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Öğe A new algorithm for accurate and fast evaluation of the Hubbell radiation rectangular source integral(Pergamon-Elsevier Science Ltd, 2005) Guseinov, Israfil Isa; Mamedov, BA; Ekenoglu, ASIn this work we present a new efficient and reliable analytical procedure for evaluation of the Hubbell radiation rectangular source (HRS) integral using a binomial expansion. The proposed procedure guarantees the reliable evaluation of the radiation field generated by a plane isotropic rectangular source (plaque) of scaled width and length a and b, respectively. The formulas obtained are numerically stable for a(2) + b(2) < 1. Numerical results are presented and compared with results using alternative evaluation schemes. (C) 2005 Elsevier Ltd. All rights reserved.Öğe 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.Öğe 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.Öğe 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 Isa; Gorgun, Nursen SeckinWith 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.Öğe 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.Öğe Addition and expansion theorems for complete orthonormal sets of exponential-type orbitals in coordinate and momentum representations(Springer-Verlag, 2003) Guseinov, Israfil IsaAnalytical properties of new complete orthonormal sets of Psi(alpha) exponential-type orbitals (Psi(alpha)-ETOs where alpha=1, 0, -1, -2, ...), introduced by the author as finite linear combinations of Slater-type orbitals (STOs), are studied. Addition and expansion theorems for Psi(alpha)-ETOs are obtained in both coordinate and momentum representations. Using expressions of Psi(alpha)-ETOs in terms of STOs, the new methods are suggested to calculate multicenter multielectron integrals over STOs.Öğe Addition theorems for Slater-type orbitals and their application to multicenter multielectron integrals of central and noncentral interaction potentials(Springer, 2003) Guseinov, Israfil IsaBy the use of complete orthonormal sets of psi(alpha)-ETOs ( alpha= 1, 0, -1, -2,...) introduced by the author, new addition theorems are derived for STOs and arbitrary central and noncentral interaction potentials (CIPs and NCIPs). The expansion coefficients in these addition theorems are expressed through the Gaunt and Gegenbauer coefficients. Using the addition theorems obtained for STOs and potentials, general formulae in terms of three-center overlap integrals are established for the multicenter t-electron integrals of CIPs and NCIPs that arise in the solution of the N-electron atomic and molecular problem ( 2less than or equal totless than or equal toN) when a Hylleraas approximation in Hartree-Fock-Roothaan theory is employed. With the help of expansion formulae for translation of STOs, the three-center overlap integrals are expressed through the two-center overlap integrals. The formulae obtained are valid for arbitrary quantum numbers, screening constants and location of orbitals.Öğe Addition theorems for Slater-type orbitals in momentum space and their application to three-center overlap integrals(Springer, 2005) Guseinov, Israfil IsaUsing addition theorems for complete orthonormal sets of exponential type orbitals in the momentum representation introduced by the author, the addition theorems are established for Slater type orbitals in momentum space. With the help of these addition theorems, the general series expansion formulae in terms of the product of two-center overlap integrals are established for the three-center overlap integrals that arise in the solution of atomic and molecular problems occurring when explicitly correlated methods are employed. The formulae obtained for addition theorems and three-center overlap integrals are valid for arbitrary location and parameters of orbitals.Öğe Algorithm for the storage of Clebsch-Gordan and Gaunt coefficients with the same selection rule and its application to multicenter integrals(Elsevier Science Bv, 2005) Guseinov, Israfil Isa; Mamedov, BACommon algorithm is presented for the generation and storage of all unique, non-zero Clebsch-Gordan and Gaunt coefficients for which the sum of the three angular momentum quantum numbers is a non-negative even integer. This algorithm is especially useful for the fast computation of arbitrary multicenter integrals over Slater type orbitals (STOs) appearing in the Hartree-Fock-Roothaan and Hylleraas approaches. The storage algorithm obtained for the Clebsch-Gordan and Gaunt coefficients is utilized, as for examples, in the computation of two-electron multicenter integrals occurring in the Hartree-Fock-Roothaan equations of a molecule. (c) 2004 Elsevier B.V. All rights reserved.Öğe Algorithm for the storage of expansion coefficients for the product of associated Legendre functions in elliptical coordinates useful for the calculations of molecular integrals(Elsevier, 2004) Guseinov, Israfil Isa; Mamedov, BAAn algorithm is presented for the generation and storage of expansion coefficients for the product of two associated Legendre functions both with different centers introduced by the one of authors [J. Phys. B 3 (1970) 1399] for the calculation of multicenter integrals over STOs using auxiliary functions. The formulae for retrieving these coefficients in a non-sequential fashion are developed and presented. We believe that the use of formulae given in this work for the storage of expansion coefficients will have important contributions in reducing requirements for computer time in the calculation of molecular integrals with the aid of auxiliary functions. (C) 2004 Elsevier B.V. All rights reserved.Öğe An improvement on ?(?*)-exponential type orbitals for atoms in standard convention(Taylor & Francis Ltd, 2014) Guseinov, Israfil Isa; Sahin, E.; Erturk, M.The complete orthonormal sets of psi((alpha)*())-exponential type orbitals (psi((alpha)*())-ETOs) in LCAO approximation are investigated for the determination of the optimal values of integer (- < 2) and non-integer * (- < * < 3) by minimising the total energies in atomic calculations. The Hartree-Fock-Roothaan calculations with the use of different values of indices and * are performed within the framework of the minimal basis sets approximation for the ground states of neutral atoms. It is found for non-integer values of * that the efficiency of psi((alpha)*())-ETOs in total energy calculations, electron density, and its derivative and cusp ratio at the nuclei is much better than the other integer values of . It should be noted that the Coulomb-Sturmian and Lambda ETOs are special classes of (())-ETOs for = 1 and = 0, respectively. The performance of psi((alpha)*())-ETOs in atomic energy calculations is also compared to those obtained by using other ETOs such as Slater and B functions. The optimal non-integer values of * are also determined for each atom examined in this work. It is shown that the notably improvement in the efficiency of psi((alpha)*())-ETOs can be obtained by the use of non-integer * values.Öğe Analytical evaluation of Coulomb potential generated by multielectron molecule at arbitrary positions in space using one-range addition theorems of Slater type orbitals(Springer, 2011) Guseinov, Israfil IsaBy the use of unsymmetrical one-range addition theorems for Slater type orbitals (STO) and Coulomb potential introduced by the author, the analytical formulae in terms of two-and three-center nuclear attraction integrals, and linear combination coefficients of molecular orbitals are derived for the potential produced by the charges of molecule. These formulae can be useful for the study of interaction between atomic-molecular systems containing any number of closed and open shells when the STO are used in the combined Hartree-Fock-Roothaan (HFR) theory suggested by the author. It should be noted that the symmetry of the potential obtained is the same as the symmetry of the molecule. As an example of application, the calculations have been performed for the potential produced by the ground state of BH3 molecule ((1a(1))(2)(2a(1))(2)(1e(x))(2)(1e(y))(2),(1)A(1)).Öğe Analytical evaluation of multicenter multielectron integrals of central and noncentral interaction potentials over Slater orbitals using overlap integrals and auxiliary functions(Kluwer Academic/Plenum Publ, 2004) Guseinov, Israfil IsaUsing expansion formulas for central and noncentral interaction potentials (CIPs and NCIPs, respectively) in terms of Slater type orbitals (STOs) obtained by the author ( I. I. Guseinov, J. Mol. Model., in press), the multicenter multielectron integrals of arbitrary interaction potentials (AIPs) are expressed through the products of overlap integrals with the same screening parameters and new auxiliary functions. For auxiliary functions, the analytic and recurrence relations are derived. The relationships obtained for multicenter multielectron integrals of AIDs are valid for the arbitrary quantum numbers, screening parameters and location of orbitals.Öğe Analytical evaluation of two-center Franck-Condon overlap integrals over harmonic oscillator wave function(Walter De Gruyter Gmbh, 2006) Guseinov, Israfil Isa; Mamedov, Bahtiyar A.; Ekenoglu, Arife S.A unified treatment of Franck-Condon (FC) overlap integrals with arbitrary values of parameters is described. These integrals are represented in terms of binomial coefficients. For quick calculations, the binomial coefficients are stored in the memory of the computer. Therefore, the CPU time has been greatly reduced. Numerical results presented agree excellently with those obtained in the literature.Öğe 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.Öğe Application of combined hartree-fock-roothaan theory to isoelectronic series of atoms using noninteger n-generalized exponential type orbitals(2009) Guseinov, Israfil Isa; Ertürk, M.We investigate the efficiency of noninteger n-generalized exponential type orbitais in energy calculations of isoelectronic series of atoms from Be to Ne and K [Ar]4s03d1 (2D) and Cr+ [Ar]4s03d5 (6S) using combined Hartree-Fock-Roothaan theory. The results of calculations are compared with the values obtained in literature. AU of the nonlinear parameters are fully optimized. It is shown that the use of noninteger n-generalized exponential type orbitais in atomic electronic structure calculations gives the superior agreement with numerical Hartree-Fock calculations. The minimum energy error, which is 0.00204432 Hartree, is observed for the neutral Be atom with respect to corresponding numerical Hartree-Fock result.Öğe Application of Combined Hartree-Fock-Roothaan Theory to Isoelectronic Series of Atoms Using Noninteger n-Generalized Exponential Type Orbitals(Univ Kragujevac, Fac Science, 2009) Guseinov, Israfil Isa; Erturk, M.We investigate the efficiency of noninteger n-generalized exponential type orbitals in energy calculations of isoelectronic series of atoms from Be to Ne and K [Ar]4s(0)3d(1) (2D) and Cr+ [Ar]4s(0) 3d(5) (6S) using combined Hartree-Fock-Roothaan theory. The results of calculations are compared with the values obtained in literature. All of the nonlinear parameters are fully optimized. It is shown that the use of noninteger n-generalized exponential type orbitals in atomic electronic structure calculations gives the superior agreement with numerical Hartree-Fock calculations. The minimum energy error, which is 0.00204432 Hartree, is observed for the neutral Be atom with respect to corresponding numerical Hartree-Fock result.Öğe Application of combined Hartree-Fock-Roothaan theory to molecules with arbitrary number of closed and open shells(Springer, 2008) Guseinov, Israfil IsaIn this study, the applicability of the combined Hartree-Fock-Roothaan (CHFR) theory of atomic-molecular and nuclear systems (Guseinov, J Math Chem 42:177, 2007) to the molecules is demonstrated using minimal basis set of Slater type orbitals (STO). As an example of application of CHFR theory, the calculations have been performed for the ground state of electronic configuration of methylene molecule CH(2) which has two open shells. The results of computer calculations for the orbital, kinetic and total energies, linear combination coefficients of symmetrized molecular orbitals and virial ratios are presented.Öğe 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.Öğe Application of complete orthonormal sets of ??-exponential-type orbitals to accurate ground and excited states calculations of one-electron diatomic molecules using single-zeta approximation(Iop Publishing Ltd, 2008) Guseinov, Israfil Isa; Aydin, R.; Bagci, A.The applicability of the complete orthonormal sets of psi(alpha)- exponential- type orbitals introduced by one of the authors to the study of electronic structure of one electron diatomic molecules is demonstrated using single- zeta approximation. As an example of application, the calculations have been performed for s, p and d states of one electron homo- and hetero- nuclear diatomic molecules H-2(+) and HeH2+, respectively. The calculation results are presented. The values for these molecules obtained in eight- digit accuracy are close to the results of solution presented in literature.
