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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 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 Comparative performance of different hyperbolic cosine functions and generalized B functions basis sets for atomic systems(Iop Publishing Ltd, 2022) Coskun, M.; Erturk, M.Recently, we reported a new set of Bessel type functions, which include the radial part of generalized Bessel functions r(n-1)e(-zeta r mu) for LCAO calculations of atomic systems. In this study, to achieve further improvement of the performance of generalized Bessel type basis sets in the Hartree-Fock-Roothaan calculations, different hyperbolic cosine functions inserted into the radial part of those generalized Bessel functions. For this purpose, three different generalized hyperbolic cosine functions have been used to construct the generalized Bessel type hyperbolic cosine basis sets. The accuracies of generalized Bessel type hyperbolic cosine functions within the minimal basis sets approach are compared to show their superiority to conventional approaches those in the literature. The performance of the presented basis functions is also compared to the numerical Hartree-Fock results. Our virial ratios are in good agreement to within 8-digits of the -2. It is shown that the results obtained by the new basis sets surpass the quality and accuracy of existing Bessel type basis sets.Öğe Double hyperbolic cosine basis sets for LCAO calculations(Taylor & Francis Ltd, 2022) Coskun, M.; Erturk, M.Recently, we reported a new set of hyperbolic cosine type basis sets, which include the radial part of exponential type functions. In this study, it is show that the double hyperbolic cosine basis sets with non-integer Slater type orbitals give extremely accurate results, with the accuracy superior to that of the previous similar calculations. Total energy differences and comparison between double hyperbolic cosine and other similar basis sets suggested in literature are presented. Using double hyperbolic cosine orbitals, combined Hartree-Fock-Roothaan calculations have been carried out on the ground states of atoms and their ions within the minimal basis sets framework to compare the performance of the basis sets. The basis sets achieved the accuracy far beyond the double-zeta quality. Proposed basis sets can also play an effective role in ion-atom collisions problems and semi-empirical methods.Öğe Exponential type orbitals with generalized hyperbolic cosine functions for atomic systems(Elsevier Science Bv, 2015) Erturk, M.Radial basis functions, constructed from Slater type r(n*-1)e(-zeta r). and generalized exponential type r(n*-1)e(-zeta r mu) functions with the generalized hyperbolic cosine type functions cosh(pq)(beta r) and cosh(pq)(beta r(mu)), where p and q are arbitrary parameters, are proposed and applied to Hartree-Fock-Roothaan calculations of atomic systems. The performance of new basis functions within the minimal basis sets framework has been compared to numerical Hartree-Fock results and previous results presented by similar basis functions in the literature. The results obtained by the new basis sets surpass the accuracy of existing basis sets of similar hyperbolic cosine type functions. (C) 2015 Elsevier B.V. All rights reserved.Öğe Further Improvements on ?(?*)-ETOs with Hyperbolic Cosine Functions and Their Effectiveness in Atomic Calculations(Elsevier Academic Press Inc, 2013) Aksoy, S.; Firat, S.; Erturk, M.In the last few years, exponential type orbitals became very important in electronic structure calculations of atoms and molecules. In this work, improvements on effectiveness of the psi-exponential type orbitals (psi)-ETOs) (-infinity < 3) containing different hyperbolic cosine functions are presented for the ground states of neutral atoms and their ions. The Hartree Fock Roothaan energies within the minimal basis set framework for some atoms up to Z=18 and their ions are listed and compared with the results obtained with other exponential type orbitals such as conventional double-zeta Slater, noninteger-n Slater with different hyperbolic cosine basis sets and numerical Hartree Fock values. The accuracy of psi-ETOs is greatly improved for all atomic systems studied. The optimal noninteger values of alpha* are determined for each atomic system examined in this work.Öğe Modified B function basis sets with generalized hyperbolic cosine functions(Elsevier Science Bv, 2018) Erturk, M.; Ozturk, E.Efficient exponential type basis sets constructed from new hyperbolic cosine type B functions have been used in self consistent field calculations for the ground states of the atoms from Helium to Argon and their ions. Different hyperbolic cosine type functions are incorporated into the B functions to increase the accuracy of atomic orbitals and correctly describe the electronic density of systems. The presented results for the minimal basis sets are shown that the quality of generalized hyperbolic cosine type B functions is one of the most appropriate basis sets of B functions, especially for increasing atomic number. A comparison with the standard B functions, hyperbolic cosine type B functions and the corresponding numerical Hartree-Fock values are given in tables. Our study shows that the modification of B functions can be an efficient way of increasing the accuracy of the atomic and molecular SCF calculations. These basis sets may also be used in the calculation of atomic properties such as cusp condition and density properties of atomic electrons. Some numerical results and comparisons are given to clarify the basis sets quality from the density point of view. An improved description of atomic orbitals based on the use of modified B functions will also play an important role in ion-atom collisions problems, semi-emprical and density functional methods. (C) 2018 Elsevier B.V. All rights reserved.Öğe Use of combined Hartree-Fock-Roothaan theory in evaluation of lowest states of K[Ar]4s03d1 and Cr+[Ar]4s03d5 isoelectronic series over noninteger n-Slater type orbitals(Indian Acad Sciences, 2011) Guseinov, Israfil Isa; Erturk, M.; Sahin, E.By using noninteger n-Slater type orbitals in combined Hartree-Fock-Roothaan method, self-consistent field calculations of orbital and lowest states energies have been performed for the isoelectronic series of open shell systems K[Ar]4s(0)3d(1) (D-2) (Z = 19-30) and Cr+[Ar]4s(0)3d(5) (S-6) (Z = 24-30). The results of the calculations for the orbital and total energies obtained by using minimal basis-sets of noninteger n-Slater type orbitals are given in the tables. The results are compared with the extended-basis Hartree-Fock computations. The orbital and total energies are in good agreement with those presented in the literature. The results can be useful in the study of various properties of heavy atomic systems when the combined Hartree-Fock-Roothaan approach is employed.Öğe Use of noninteger n-generalized exponential type orbitals with hyperbolic cosine in atomic calculations(Wiley, 2012) Guseinov, Israfil Isa; Erturk, M.The efficiency of noninteger n-generalized exponential type orbitals (NGETO) rn*-1 e?-? r?mu with hyperbolic cosine (HC) cosh (beta r mu) as radial basis functions in atomic ground state total energy calculations is studied. By the use of these functions, the combined Hartree-Fock-Roothaan calculations have been performed for some closed and open shell neutral atoms and their anions and cations with Z = 21. The performance of new basis functions within the minimal basis framework has been compared with numerical Hartree-Fock (NHF) results. Our total energy values are significantly close to NHF results. The presented minimal basis total energies obtained from the noninteger NGETO with HC are notably better than minimal basis functions total energies previously reported in the literature. It is found that the accuracy of new noninteger NGETO with HC almost correspond to the accuracy of the conventional double-zeta functions. All the nonlinear parameters are fully optimized. (c) 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012
