Theoretica chimica acta

, Volume 76, Issue 2, pp 73–84 | Cite as

Gaussian basis sets for calculation of spin densities in first-row atoms

  • Daniel M. Chipman


The suitability of Gaussian basis sets for ab initio calculation of Fermi contact spin densities is established by application to the prototype first-row atoms B-F having open shell p electrons. Small multiconfiguration self-consistent-field wave functions are used to describe relevant spin and orbital polarization effects. Basis sets are evaluated by comparing the results to highly precise numerical grid calculations previously carried out with the same wave function models. It is found that modest contracted Gaussian basis sets developed primarily for Hartree-Fock calculations can give semiquantitative results if augmented by diffuse functions and if further uncontracted in the outer core-inner valence region.

Key words

Spin density Gaussian basis sets First row atoms Polarization wave function 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References and notes

  1. 1.
    Hibbert A (1975) Rep Prog Phys 38:1217–1338. This review contains comprehensive references to earlier work on this topicGoogle Scholar
  2. 2.
    Bagus PS, Liu B, Schaefer HF (1970) Phys Rev A 2:555–560Google Scholar
  3. 3.
    Goddard WA (1969) Phys Rev 182:48–64Google Scholar
  4. 4.
    Meyer W (1969) J Chem Phys 51:5149–5162Google Scholar
  5. 5.
    Schaefer HF, Klemm RA, Harris FE (1968) Phys Rev 176:49–58Google Scholar
  6. 6.
    Schaefer HF, Klemm RA, Harris FE (1969) Phys Rev 181:137–143Google Scholar
  7. 7.
    Larsson S, Brown RE, Smith VH (1972) Phys Rev A 6:1375–1391Google Scholar
  8. 8.
    Nakatsuji H, Hirao K (1978) J Chem Phys 68:4279–4291Google Scholar
  9. 9.
    Feller D, Davidson ER (1988) J Chem Phys 88:7580–7587Google Scholar
  10. 10.
    Bauschlicher CW, Langhoff SR, Partridge H, Chong DP (1988) J Chem Phys 89:2985–2992Google Scholar
  11. 11.
    Carmichael I (1989) J Phys Chem 93:190–193Google Scholar
  12. 12.
    Chipman DM (1989) Phys Rev A 39:475–480Google Scholar
  13. 13.
    The surprising importance of diffuse functions in Fermi contact spin density calculations that utilize Gaussian functions was first pointed out by us in a poster presentation communicating preliminary results of this work at the Sixth American Conference on Theoretical Chemistry (Gull Lake, 1987)Google Scholar
  14. 14.
    Huzinaga S (1965) J Chem Phys 42:1293–1302Google Scholar
  15. 15.
    Dunning TH (1970) J Chem Phys 53:2823–2833Google Scholar
  16. 16.
    Cheung LM, Elbert ST, Ruedenberg K (1979) Int J Quantum Chem 16:1069–1101Google Scholar
  17. 17.
    Ruedenberg K, Elbert ST (1988) Private communicationGoogle Scholar
  18. 18.
    Salmon WI, Ruedenberg K, Cheung LM (1972) J Chem Phys 57:2787–2790Google Scholar
  19. 19.
    It is interesting to note that the Serber spin functions are particularly convenient for calculations in open shell systems. In the present context, the unpaired electrons in each important (s→s) single excitation configuration with triplet intermediate spin coupling (such as occurs in Ψ1 and Ψ2) can be expressed with a single Serber function multiplying an appropriately ordered product of spatial functions. Other choices, e.g. a genealogical construction, would generally require a linear combination of spin eigenfunctions to form such a configuration for an overall triplet or quartet stateGoogle Scholar
  20. 20.
    Harvey JSM, Evans L, Lew H (1972) Can J Phys 50:1719–1727Google Scholar
  21. 21.
    Graham WRM, Weltner W (1976) J Chem Phys 65:1516–1521Google Scholar
  22. 22.
    MacDonald JR, Golding RM (1978) Theor Chim Acta 47:1–16Google Scholar
  23. 23.
    Holloway WW, Luscher E, Novick R (1962) Phys Rev 126:2109–2115Google Scholar
  24. 24.
    Harvey JSM (1965) Proc Roy Soc A (London) 285:581–596Google Scholar
  25. 25.
    The shells of diffuse exponents used here have values B (0.0330s, 0.0106s, 0.0226p, 0.0073p); C (0.0479s, 0.0150s, 0.0358p, 0.0122p); N (0.0667s, 0.0208s, 0.0517p, 0.0162p); O (0.0862s, 0.0261s, 0.0648p, 0.0196p); F (0.1101s, 0.0334s, 0.0828p, 0.0251p).Google Scholar
  26. 26.
    The total energy was minimized with respect to the d exponent for the [6s3p] + diffuse sp basis set described in this work with an MCSCF wave function consisting of terms Ψ0, Ψ1, Ψ2, Ψ4 and, for O and F only, Ψ5. The optimum single d exponent was found to have the values:B (0.32d), C (0.51d), N (0.73d), O (1.01d), and F (1.33d).Google Scholar
  27. 27.
    Davidson ER (1988) Private communicationGoogle Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Daniel M. Chipman
    • 1
  1. 1.Radiation LaboratoryUniversity of Notre DameNotre DameUSA

Personalised recommendations