Calculation of Negative Ions of B,C, N,O and F Using Noninteger n Slater Type Orbitals

Combined Hartree‐Fock‐Roothaan calculations have been performed using noninteger n Slater type orbitals for the ground states of the lowest electron configurations 1s²2s²2pⁿ (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.     

Calculations of Isoelectronic Series of He Using Noninteger n‐Slater Type Orbitals in Single and Double Zeta Approximations

Using integer and noninteger n-Slater type orbitals in single- and double-zeta approximations, the Hartree-Fock-Roothaan calculations were performed for the ground states of first ten cationic members of the isoelectronic series of He atom. All the noninteger parameters and orbital exponents were fully optimized. In the case of noninteger n-Slater type orbitals in double zeta basis sets, the results of calculations obtained are more close to the numerical Hatree-Fock values and the average deviations of our ground state energies do not exceed 2×10^－6 hartrees of their numerical results.     

Unified treatment for the evaluation of arbitrary multielectron multicenter molecular integrals over Slater‐type orbitals with noninteger principal quantum numbers

The expansion formula has been presented for Slater‐type orbitals with noninteger principal quantum numbers (noninteger n‐STOs), which involves conventional STOs (integer n‐STOs) with the same center. By the use of this expansion formula, arbitrary multielectron multicenter molecular integrals over noninteger n‐STOs are expressed in terms of counterpart integrals over integer n‐STOs with a combined infinite series formula. The convergence of the method is tested for two‐center overlap, nuclear attraction, and two‐electron one‐center integrals, due to the scarcity of the literature, and fair uniform convergence and great numerical stability under wide changes in molecular parameters is achieved. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Use of noninteger n‐generalized exponential type orbitals with hyperbolic cosine in atomic calculations

The efficiency of noninteger n‐generalized exponential type orbitals (NGETO) r^n*?1 e with hyperbolic cosine (HC) cosh (βr^μ) 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. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Hartree-Fock-Roothaan Calculations for Ground States of Some Atoms Using Minimal Basis Sets of Integer and Noninteger n-STOs

Hartree-Fock-Roothaan (HFR) calculations for ground states of some atoms, i.e. He, Be, Ne, Ar, and Kr have been performed using minimal basis sets of Slater type orbitals (STOs) with integer and noninteger principal quantum numbers (integer n-STOs and noninteger n-STOs). The obtained total energies for these atoms using minimal basis sets of integer n-STOs are in good agreement with those in the previous literature. On the other hand, for the case of minimal basis sets of noninteger n-STOs, although the calculated total energies of these atoms agree well with the results in literature, some striking results have been obtained for atoms Ar and Kr. Our computational resuits for the energies of atoms Ar and Kr are slightly better than those in literature, by amount of 0.00222 and 0.000054 a.u., respectively. The improvement in the energies of atoms Ar and Kr may result from the efficient calculations of one-center two-electron integrals over noninteger n-STOs. For some atomic ions in their ground state, HFR calculations have been carried out using minimal basis sets of noninteger n-STOs. The obtained total energies for these atomic ions are substantially lower than those available in literature.     

Use of Recursion and Analytical Relations in Evaluation of Hypergeometric Functions Arising in Multicenter Integrals with Noninteger <Emphasis Type="Italic">n</Emphasis> Slater Type Orbitals

In this work we present the new recursion and analytical relations for the calculation of hypergeometric functions F(1,b;c;z) occurring in multicenter integrals of noninteger n Slater type orbitals. The formulas obtained are numerically stable for 0 < z < 1 and all integer and noninteger values of parameters b and c The Author cordially congratulates Prof. I.I. Guseinov on his 70th birthday     

Evaluation of Orbital- and Ground State Energies of Some Open- and Closed-Shell Atoms over Integer and Noninteger Slater Type Orbitals

Ab initio calculations of the orbital and the ground state energies of some open- and closed-shell atoms over Slater type orbitals with quantum numbers integer and Slater type orbitals with quantum numbers noninteger have been performed. In order to increase the efficiency of these calculations the atomic two-electron integrals were expressed in terms of incomplete beta function. Results were observed to be in good agreement with the literature.     

Hulthén and slater type 2d functions in some excited configurations of sulphur and phosphorus

It is shown that a substantial energy improvement is gained by the variational use of Hulthén orbitals, instead of single Slater orbitals, in the 3d shells of some excited configurations of sulphur and phosphorus. The energies obtained are close to those attained with two-term Slater functions. In some cases the radial distribution functions from Hulthén orbitals are as good an approximation of SCF radial distributions as those from two-term Slater orbitals. Single term 2d functions with only one parameter are found to give almost identical energies and radial distribution functions as those obtained from two-parameter Hulthén orbitals. It is shown that the relationship between one-term 2d orbitals and Hulthén orbitals gives a method of enforcing nuclear cusp conditions on the former with little effect on the energy.     

A quantum chemical calculation on Fe(CO)5 revealing the operation of the Dewar–Chatt–Duncanson model

A nonstandard computational scheme has been applied to calculate Fe(CO)₅ with the aim to illustrate the operation of the Dewar–Chatt–Duncanson model by computation. A full configuration interaction (CI) calculation in an active space has been performed. The active space is built from naturally localized molecular orbitals (NLMOs) localized in bond regions or forming lone pairs. For selecting this active space, Weinhold's perturbation theory formulated in the natural bond orbital (NBO) space has been applied. Bonding, lone pair, and antibond NBOs exhibiting large interaction energies serve to define the active space. The actually applied active space, however, comprises NLMOs that are close in shape to the NBOs indicated by perturbation theory. Thus, a CI calculation with localized orbitals has been performed meeting the classical reasoning of chemists that is often based on local bonding concepts. The computational scheme yields the Lewis structure for Fe(CO)₅ whose energy is identical to the Hartree–Fock energy. The Lewis energy comprises CO → Fe σ‐electron transfer (ET) and CO ← Fe electron back donation (BD). This Lewis energy gets lowered by localized correlation energy contributions caused by ET processes where electrons are back donated from the Fe d‐lone pairs into the CO ligands. Thus, electron correlation within the selected active space is dominated by electron BD. Energies and electron populations of the NBOs support the notion that electrons are preferentially back donated into the equatorial CO ligands. Weights of local Slater determinants, determining the correlation energy, also point to a predominant BD into the equatorial CO ligands. Correlation energy increments resulting from electron BD into single antibond orbitals of the CO ligands have been calculated. These energy quantities also demonstrate that BD into the equatorial CO ligands is more energy lowering than BD into the axial CO ligands. © 2012 Wiley Periodicals, Inc.     

Evaluation of Multicenter Electric Multipole Moment Integrals over Integer and Noninteger n‐STOs

Multicenter electric multipole moment integrals over Slater type orbitals with integer and noninteger principal quantum numbers are expressed in terms of overlap integrals. The computer results for the integer case agree best with the prior literature. The accuracy of the computer results for noninteger case is not compared with the literature due to the lack of relevant literature, but the limit of the noninteger case is compared with the integer case and good agreement is achieved for wide changes in the relevant molecular parameters.     

Theoretical study of the Au–ethylene interaction

The basis‐set dependence and quasirelativistic and nonrelativistic effects on the Au C₂H₄ interaction are examined at the ab initio level. The effects on the interaction energies are modulated by f‐type polarization orbitals, using 19‐VE quasirelativistic pseudopotentials. Oscillation in the equilibrium Au C distance as well as in the interaction energy are sensitive to the electron correlation potential. These effects are evaluated at several levels of theory, ranging from MP2 to CCSD(T). The nature of the Au C₂H₄ interaction is related to a simple dispersion expression involving the individual properties of each component and its long‐distance behavior. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 317–324, 1999     

Evaluation of multicenter one-electron integrals of noninteger u screened Coulomb type potentials and their derivatives over noninteger n Slater orbitals

Multicenter integrals over noninteger n Slater type orbitals with integer and noninteger values of indices u of screened Coulomb type potentials, f(u)(eta,r)=r(u-1)e(-etar), and their first and second derivatives with respect to Cartesian coordinates of the nuclei of a molecule are described. Using complete orthonormal sets of Psi(alpha) exponential type orbitals and rotation transformation of two-center overlap integrals, these integrals are expressed through the noncentral potential functions depending on the molecular auxiliary functions A(k) and B(k). The series expansion formulas derived for molecular integrals of screened Coulomb potentials and their derivatives are especially useful for the computation of multicenter electronic attraction, electric field, and electric field gradient integrals. The convergence of series is tested for arbitrary values of parameters of potentials and orbitals.     

On the calculation of arbitrary multielectron molecular integrals over Slater‐type orbitals using recurrence relations for overlap integrals. II. Two‐center expansion method

Using expansion formulas for the charge‐density over Slater‐type orbitals (STOs) obtained by the one of authors [I. I. Guseinov, J Mol Struct (Theochem) 1997, 417, 117] the multicenter molecular integrals with an arbitrary multielectron operator are expressed in terms of the overlap integrals with the same screening parameters of STOs and the basic multielectron two‐center Coulomb or hybrid integrals with the same operator. In the special case of two‐electron electron‐repulsion operator appearing in the Hartree–Fock–Roothaan (HFR) equations for molecules the new auxiliary functions are introduced by means of which basic two‐center Coulomb and hybrid integrals are expressed. Using recurrence relations for auxiliary functions the multicenter electron‐repulsion integrals are calculated for extremely large quantum numbers. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 117–125, 2001     

Use of Auxiliary Functions for Construction of Series Expansion Relations of Noninteger Slater Functions in Standard Convention

Using complete orthonormal sets of ψ ^(α*) ‐self‐frictional exponential type orbitals (ψ ^(α*) ‐SFETOs) and Q^q‐noninteger auxiliary functions (Q^q‐NIAFs) introduced by the author, the combined formulas for the one‐ and two‐center one‐range addition theorems of χ‐noninteger Slater type orbitals (χ‐NISTOs) with arbitrary values of distances between centers R_ab (for R_ab = 0 and R_ab ≠ 0), and of integer (for α* = α, –∞ < α ≤ 2) and noninteger (for α* ≠ α, –∞ < α* < 3) self‐frictional (SF) quantum numbers are suggested. The presented relations for the one‐range addition theorems can be useful tools especially in the electronic structure studies of atoms, molecules and solids when χ‐NISTOs are employed as basis functions.     

Evaluation of two‐center overlap and nuclear attraction integrals over Slater‐type orbitals with integer and noninteger principal quantum numbers

A general formula has been established for the expansion of the product of two normalized associated Legendre functions centered on the nuclei a and b. This formula has been utilized for the evaluation of two‐center overlap and nuclear attraction integrals over Slater‐type orbitals (STOs) with integer and noninteger principal quantum numbers. The formulas given in this study for the evaluation of two‐center overlap and nuclear attraction integrals show good rate of convergence and great numerical stability under wide range of quantum numbers, orbital exponents, and internuclear distances. © 2001 Wiley Periodicals, Inc. Int J Quantum Chem, 2001     

Evaluation of one‐electron molecular integrals over complete orthonormal sets of Ψα ‐ETO using auxiliary functions

By the use of expansion and one‐range addition theorems, the one‐electron molecular integrals over complete orthonormal sets of Ψ^α ‐exponential type orbitals arising in Hartree–Fock–Roothaan equations for molecules are evaluated. These integrals are expressed through the auxiliary functions in ellipsoidal coordinates. The comparison is made using Slater‐, Coulomb‐Sturmian‐, and Lambda‐type basis functions. Computation results are in good agreement with those obtained in the literature. The relationships obtained are valid for the arbitrary quantum numbers, screening constants, and location of orbitals. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Extended Hartree–Fock calculations for the helium ground state

The extended Hartree–Fock (EHF) wave function of an n-electron system is defined (Löwdin, Phys. Rev. 97 , 1509 (1955)) as the best Slater determinant built on one-electron spin orbitals having a complete flexibility and projected onto an appropriate symmetry subspace. The configuration interaction equivalent to such a wavefunction for the ¹S state of a two-electron atom is discussed. It is shown that there is in this case an infinite number of solutions to the variational problem with energies lower than that of the usual Hartree–Fock function, and with spin orbitals satisfying all the extremum conditions. Two procedures for obtaining EHF spin orbitals are presented. An application to the ground state of Helium within a basic set made up of 4(s), 3(p₀), 2(d₀) and 1 (f₀) Slater orbitals has produced 90% of the correlation energy.     

Intramolecular electronic communication in a dimethylaminoazobenzene–fullerene C60 dyad: An experimental and TD‐DFT study

An electronically push–pull type dimethylaminoazobenzene–fullerene C₆₀ hybrid was designed and synthesized by tailoring N,N‐dimethylaniline as an electron donating auxochrome that intensified charge density on the β‐azonitrogen, and on N‐methylfulleropyrrolidine (NMFP) as an electron acceptor at the 4 and 4′ positions of the azobenzene moiety, respectively. The absorption and charge transfer behavior of the hybrid donor‐bridge‐acceptor dyad were studied experimentally and by performing TD‐DFT calculations. The TD‐DFT predicted charge transfer interactions of the dyad ranging from 747 to 601 nm were experimentally observed in the UV‐vis spectra at 721 nm in toluene and dichloromethane. A 149 mV anodic shift in the first reduction potential of the N?N group of the dyad in comparison with the model aminoazobenzene derivative further supported the phenomenon. Analysis of the charge transfer band through the orbital picture revealed charge displacement from the n_(N?N) (nonbonding) and π _(N?N) type orbitals centered on the donor part to the purely fullerene centered LUMOs and LUMO+n orbitals, delocalized over the entire molecule. The imposed electronic perturbations on the aminoazobenzene moiety upon coupling it with C₆₀ were analyzed by comparing the TD‐DFT predicted and experimentally observed electronic transition energies of the dyad with the model compounds, NMFP and (E)‐N,N‐dimethyl‐4‐(p‐tolyldiazenyl)aniline (AZNME). The n_(N?N) → π*_(N?N) and π_(N?N) → π*_(N?N) transitions of the dyad were bathochromically shifted with a significant charge transfer character. The shifting of π_(N?N) → π*_(N?N) excitation energy closer to the n → π*_(N?N) in comparison with the model aminoazobenzene emphasized the predominant existence of charge separated quinonoid‐like ground state electronic structure. Increasing solvent polarity introduced hyperchromic effect in the π_(N?N) → π*_(N?N) electronic transition at the expense of transitions involved with benzenic states, and the extent of intensity borrowing was quantified adopting the Gaussian deconvolution method. On a comparative scale, the predicted excitation energies were in reasonable agreement with the observed values, demonstrating the efficiency of TD‐DFT in predicting the localized and the charge transfer nature of transitions involved with large electronically asymmetric molecules with HOMO and LUMO centered on different parts of the molecular framework. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Representation of Kohn–Sham free atom eigenfunctions by Slater‐type orbitals

Slater‐type orbitals are applied to represent the numerically obtained Kohn–Sham eigenfunction of free atom. The algorithm evaluating the nonlinear expansion coefficients of this approximation is described. Standard iterative solution of Kohn–Sham equation to obtain the nonlinear expansion coefficients is avoided and replaced by the projection method. First, the eigenfunction is obtained in the B‐spline space based on the Galerkin formulation of the finite element method. Then, based on the density functional theory, the conditions are formulated, which leads to the set of nonlinear equations. The proposed algorithm is general and can be applied for any atomic Kohn–Sham eigenfunction. As an examplary application of the proposed algorithm, the set of nonlinear equations is derived for occupied states of N, Al, Ga, and In atoms. The expansion coefficients, obtained for these atoms, are evaluated numerically by Newton procedure and listed in the tables. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Calculation of Two-Center Nuclear Attraction Integrals over Integer and Noninteger n-Slater Type Orbitals in Nonlined-Up Coordinate Systems

Two-center nuclear attraction integrals over Slater type orbitals with integer and noninteger principal quantum numbers in nonlined up coordinate systems have been calculated by means of formulas in our previous work (T. Özdoan and M. Orbay, Int. J. Quant. Chem. 87 (2002) 15). The computer results for integer case are in best agreement with the prior literature. On the other hand, the results for noninteger case are not compared with the literature due to the scarcity of the literature, but also compared with the limit of integer case and good agreements are obtained. The proposed algorithm for the calculation of two-center nuclear attraction integrals over Slater type orbitals with noninteger principal quantum numbers in nonlined-up coordinate systems permits to avoid the interpolation procedure used to overcome the difficulty introduced by the presence of noninteger principal quantum numbers. Finally, numerical aspects of the presented formulae are analyzed under wide range of quantum numbers, orbital exponents and internuclear distances.