Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions

III. First row transition metal atoms


Generally contracted basis sets for the first row transition metal atoms Sc-Zn have been constructed using the atomic natural orbital (ANO) approach, with modifications for allowing symmetry breaking and state averaging. The ANOs are constructed by averaging over the three electronic configurationsd n,d n−1 s, andd n−2 s 2 for the neutral atom as well as the ground state for the cation and the ground state atom in an external electric field. The primitive sets are 21s15p10d6f4g. Contraction to 6s5p4d3f2g yields results that are virtually identical to those obtained with the corresponding uncontracted basis sets for the atomic properties, which they have been designed to reproduce. Slightly larger deviations are obtained with the 5s4p3d2f1g for the polarizability, while energetic properties still have only small errors. The design objective has been to describe the ionization potential, the polarizability and the valence spectrum as accurately as possible. The result is a set of well-balanced basis sets for molecular calculations, which can be used together with basis sets of the same quality for the first and second row atoms.

This is a preview of subscription content, log in to check access.


  1. 1.

    Almlöf J, Taylor PR (1987) J Chem Phys 86:4070

  2. 2.

    Almlöf J, Taylor PR (1992) Adv Quantum Chem 22:301

  3. 3.

    Bauschlicher CW Jr (1995) Theor Chim Acta 92:183

  4. 4.

    Bauschlicher CW Jr, Taylor PR (1993) Theor Chim Acta, 86:13

  5. 5.

    Widmark PO, Malmqvist PÅ, Roos BO (1990) Theor Chim Acta 77:291

  6. 6.

    Widmark PO, Persson BJ, Roos BO (1991) Theor Chim Acta 79:419

  7. 7.

    Andersson K, Roos BO (1993) Int J Quantum Chem 45:591

  8. 8.

    Pierloot K, Dumez B, Widmark PO, Roos BO (1995) Theor Chim Acta 90:87

  9. 9.

    Andersson K, Blomberg MRA, Fülscher MP, Kellö V, Lindh R, Malmqvist PÅ, Noga J, Olsen J, Roos BO, Sadlej AJ, Siegbahn PEM, Urban M, Widmark PO (1994) Dept. of Theor. Chem., Chem. Centre, Univ. of Lund, Lund, Sweden

  10. 10.

    Partridge H (1989) J Chem Phys 90:1043

  11. 11.

    Chong DP, Langhoff SR (1986) J Chem Phys 84:5606

  12. 12.

    Pou-Amérigo R, Merchán M, Nebot-Gil I, Malmqvist PÅ, Roos BO (1994) J Chem Phys 101:4893

  13. 13.

    Moore CE, US GPO, Washington, (1952) NBS Circular 467

  14. 14.

    Armentrout PB, Sunderlin LS (1992) In: Transition Metal Hydrides Dedieu A (ed) VCH Publishers, Vol. 1, and references cited therein

  15. 15.

    Beaton SP, Evenson KM, Brown JM (1994) J Mol Spectrosc 164:395

  16. 16.

    Gray JA, Li M, Nelis T, Field RW (1991) J Chem Phys 95:7164

  17. 17.

    Ram RS, Bernath PF, Brault JW (1985) J Mol Spectrosc 113:269

  18. 18.

    Huber KP, Herzberg G (1979) Molecular Spectra and Molecular Structure, Van Nostrand Reinhold, New York

  19. 19.

    Chen YM, Clemmer DE, Armentrout PB (1993) J Chem Phys 98:4929

  20. 20.

    Chong DP, Langhoff SR, Bauschlicher CW Jr, Walch SP, Partridge H (1986) J Chem Phys 85:2850

  21. 21.

    Steimle TC, Shirley JE, Simard B, Vasseur M, Hackett P (1991) J Chem Phys 95:7179

  22. 22.

    Gray JA, Rice SF, Field RW (1985) J Chem Phys 82:4717

  23. 23.

    Ram RS, Jarman CN, Bernath PF (1992) J Mol Spectrosc 156:468

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Pou-Amérigo, R., Merchán, M., Nebot-Gil, I. et al. Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions. Theoret. Chim. Acta 92, 149–181 (1995). https://doi.org/10.1007/BF01114922

Download citation

Key words

  • Basis sets
  • Atomic natural orbitals
  • General contraction