Skip to main content
SpringerLink
Log in

Two‐center p‐space integrals: diatomic molecular moments

  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

Analytical expressions for the calculation of both orbital and total moments of diatomic molecules using Gaussian‐type orbitals are formulated. Moments \(\left\langle {p^t } \right\rangle \) with \( - 2 \leqslant t \leqslant 4\) are computed for the ground state of 35 diatomic molecules at equilibrium bond length using 6‐311G(d,p) basis sets. In order to test our expressions, these expectation momentum values are compared with the values calculated using self‐consistent‐field wave functions of Hartree–Fock quality, which give Hartree–Fock limit energies.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions (Dover Publications, New York, 1972) p. 508.

    Google Scholar 

  2. N.L. Allan and D.L. Cooper, J. Chem. Phys. 84 (1986) 5594.

    Article  CAS  Google Scholar 

  3. N.L. Allan and D.L. Cooper, J. Chem. Soc. Faraday Trans. 83 (1987) 449.

    Article  Google Scholar 

  4. N.L. Allan and D.L. Cooper, Top. Curr. Chem. 173 (1995) 85.

    CAS  Google Scholar 

  5. N.L. Allan, D.L. Cooper, C.G. West, P.J. Grout and N.H. March, J. Chem. Phys. 83 (1985) 239.

    Article  CAS  Google Scholar 

  6. N.L. Allan, C.G. West, D.L. Cooper, P.J. Grout and N.H. March, J. Chem. Phys. 83 (1985) 4562.

    Article  CAS  Google Scholar 

  7. R. Benesch and V.H. Smith, Jr., Phys. Rev. A5 (1972) 114.

    Google Scholar 

  8. R. Benesch and V.H. Smith, Jr., in: Wave Mechanics – The First Fifty Years, eds. W.C. Price, S.S. Chissick and T. Ravensdale (Butterworths, London, 1973) p. 357.

    Google Scholar 

  9. J.L. de Boer and A. Vos, Acta Crystallogr. B35 (1979) 1809.

    CAS  Google Scholar 

  10. C.E. Brion, in: The Physics of Electronic and Atoms Collisions, eds. T. Anderson et al. (American Institute of Physics Press, New York, 1993) p. 350.

    Google Scholar 

  11. P.E. Cade and W. Huo, At. Data Nucl. Data Tables 12 (1973) 415.

    Article  CAS  Google Scholar 

  12. P.E. Cade and W. Huo, At. Data Nucl. Data Tables 15 (1975) 1.

    Article  CAS  Google Scholar 

  13. P.E. Cade and A.C. Wahl, At. Data Nucl. Data Tables 13 (1974) 339.

    Article  CAS  Google Scholar 

  14. E.U. Condon and G.H. Shortley, The Theory of Atomic Spectra (Cambridge University Press, Cambridge, 1963) p. 176.

    Google Scholar 

  15. D.L. Cooper and N.L. Allan, in: Molecular Similarity and Reactivity: From Quantum Chemical to Phenomenological Approaches, ed. R. Carbó (Kluwer, Dordrecht, 1995) p. 31

    Google Scholar 

  16. D.L. Cooper, N.L. Allan and P.J. Grout, J. Chem. Soc. Faraday Trans. 85 (1989) 1519.

    Article  CAS  Google Scholar 

  17. I.R. Epstein, Chem. Phys. Lett. 9 (1971) 9.

    Article  CAS  Google Scholar 

  18. R.O. Esquivel, A.N. Tripathi, R.P. Sagar and V.H. Smith, Jr., J. Phys. B26 (1992) 2925.

    Google Scholar 

  19. D. Feller, C.M. Boyle and E.R. Davidson, J. Chem. Phys. 86 (1987) 3424.

    Article  CAS  Google Scholar 

  20. M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson, M.W. Wong, J.B. Foresman, M.A. Robb, M. Head-Gordon, E.S. Replogle, R. Gomperts, J.L. Andres, K. Raghavachari, J.S. Binkley, C. Gonzalez, R.L. Martin, D.J. Fox, D.J. Defrees, J. Baker, J.J.P. Stewart and J.A. Pople, Gaussian 92/DFT, Revision F.2 (Gaussian, Pittsburgh, PA, 1993).

    Google Scholar 

  21. J.M. García de la Vega and B. Miguel, J. Math. Chem. 14 (1993) 219.

    Article  Google Scholar 

  22. J.M. García de la Vega and B. Miguel, At. Data Nucl. Data Tables 541 (1993) 3.

    Google Scholar 

  23. J.M. García de la Vega and B. Miguel, J. Mol. Struct. (Theochem) 287 (1993) 39.

    Article  Google Scholar 

  24. J.M. García de la Vega and B. Miguel, At. Data Nucl. Data Tables 587 (1994) 307.

    Google Scholar 

  25. J.M. García de la Vega and B. Miguel, At. Data Nucl. Data Tables 60 (1995) 321.

    Article  Google Scholar 

  26. J.M. García de la Vega and B. Miguel, Chem. Phys. Lett. 236 (1995) 616.

    Article  Google Scholar 

  27. I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series and Products, 4th ed. (Academic Press, San Diego, 1980) equation (8.751).

    Google Scholar 

  28. P. Kaijser and V.H. Smith, Jr., Adv. Quantum Chem. 10 (1980) 37.

    Article  Google Scholar 

  29. R. Krishnan, J.S. Binkley, R. Seeger and J.A. Pople, J. Chem. Phys. 72 (1980) 650.

    Article  CAS  Google Scholar 

  30. A.D. McLean and G.S. Chandler, J. Chem. Phys. 72 (1980) 5639.

    Article  CAS  Google Scholar 

  31. A.D. McLean and M. Yoshimine, Tables of Linear Molecule Function (IBM, San José, 1967).

  32. A.D. McLean and M. Yoshimine, IBM J. Res. Dev. 12 (1968) 206.

    Article  CAS  Google Scholar 

  33. P.T. Measures, N.L. Allan and D.L. Cooper, Int. J. Quantum Chem. 60 (1996) 579.

    Article  CAS  Google Scholar 

  34. P.A.G. O'Hare and A.C. Wahl, J. Chem. Phys. 53 (1970) 2469.

    Article  Google Scholar 

  35. R.K. Pathak, B.S. Sharma and A.J. Thakkar, J. Chem. Phys. 85 (1986) 958.

    Article  CAS  Google Scholar 

  36. G.A. Petersson and M.A. Al-Laham, J. Chem. Phys. 94 (1991) 6081.

    Article  CAS  Google Scholar 

  37. G.A. Petersson, A. Bennett, T.G. Tensfeld, M.A. Al-Laham, W.A. Shirley and J. Mantzaris, J. Chem. Phys. 89 (1988) 2193.

    Article  CAS  Google Scholar 

  38. B.I. Ramírez, J. Phys. B15 (1982) 4339.

    Google Scholar 

  39. B.I. Ramírez, J. Phys. B16 (1983) 343.

    Google Scholar 

  40. D.C. Rawlings and E.R. Davidson, J. Phys. Chem. 89 (1985) 969.

    Article  CAS  Google Scholar 

  41. P.E. Regier, J. Fisher, B.S. Sharma and A.J. Thakkar, Int. J. Quantum Chem. 28 (1985) 429.

    Article  CAS  Google Scholar 

  42. J. Rolke, N. Cann, Y. Zheng, B.P. Hollebone, C.E. Brion, Y.A. Wang and E.R. Davids, Chem. Phys. 201 (1995) 1.

    Article  CAS  Google Scholar 

  43. H. Schmider, R.O. Esquivel, R.P. Sagar and V.H. Smith, Jr., J. Phys. B26 (1993) 2943.

    Google Scholar 

  44. J.A. Tossell, J.H. Moore, M.A. Coplan, G. Stefani and R. Camilloni, J. Am. Chem. Soc. 104 (1982) 7416s.

  45. A.N. Tripathi, R.P. Sagar, R.O. Esquivel and V.H. Smith, Jr., Phys. Rev. A45 (1992) 4385.

    Google Scholar 

  46. A.N. Tripathi, V.H. Smith, Jr., R.P. Sagar and R.O. Esquivel, Phys. Rev. A54 (1996) 1877.

    Google Scholar 

  47. J. Wang, J. Clark, H. Schmider and V.H. Smith, Jr., Can. J. Chem. 74 (1996) 1187.

    Article  CAS  Google Scholar 

  48. J. Wang, V.H. Smith, Jr., and R. Jauregui, Acta Crystalogr. A52 (1996) 649.

    Article  CAS  Google Scholar 

  49. B.G. Williams, ed., Compton Scattering (McGraw-Hill, New York, 1977).

  50. G. de With and D. Feil, Chem. Phys. Lett. 30 (1975) 279.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Química Física Aplicada, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049, Madrid, Spain

    J.M. García de la Vega, B. Miguel & G. Ramírez

Authors
  1. J.M. García de la Vega
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. Miguel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. Ramírez
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

García de la Vega, J., Miguel, B. & Ramírez, G. Two‐center p‐space integrals: diatomic molecular moments. Journal of Mathematical Chemistry 21, 211–222 (1997). https://doi.org/10.1023/A:1019126520292

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1019126520292

Keywords

Search

Navigation