical Properties of Two-Center Overlap Integrals Over Arbitrary Atomic Orbitals and Translation Coefficients for Slater-Type Orbitals(1995) Guseinov, I. I.The orthogonality relations are derived for the rotation coefficients of two-center overlap integrals over arbitrary atomic orbitals (AAOs) and expansion coefficients for translation of Slater-type orbitals (STOs). Using these formulas, a very interesting theorem regarding the angular dependence is established. If we add the products of all the overlap integrals or all the translation coefficients with the same n and l values, but different m values, the result is independent of orientation. The final results are of a simple structure and are, therefore, especially useful for machine computations of multielectron multicenter molecular integrals by expanding one- and two-center electron charge density over STOs in terms of STOs about a new center. © 1995.Öğe Unified Treatment of 2-Center Coulomb, Hybrid, and Exchange Integrals Over Slater-Type Orbitals(JOHN WILEY & SONS INC, 1995) Guseinov, I. I.; Yassen, R. F.Using Neumann expansion for 1/r(12) in elliptical coordinates a combined formula has been obtained for two-center Coulomb, hybrid, and exchange integrals with Slater-type orbitals. (C) 1995 John Wiley & Sons, Inc.
