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Journal articles on the topic 'Slater Type Orbitals'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 April 2022

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1

Magalhães, Alexandre L. "Gaussian-Type Orbitals versus Slater-Type Orbitals: A Comparison." Journal of Chemical Education 91, no. 12 (September 19, 2014): 2124–27. http://dx.doi.org/10.1021/ed500437a.

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2

HOGGAN, P. E. "NOTE ON HYDROGENIC ATOMIC ORBITALS TO EVALUATE SENSITIVE PROPERTIES OF MOLECULES: AN EXAMPLE OF NMR CHEMICAL SHIFTS." Journal of Theoretical and Computational Chemistry 03, no. 02 (June 2004): 163–68. http://dx.doi.org/10.1142/s0219633604000945.

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Now that the problems surrounding ab initio calculations over a Slater Type Orbital basis have been solved, it is available in several software packages. For general structures the STOP package (Slater Type Orbital Package) has offered ab initio SCF molecular properties since 1996, the requisite integrals all being evaluated analytically, including the four center term available since 1994. SMILES (Slater Molecular Integrals for Large Electronic Systems) has offered various basis sets, geometry optimization and CI since 2001. For density functional work, ADF, the Amsterdam Density Functional suite of programs, is a project dating from the 1970s with a 2003 edition. In this work the preferred ETOs (Exponential Type Orbitals) will be shown to be the hydrogenic orbitals and similar Coulomb Sturmians. Slater Type Functions (STFs) will be compared to them and suitable equivalent combinations, which are rarely used, given. The correct shielding of the nucleus, resulting from radial factors of hydrogenic orbitals is shown to be essential in the evaluation of precise nuclear shielding tensors for NMR spectroscopy of molecules using ab initio or DFT methods. The case study of benzothiazoles using natural abundance 15N is re-examined and compared with previous work including measurements.

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3

GUSEINOV, I. I. "COMBINED THEORY OF NONRELATIVISTIC AND QUASIRELATIVISTIC ATOMIC INTEGRALS OVER INTEGER AND NONINTEGER N-SLATER-TYPE ORBITALS." Journal of Theoretical and Computational Chemistry 08, no. 01 (February 2009): 47–56. http://dx.doi.org/10.1142/s0219633609004393.

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One- and two-electron nonrelativistic and quasirelativistic basic functions are introduced. The combined analytical relations in terms of these basic functions are derived for the non- and quasi-relativistic atomic integrals over integer and noninteger n-Slater-type orbitals. The relationships obtained are valid for the arbitrary values of principal quantum numbers and screening constants of Slater orbitals.

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4

Fernández Rico, J., R. López, G. Ramírez, and I. Ema. "Electric field integrals for Slater-type orbitals." International Journal of Quantum Chemistry 100, no. 2 (2004): 131–41. http://dx.doi.org/10.1002/qua.20177.

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5

Özdogan, Telhat. "Evaluation of Two-Center Overlap Integrals Over Slater-Type Orbitals Using Fourier Transform Convolution Theorem." Collection of Czechoslovak Chemical Communications 69, no. 2 (2004): 279–91. http://dx.doi.org/10.1135/cccc20040279.

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Analytical expressions are presented for two-center overlap integrals over Slater-type orbitals using Fourier transform convolution theorem. The efficiency of calculation of these expressions is compared with those of other methods and good rate of convergence and great numerical stability is obtained for wide range of quantum numbers, orbital exponents and internuclear distances.

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6

Di Rocco, H. O. "Analytic Atomic Screening Parameters for Slater Type Orbitals." Spectroscopy Letters 26, no. 9 (November 1993): 1573–82. http://dx.doi.org/10.1080/00387019308010757.

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7

Förster, Arno, and Lucas Visscher. "Double hybrid DFT calculations with Slater type orbitals." Journal of Computational Chemistry 41, no. 18 (April 16, 2020): 1660–84. http://dx.doi.org/10.1002/jcc.26209.

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8

Gomes, Andr� Severo Pereira, and Rog�rio Custodio. "Exact Gaussian expansions of Slater-type atomic orbitals." Journal of Computational Chemistry 23, no. 10 (May 22, 2002): 1007–12. http://dx.doi.org/10.1002/jcc.10090.

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9

Gümüş, Sedat. "On The Computation Of Two-Center Coulomb Integrals Over Slater Type Orbitals Using The Poisson Equation." Zeitschrift für Naturforschung A 60, no. 7 (July 1, 2005): 477–83. http://dx.doi.org/10.1515/zna-2005-0702.

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In this paper, a new analytical formula has been derived for the two-center Coulomb integrals over Slater type orbitals using the Poisson equation. The obtained results from constructed computer program for the presented formula have been compared with the available literature and it is seen that the efficiency of the presented algorithm for a wide range of quantum numbers, orbital exponents and internuclear distances is satisfactory.

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10

Beylkin, G., and T. S. Haut. "Nonlinear approximations for electronic structure calculations." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2158 (October 8, 2013): 20130231. http://dx.doi.org/10.1098/rspa.2013.0231.

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We present a new method for electronic structure calculations based on novel algorithms for nonlinear approximations. We maintain a functional form for the spatial orbitals as a linear combination of products of decaying exponentials and spherical harmonics centred at the nuclear cusps. Although such representations bare some resemblance to the classical Slater-type orbitals, the complex-valued exponents in the representations are dynamically optimized via recently developed algorithms, yielding highly accurate solutions with guaranteed error bounds. These new algorithms make dynamic optimization an effective way to combine the efficiency of Slater-type orbitals with the adaptivity of modern multi-resolution methods. We develop numerical calculus suitable for electronic structure calculations. For any spatial orbital in this functional form, we represent its product with the Coulomb potential, its convolution with the Poisson kernel, etc., in the same functional form with optimized parameters. Algorithms for this purpose scale linearly in the number of nuclei. We compute electronic structure by casting the relevant equations in an integral form and solving for the spatial orbitals via iteration. As an example, for several diatomic molecules we solve the Hartree–Fock equations with speeds competitive to those of multi-resolution methods and achieve high accuracy using a small number of parameters.

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11

Guseinov, I. I. "Quantum Self-Frictional Relativistic Nucleoseed Spinor-Type Tensor Field Theory of Nature." Advances in High Energy Physics 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/6049079.

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For study of quantum self-frictional (SF) relativistic nucleoseed spinor-type tensor (NSST) field theory of nature (SF-NSST atomic-molecular-nuclear and cosmic-universe systems) we use the complete orthogonal basis sets of22s+1-component column-matrices type SFΨnljmjδ⁎s-relativistic NSST orbitals (Ψδ⁎s-RNSSTO) and SFXnljmjs-relativistic Slater NSST orbitals (Xs-RSNSSTO) through theψnlmlδ⁎-nonrelativistic scalar orbitals (ψδ⁎-NSO) andχnlml-nonrelativistic Slater type orbitals (χ-NSTO), respectively. Hereδ⁎=pl⁎orδ⁎=α⁎andpl⁎=2l+2-α⁎, α⁎are the integer(α⁎=α, -∞<α≤2) or noninteger(α⁎≠α, -∞<α⁎<3) SF quantum numbers, wheres=0,1/2,1,3/2,2,…. We notice that the nonrelativisticψδ⁎-NSO andχ-NSTO orbitals themselves are obtained from the relativisticΨδ⁎s-RNSSTO andXs-RSNSSTO functions fors=0, respectively. The column-matrices-type SFY1jmjls-RNSST harmonics (Y1ls-RNSSTH) andY2jmjls-modified NSSTH (Y2ls-MNSSTH) functions for arbitrary spinsintroduced by the author in the previous papers are also used. The one- and two-center one-range addition theorems forψδ⁎-NSO and nonintegern χ-NSTO orbitals are presented. The quantum SF relativistic nonperturbative theory forVnljmjδ⁎-RNSST potentials (Vδ⁎-RNSSTP) and their derivatives is also suggested. To study the transportations of mass and momentum in nature the quantum SF relativistic NSST gravitational photon (gph) withs=1is introduced.

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12

García, Victor, David Zorrilla, and Manuel Fernández. "Simplified box orbitals: A spatially restricted alternative to the slater-type orbitals." International Journal of Quantum Chemistry 114, no. 23 (June 28, 2014): 1581–93. http://dx.doi.org/10.1002/qua.24727.

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13

Desmarais, N., G. Dancausse, and S. Fliszár. "A simple quality test for self-consistent-field atomic orbitals." Canadian Journal of Chemistry 71, no. 2 (February 1, 1993): 175–79. http://dx.doi.org/10.1139/v93-025.

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A quality test is proposed for SCF atomic orbitals, [Formula: see text] approximated as finite linear combinations of suitable basis functions [Formula: see text] The key is in a function, readily derived from the Hartree–Fock equation [Formula: see text] which is identically zero for true Hartree–Fock spin orbitals and not so for approximate orbitals. In this way, our test measures how closely approximate orbital descriptions approach the true Hartree–Fock limit and thus provides a quality ordering of orbital bases with respect to one another and with respect to that limit, in a scale uniquely defined by the latter. Moreover, this analysis also holds for atomic subspaces of our choice, e.g., the valence region. Examples are offered for representative collections of Slater- and Gaussian-type orbital expansions.

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14

Zheng, Xuehe, and Michael C. Zerner. "Electric multipole moment integrals evaluated over slater-type orbitals." International Journal of Quantum Chemistry 48, S27 (March 13, 1993): 431–50. http://dx.doi.org/10.1002/qua.560480843.

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15

Fern�ndez Rico, J., R. L�pez, A. Aguado, I. Ema, and G. Ram�rez. "Reference program for molecular calculations with Slater-type orbitals." Journal of Computational Chemistry 19, no. 11 (August 1998): 1284–93. http://dx.doi.org/10.1002/(sici)1096-987x(199808)19:11<1284::aid-jcc8>3.0.co;2-g.

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16

Fern�ndez Rico, J., R. L�pez, A. Aguado, I. Ema, and G. Ram�rez. "New program for molecular calculations with Slater-type orbitals." International Journal of Quantum Chemistry 81, no. 2 (2000): 148–53. http://dx.doi.org/10.1002/1097-461x(2001)81:2<148::aid-qua6>3.0.co;2-0.

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17

Gebremedhin, Daniel, and Charles Weatherford. "Canonical two-range addition theorem for slater-type orbitals." International Journal of Quantum Chemistry 113, no. 1 (August 28, 2012): 71–75. http://dx.doi.org/10.1002/qua.24319.

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18

Avery, James Emil, and John Scales Avery. "Molecular integrals for slater type orbitals using coulomb sturmians." Journal of Mathematical Chemistry 52, no. 1 (September 28, 2013): 301–12. http://dx.doi.org/10.1007/s10910-013-0264-2.

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19

Ema, Ignacio, Rafael López, Guillermo Ramírez, and Jaime Fernández Rico. "Direct calculation of the Coulomb matrix: Slater-type orbitals." Theoretical Chemistry Accounts 128, no. 1 (June 15, 2010): 115–25. http://dx.doi.org/10.1007/s00214-010-0771-1.

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20

Wojnecki, R., and P. Modrak. "Calculation of two-center integrals between Slater-type orbitals." Computers & Chemistry 17, no. 3 (September 1993): 287–90. http://dx.doi.org/10.1016/0097-8485(93)80009-3.

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21

Righi, A. F. M., and C. A. Kuhnen. "Molecular Orbitals Calculation on LiH with Algebraic Treatment of the Integrals." International Journal of Modern Physics C 08, no. 05 (October 1997): 1159–68. http://dx.doi.org/10.1142/s0129183197001028.

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In this work we employ an algebraic computational method to solve the integrals which arise in the study of diatomic molecules. Using the Slater-type orbitals (STO), we obtain analytical solutions for the one-center and two-center hybrid and Coulomb integrals. The exchange integrals are considered, as much as possible, in a similar manner. These results are used to calculate the electronic properties of the ground state of the LiH molecule, by means of a variational calculation using a basis of molecular orbitals. The behavior of the Slater exponents of the atomic orbitals are studied as functions of internuclear distance. We show that the STO undergo a lengthening of their shape when the nuclear separation increases.

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22

Guseinov, I. I., and B. A. Mamedov. "Unified treatment of overlap integrals with integer and noninteger n Slater-type orbitals using translational and rotational transformations for spherical harmonics." Canadian Journal of Physics 82, no. 3 (March 1, 2004): 205–11. http://dx.doi.org/10.1139/p03-116.

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A unified treatment of two-center overlap integrals over Slater-type orbitals (STO) with integer and noninteger values of the principal quantum numbers is described. Using translation and rotation formulas for spherical harmonics, the overlap integrals with integer and noninteger n Slater-type orbitals are expressed through the basic overlap integrals and spherical harmonics. The basic overlap integrals are calculated using auxiliary functions Aσ and Bk. The analytical relations obtained in this work are especially useful for the calculation of overlap integrals for large integer and noninteger principal quantum numbers. The formulas established in this study for overlap integrals can be used for the construction of series expansions based on addition theorems. PACS Nos.: 31.15.p, 31.20.Ej

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23

Mitroy, J. "A Hartree - Fock Program for Atomic Structure Calculations." Australian Journal of Physics 52, no. 6 (1999): 973. http://dx.doi.org/10.1071/ph99042.

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The Hartree–Fock equations for a general open shell atom are described. The matrix equations that result when the single particle orbitals are written in terms of a linear combination of analytic basis functions are derived. Attention is paid to the complexities that occur when open shells are present. The specifics of a working FORTRAN program which is available for public use are described. The program has the flexibility to handle either Slater-type orbitals or Gaussian-type orbitals.

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24

Özdoğan, Telhat, Metin Orbay, and Salih Değirmenci. "Evaluation of two-center overlap integrals using slater type orbitals in terms of bessel type orbitals." Journal of Mathematical Chemistry 37, no. 1 (January 2005): 27–36. http://dx.doi.org/10.1007/s10910-004-7661-5.

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25

Berlu, Lilian, and Philip Hoggan. "Useful Integrals for Ab-Initio Molecular Quantum Similarity Measurements Using Slater Type Atomic Orbitals." Journal of Theoretical and Computational Chemistry 02, no. 02 (June 2003): 147–61. http://dx.doi.org/10.1142/s0219633603000513.

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Molecular quantum similarity measurements are based on a quantitative comparison of the one-electron densities of two molecules superposed and aligned to optimize a well-defined similarity function. In most previous work the densities have been related using a Dirac delta leading to the overlap-like quantum similarity function. The densities for the two molecules compared have generally been approximated often with a simple LCAO of s-gaussian functions. In this work, we present a one center two range expansion method for the evaluation of the overlap integrals involved in the overlap-like quantum similarity function over Slater type orbitals (STO). The single center and three types of two-center overlap integrals (involving four atomic orbitals; two in each molecule) have led to finite sums using a single center approach combined with selection rules obtained by analysis of orbital angular momentum (conservation). The three- and four-center integrals are also obtained analytically but involve infinite sums which require further study before leading to a complete set of integral codes for ab-initio quantum similarity.

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26

Kolakowska, A., and J. D. Talman. "Energy derivatives in variational calculations using Slater-type and Gauss-type orbitals." Physical Review E 53, no. 4 (April 1, 1996): 4236–39. http://dx.doi.org/10.1103/physreve.53.4236.

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27

Guseinov, I. I., E. Akin, and A. M. Rzaeva. "Evaluation of molecular electric multipole moments using Slater-type orbitals." Journal of Molecular Structure: THEOCHEM 453, no. 1-3 (October 1998): 163–67. http://dx.doi.org/10.1016/s0166-1280(98)00197-3.

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28

Jones, Herbert W. "Exact formulas for multipole moments using Slater-type molecular orbitals." Physical Review A 33, no. 3 (March 1, 1986): 2081–83. http://dx.doi.org/10.1103/physreva.33.2081.

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29

Datta, S. "Evaluation of Coulomb integrals with hydrogenic and Slater-type orbitals." Journal of Physics B: Atomic and Molecular Physics 18, no. 5 (March 14, 1985): 853–57. http://dx.doi.org/10.1088/0022-3700/18/5/006.

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30

Etemadi, Babak, and Herbert W. Jones. "AccurateLCAO ground state calculations of HeH2+ using slater-type orbitals." International Journal of Quantum Chemistry 48, S27 (March 13, 1993): 755–58. http://dx.doi.org/10.1002/qua.560480867.

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31

Jones, Herbert W. "Computer-generated formulas for hybrid integrals over slater-type orbitals." International Journal of Quantum Chemistry 20, S15 (June 19, 2009): 287–91. http://dx.doi.org/10.1002/qua.560200831.

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32

Guseinov, I. I. "Evaluation of multicenter electron-repulsion integrals over slater-type orbitals." International Journal of Quantum Chemistry 28, S19 (June 19, 2009): 149–55. http://dx.doi.org/10.1002/qua.560280814.

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33

Jones, Herbert W. "Computer-generated formulas for exchange integrals over slater-type orbitals." International Journal of Quantum Chemistry 28, S19 (June 19, 2009): 157–63. http://dx.doi.org/10.1002/qua.560280815.

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34

Guseinov, Israfil. "One-range addition theorems for derivatives of Slater-type orbitals." Journal of Molecular Modeling 10, no. 3 (June 1, 2004): 212–15. http://dx.doi.org/10.1007/s00894-004-0188-7.

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35

Chong, Delano P., Erik Van Lenthe, Stan Van Gisbergen, and Evert Jan Baerends. "Even-tempered slater-type orbitals revisited: From hydrogen to krypton." Journal of Computational Chemistry 25, no. 8 (2004): 1030–36. http://dx.doi.org/10.1002/jcc.20030.

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36

Özdoğan, Telhat. "Unified Treatment for Two-Center One-Electron Molecular Integrals Over Slater Type Orbitals with Integer and Noninteger Principal Quantum Numbers." Zeitschrift für Naturforschung A 59, no. 11 (November 1, 2004): 743–49. http://dx.doi.org/10.1515/zna-2004-1103.

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A unified expression has been obtained for two-center one-electron molecular integrals over Slater type orbitals with integer and noninteger principal quantum numbers by the use of the expansion formula for the product of two normalized associated Legendre functions. The presented expression for two-center one-electron molecular integrals contains the expansion coefficients akk' us and Mulliken integrals An and Bn. The efficiency of the presented calculation has been compared with that of other methods, indicating good convergence and great numerical stability for a wide range of quantum numbers, orbital exponents and internuclear distances

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37

Guseinov, I. I., B. A. Mamedov, F. Öner, and S. Hüseyin. "Computation of molecular integrals over Slater-type orbitals. VIII. Calculation of overlap integrals with different screening parameters using series expansion formulas for Slater-type orbitals." Journal of Molecular Structure: THEOCHEM 545, no. 1-3 (July 2001): 265–70. http://dx.doi.org/10.1016/s0166-1280(01)00410-9.

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38

BERLU, LILIAN. "A FOURIER TRANSFORM APPROACH FOR TWO-CENTER OVERLAP-LIKE QUANTUM SIMILARITY INTEGRALS OVER SLATER TYPE ORBITALS." Journal of Theoretical and Computational Chemistry 03, no. 02 (June 2004): 257–67. http://dx.doi.org/10.1142/s0219633604001033.

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In previous work,1 we presented a one center two range expansion method for the evaluation of the two-center overlap-like quantum similarity integrals over Slater type orbitals which are four orbitals overlap integrals. In this work, to improve the accuracy and to reduce the calculation times, the above integrals are developed using the Fourier transform approach and the so-called B functions. With the help of angular momentum selection rules, two-center overlap-like quantum similarity integrals are expressed as combinations of usual overlap integrals (e.g. two-orbitals) which could be evaluated very accurately using the Fourier transform method combinated with B functions.

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39

Mrovec, Martin. "Low-rank tensor representation of Slater-type and Hydrogen-like orbitals." Applications of Mathematics 62, no. 6 (December 1, 2017): 679–98. http://dx.doi.org/10.21136/am.2017.0177-17.

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40

Guseinov, Israfil, Ramazan Aydin, and Bahtiyar Mamedov. "Computation of multicenter overlap integrals with Slater-type orbitals using ??-ETOs." Journal of Molecular Modeling 9, no. 5 (October 1, 2003): 325–28. http://dx.doi.org/10.1007/s00894-003-0151-z.

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41

Belkić, Dževad, and Howard S. Taylor. "A unified formula for the Fourier transform of Slater-type orbitals." Physica Scripta 39, no. 2 (February 1, 1989): 226–29. http://dx.doi.org/10.1088/0031-8949/39/2/004.

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42

Romanowski, Zbigniew, and Abraham F. Jalbout. "Representation of Kohn–Sham free atom eigenfunctions by Slater-type orbitals." International Journal of Quantum Chemistry 108, no. 9 (2008): 1465–76. http://dx.doi.org/10.1002/qua.21668.

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43

Gümüş, Sedat, and Telhat Özdoǧan. "Symbolic Calculation of Two-Center Overlap Integrals Over Slater-Type Orbitals." Journal of the Chinese Chemical Society 51, no. 2 (April 2004): 243–52. http://dx.doi.org/10.1002/jccs.200400039.

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44

Jones, Herbert W. "Semianalytical method for four-center molecular integrals over Slater-type orbitals." International Journal of Quantum Chemistry 42, no. 4 (May 20, 1992): 779–84. http://dx.doi.org/10.1002/qua.560420417.

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45

Jones, Herbert W. "Benchmark values for two-center Coulomb integrals over slater-type orbitals." International Journal of Quantum Chemistry 45, no. 1 (1993): 21–30. http://dx.doi.org/10.1002/qua.560450105.

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46

Jones, Herbert W. "Computer-generated formulas for four-center integrals over slater-type orbitals." International Journal of Quantum Chemistry 29, no. 2 (February 1986): 177–83. http://dx.doi.org/10.1002/qua.560290206.

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47

Akdemir, Selda. "Convergence of Slater-Type Orbitals in Calculations of Basic Molecular Integrals." Iranian Journal of Science and Technology, Transactions A: Science 42, no. 3 (March 15, 2017): 1613–21. http://dx.doi.org/10.1007/s40995-017-0177-1.

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48

Ema, I., J. M. García de la Vega, G. Ramírez, R. López, J. Fernández Rico, H. Meissner, and J. Paldus. "Polarized basis sets of Slater-type orbitals: H to Ne atoms." Journal of Computational Chemistry 24, no. 7 (May 2003): 859–68. http://dx.doi.org/10.1002/jcc.10227.

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49

Guseinov, I. I., A. �zmen, �. Atav, and H. Y�ksel. "Computation of overlap integrals over Slater-type orbitals using auxiliary functions." International Journal of Quantum Chemistry 67, no. 4 (1998): 199–204. http://dx.doi.org/10.1002/(sici)1097-461x(1998)67:4<199::aid-qua1>3.0.co;2-q.

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50

Çopuroğlu, Ebru. "Evaluation of Self-Friction Three-Center Nuclear Attraction Integrals with Integer and Noninteger Principal Quantum Numbers n over Slater Type Orbitals." Journal of Chemistry 2017 (2017): 1–6. http://dx.doi.org/10.1155/2017/1598951.

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We have proposed a new approach to evaluate self-friction (SF) three-center nuclear attraction integrals over integer and noninteger Slater type orbitals (STOs) by using Guseinov one-range addition theorem in standard convention. A complete orthonormal set of Guseinov ψα exponential type orbitals (ψα-ETOs, α=2,1,0,-1,-2,…) has been used to obtain the analytical expressions. The overlap integrals with noninteger quantum numbers occurring in SF three-center nuclear attraction integrals have been evaluated using Qnsq auxiliary functions. The accuracy of obtained formulas is satisfactory for arbitrary integer and noninteger principal quantum numbers.

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