Bulletin of the Korean Chemical Society

Korean Chemical Society (대한화학회)
권호 표지
DOI QR코드

DOI QR Code

Evaluation of Multicenter Multielectron Integrals Using One-range Addition Theorems in Terms of STOs for STOs and Coulomb-Yukawa Like Correlated Interaction Potentials with Integer and Noninteger Indices

  • Guseinov, I. I. (Department of Physics, Faculty of Arts and Sciences, Onsekiz Mart University)
  • Published : 2009.07.20
Download PDF
⟨ Previous Next ⟩

Abstract

Using one-range addition theorems for Slater type orbitals (STOs) and Coulomb-Yukawa like correlated interaction potentials (CIPs) introduced by the author, the series expansion formulae are derived for the multicenter multielectron integrals. The expansion coefficients occurring in these relations are presented through the overlap integrals of two STOs. The convergence of series expansion relations is tested by calculating concrete cases. The accuracy of the results is quite high for quantum number, screening constants and location of orbitals. The final results are especially useful in the calculation of multielectron properties for atoms and molecules when Hartree-Fock-Roothaan (HFR) and explicitly correlated methods are employed.

Keywords

References

  1. Hylleraas, E. A. Z. Phys. 1928, 48, 469 https://doi.org/10.1007/BF01340013
  2. Hylleraas, E. A. Z. Physik. 1930, 60, 624 https://doi.org/10.1007/BF01339758
  3. Hylleraas, E. A. Z. Physik. 1930, 65, 209 https://doi.org/10.1007/BF01397032
  4. Löwdin, P. O. Phys. Rev. 1955, 97, 1474 https://doi.org/10.1103/PhysRev.97.1474
  5. Löwdin, P. O. Rev. Mod. Phys. 1960, 32, 328 https://doi.org/10.1103/RevModPhys.32.328
  6. Szasz, L. Phys. Rev. 1962, 126, 169 https://doi.org/10.1103/PhysRev.126.169
  7. James, H. M.; Coolidge, A. S. J. Chem. Phys. 1933, 1, 825 https://doi.org/10.1063/1.1749252
  8. Kolos, W.; Roothaan, C. C. J. Rev. Mod. Phys. 1960, 32, 205 https://doi.org/10.1103/RevModPhys.32.205
  9. Kolos, W.; Wolniewicz, L. J. Chem. Phys. 1964, 41, 3663 https://doi.org/10.1063/1.1725796
  10. Lüchow, A.; Kleindienst, H. Int. J. Quantum Chem. 1993, 45, 445 https://doi.org/10.1002/qua.560450504
  11. Levine, I. N. Quantum Chemistry, 5th Ed.; Prentice Hall: New Jersey, 2000
  12. Sims, J. S.; Hagstrom, S. A. In. J. Quantum Chem. 2002, 90, 1600 https://doi.org/10.1002/qua.10344
  13. Klopper, W.; Manby, F. R.; Ten-no, S.; Valeev, E. F. Int. Rev. Phys. Chem. 2006, 25, 427 https://doi.org/10.1080/01442350600799921
  14. Guseinov, I. I. Int. J. Quantum Chem. 2002, 90, 114 https://doi.org/10.1002/qua.927
  15. Guseinov, I. I. J. Theor. Comput. Chem. 2008, 7, 257 https://doi.org/10.1142/S0219633608003691
  16. Guseinov, I. I. J. Math. Chem. 2007, 42, 415 https://doi.org/10.1007/s10910-006-9111-z
  17. Guseinov, I. I. J. Mol. Struct.(Theochem) 1998, 422, 75 https://doi.org/10.1016/S0166-1280(97)00090-0
  18. Guseinov, I. I. J. Mol. Model. 2003, 9, 190 https://doi.org/10.1007/s00894-003-0134-0
  19. Guseinov, I. I. Chin. Phys. Lett. 2008, 25, 4240 https://doi.org/10.1088/0256-307X/25/12/015
  20. Guseinov, I. I. J. Math. Chem. 2005, 38, 489 https://doi.org/10.1007/s10910-004-6902-y
  21. Guseinov, I. I.; Aydın, R.; Mamedov, B. A. J. Mol. Model. 2003, 9, 325 https://doi.org/10.1007/s00894-003-0151-z
  22. Guseinov, I. I.; Mamedov, B. A. Z. Naturforsch 2007, 62a, 467

Cited by

  1. Analytical evaluation of Coulomb potential generated by multielectron molecule at arbitrary positions in space using one-range addition theorems of Slater type orbitals vol.17, pp.12, 2011, https://doi.org/10.1007/s00894-011-1027-2
  2. On the mathematical nature of Guseinov’s rearranged one-range addition theorems for Slater-type functions vol.50, pp.1, 2012, https://doi.org/10.1007/s10910-011-9914-4
  3. Israfil I. Guseinov: A pioneer of the quantum theory of atomic, molecular, and nuclear systems* vol.114, pp.5, 2013, https://doi.org/10.1002/qua.24574
  4. Use of Coulomb-Yukawa Like Correlated Interaction Potentials of Integer and Noninteger Indices and One-range Addition Theorems for Ψα-ETO in Evaluation of Potential of Electri vol.30, pp.11, 2009, https://doi.org/10.5012/bkcs.2009.30.11.2617