Skip to main content
SpringerLink
Log in

Density Functionals for Correlation Energies of Atoms and Molecules

  • Chapter
Density Functional Methods In Physics

Part of the book series: NATO ASI Series ((ASIB,volume 123))

Abstract

The correlation energy, Ec, is usually defined as the difference of the exact (non-relativistic) energy, E, and the Hartree-Fock (HF) energy, EHF .1 Ec is a very small part of E only (1.4% for the He atom, 0.3% for Ne, 0.1% for Ar), but it is non-negligible in absolute value: for valence-shell removal, ...Ec is 1.1 eV for He, 9.5 eV for Ne, and 9.3 eV for Ar. Inclusion of Ec is important in cases where the number of (strongly interacting) electron pairs is changed, for dissociation energies (De), ionization potentials and excitation energies, e.g.. Correlation is responsible for 23% of Dein the case of H2, and for 84% of De in the case of Li2; Na2 and K2 are unbound at the HF level.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. P. O. Löwdin, Quantum theory of many-particle systems I, Phys. Rev. 97: 1474 (1955)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. H. F. Schaefer III (ed.), “Methods of Electronic Structure Theory”, Plenum Press, New York (1977)

    Google Scholar 

  3. W. Meyer, PNO-CI studies of electron correlation effects I, J. Chem. Phys. 58: 1017 (1973)

    Article  ADS  Google Scholar 

  4. M. A. Robb, Correlation energy as a stabilizing factor in molecular structure, in: “Molecular Structure and Conformation”, I. G. Csizmadia, ed., Elsevier, Amsterdam (1982)

    Google Scholar 

  5. W. Meyer, P. Botschwina, P. Rosmus, and H. J. Werner, Computed physical properties of small molecules, in: “Computational Methods in Chemistry”, J. Bargon, ed., Plenum Press, New York (1980)

    Google Scholar 

  6. D. Cremer, Thermochemical data from ab-initio calculations II, J. Comput. Chem. 3: 165 (1982)

    Article  Google Scholar 

  7. A. Savin, Die explizite Behandlung von Korrelationseffekten in Dichtefunktional-and Pseudopotentialmethoden, thesis, Stuttgart (1983)

    Google Scholar 

  8. A. C. Hurley, Thermochemistry in the Hartree-Fock approximation, Adv. Quantum Chem. 7: 315 (1973)

    Article  Google Scholar 

  9. W. Meyer and P. Rosmus, PNO-CI and CEPA studies of electron correlation effects III, J. Chem. Phys. 63: 2356 (1975)

    Article  ADS  Google Scholar 

  10. M. Levy, Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem, Proc. Natl. Acad. Sci. (USA) 76: 6062 (1979)

    Article  ADS  Google Scholar 

  11. P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136: B864 (1964)

    Article  MathSciNet  Google Scholar 

  12. W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140: A1133 (1965)

    Article  MathSciNet  Google Scholar 

  13. U. von Barth and L. Hedin, A local exchange-correlation potential for the spin-polarized case I, J. Phys. C 5: 1629 (1972)

    Article  ADS  Google Scholar 

  14. O. Gunnarsson and B. I. Lundqvist, Exchange and correlation in atoms, molecules and solids by the spin-density functional formalism, Phys. Rev. B 13: 4274 (1976)

    Article  Google Scholar 

  15. S. H. Vosko, L. Wilk, and M. Nusair, Accurate spin-dependent electron liquid correlation energies for local-spin density calculations: a critical analysis, Can. J. Phys. 58: 1200 (1980)

    ADS  Google Scholar 

  16. D. M. Ceperley and B. J. Alder, Ground state of the electron gas by a stochastic method, Phys. Rev. Lett. 45: 566 (1980)

    Article  ADS  Google Scholar 

  17. L. Wilk and S. H. Vosko, Estimates of non-local corrections to total ionisation and single-particle energies, J. Phys. C 15: 2139 (1982)

    Article  ADS  Google Scholar 

  18. G. S. Painter and F. W. Averill, Bonding in the first-row diatomic molecules within the local spin-density approximation, Phys. Rev. B 26: 1781 (1982)

    Article  Google Scholar 

  19. E. Clementi, Correlation energy for atomic systems, J. Chem. Phys. 38: 2248 (1963); 39: 175 (1963)

    Google Scholar 

  20. B. Y. Tong and L. J. Sham, Application of a self-consistent scheme including exchange and correlation effects to atoms, Phys. Rev. 144: 1 (1966)

    Article  Google Scholar 

  21. R. D. Cowan, Atomic self-consistent-field calculations using statistical approximations for exchange and correlation, Phys. Rev. 163: 54 (1967)

    Article  Google Scholar 

  22. H. Stoll, C. M. E. Pavlidou, and H. Preuss, On the calculation of correlation energies in the spin-density functional formalism, Theoret. Chim. Acta 49: 143 (1978)

    Article  Google Scholar 

  23. E. Eggarter and T. P. Eggarter, Atomic correlation energies, J. Phys. B 11: 1157, 2069, 2969 (1978)

    Google Scholar 

  24. J. P. Perdew and A. Zunger, Self-interaction correction to densityfunctional approximations for many-electron systems, Phys. Rev. B 23: 5048 (1981)

    Article  Google Scholar 

  25. P. Rosmus and W. Meyer, PNO-CI and CEPA studies of electron correlation effects IV, J. Chem. Phys. 66: 13 (1977)

    Article  ADS  Google Scholar 

  26. O. Gunnarsson and R. O. Jones, Self-interaction corrections in the density-functional formalism, Solid State Commun. 37: 249 (1981)

    Article  ADS  Google Scholar 

  27. H. Stoll, E. Golka, and H. Preuss, Correlation energies in the spin-density functional formalism II, Theoret. Chim. Acta 55: 29 (1980)

    Article  Google Scholar 

  28. J. P. Perdew, E. R. McMullen and A. Zunger, Density functional theory of the correlation energy in atoms and ions: a simple analytic model and a challenge, Phys. Rev. A 23: 2785 (1981)

    Article  Google Scholar 

  29. A. Savin, H. Stoll and H. Preuss, Pair correlation energies and local spin-density functionals, in: “Local Density Approximations in Quantum Chemistry and Solid State Physics”, J. Avery and J. P. Dahl, eds., Plenum Press, New York, in press

    Google Scholar 

  30. K. Jankowski, P. Malinowski and M. Polasik, Second-order correlation energies of Mg and Ar, J. Phys. B 12: 3157 (1979)

    Article  ADS  Google Scholar 

  31. A. Savin, P. Schwerdtfeger, H. Preuss, H. Silberbach, and H. Stoll, Relativistic effects on the contribution of the local-spin-density correlation energy to ionization potentials, Chem. Phys. Lett. 98: 226 (1983)

    Article  ADS  Google Scholar 

  32. P. Fuentealba, unpublished results

    Google Scholar 

  33. H. Stoll, P. Fuentealba, M. Dolg, J. Flad, L. v. Szentpâly and H. Preuss, Cu and Ag as one-valence-electron atoms, J. Chem. Phys., submitted

    Google Scholar 

  34. L. A. Cole and J. P. Perdew, Calculated electron affinities of elements, Phys. Rev. A 25: 1265 (1982)

    Article  Google Scholar 

  35. G. Verhaegen and C. M. Moser, Hartree-Fock, correlation and term energies of valence excited states of atoms and ions of the second-row of the periodic table, Mol. Phys. 3: 478 (1970)

    Google Scholar 

  36. P. Schwerdtfeger, H. Stoll and H. Preuss, A study of potential curve crossing in X-Ar complexes (X=Mg,Ca,Sr,Ba), J. Phys. B 15: 1061 (1982)

    Article  ADS  Google Scholar 

  37. O. Gunnarsson and R. O. Jones, Extensions of the LSD approximation in density functional calculations, J. Chem. Phys. 72: 53–57 (1980)

    Article  Google Scholar 

  38. A. Savin, in preparation

    Google Scholar 

  39. B. I. Dunlap, private communication

    Google Scholar 

  40. G. C. Lie, J. Hinze, and B. Liu, Valence excited states of CH, J. Chem. Phys. 59: 1872 (1973)

    Article  ADS  Google Scholar 

  41. M. F. Guest and D. M. Hirst, Ab-initio potential curves for the valence states of the NH+ ion, Mol. Phys. 34: 1611 (1977)

    Google Scholar 

  42. H. Preuss, H. Stoll, U. Wedig, and Th. Krüger, A combination of pseudo-potentials and density functionals, Int. J. Quantum Chem. 19: 113 (1981)

    Google Scholar 

  43. J. Flad, G. Igel, M. Dolg, H. Stoll and H. Preuss, A combination of pseudootentials and density functionals: results for Lim+, Nam+ and Kn clusters (n44, m=o, 1), Chem. Phys. 75: 331 ( 1983

    Article  Google Scholar 

  44. J. L. Martins, R. Car, and J. Buttet, Electronic properties of alkali trimers, J. Chem. Phys. 78: 5646 (1983)

    Article  ADS  Google Scholar 

  45. M. R. A. Blomberg, P. E. M. Siegbahn, and B. O. Roos, The ground-state potential curve of the Beryllium dimer, Int. J. Quantum Chem S 14: 229 (1980)

    Google Scholar 

  46. B. Liu and A. D. McLean, Ab-initio potential curve for Be2(1Zy+) from the interacting correlated fragments method, J. Chem. Phys. 72: 3418 (1980)

    Article  ADS  Google Scholar 

  47. E. J. Baerends and P. Ros, Evaluation of the LCAO Hartree-Fock-Slater method, Int. J. Quantum Chem. S 12: 169 (1978)

    Google Scholar 

  48. A. Gupta and R. J. Boyd, Density difference representation of electron correlation, J. Chem. Phys. 68: 1951 (1978)

    Article  ADS  Google Scholar 

  49. D. W. Smith, S. Jagannathan, and G. S. Handler, Density-functional theory of atomic structure I, Int. J. Quantum Chem. S 13: 103 (1979)

    Google Scholar 

  50. A. Savin, U. Wedig, H. Stoll, and H. Preuss, The correlated density of the Li atom: a test for density functionals and semi-empirical pseudopotentials, Chem. Phys. Lett. 92: 503 (1982)

    Article  ADS  Google Scholar 

  51. B. Y. Tong, Exchange-and correlation-energy calculations in finite systems, Phys. Rev. A 4: 1375 (1971)

    Article  Google Scholar 

  52. W. J. Schneider, Statistical correlation energies in atomic and molecular systems, J. Phys. B 11: 2589 (1978)

    Article  ADS  Google Scholar 

  53. S. K. Ma and K. A. Brueckner, Correlation energy of an electron gas with a slowly varying high density, Phys. Rev. 165: 18 (1968)

    Article  Google Scholar 

  54. D. C. Langreth and M. J. Mehl, Easily implementable non-local exchange-correlation energy functional, Phys. Rev. Lett. 47: 446 (1981)

    Article  ADS  Google Scholar 

  55. A. K. Rajagopal, Theory of inhomogeneous electron systems: spindensity-functional formalism, Adv. Chem. Phys. 41: 59 (1980)

    Google Scholar 

  56. P. Ros, Exact and simulated Coulomb holes and Coulomb correlation potentials for the ground state of the He isoelectronic series, Chem. Phys. 42: 9 (1979)

    Article  ADS  Google Scholar 

  57. I. L. Cooper and C. N. M. Pounder, Effect of modified virtual orbitals on local correlation holes inFCN, Int. J. Quantum Chem. 23: 257 (1983)

    Article  Google Scholar 

  58. J. Keller and J. L. Gazquez, Self-consistent field electron-gas local-spin-density model including correlation for atoms, Phys. Rev. A 20: 1289 (1979)

    Article  Google Scholar 

  59. J. A. Alonso and L. C. Balbâs, A non-local approximation to the correlation energy of inhomogeneous electron systems, Phys. Lett. A 81A: 467 (1981)

    Article  ADS  Google Scholar 

  60. O. Gunnarsson, M. Jonson, and B. I. Lundqvist, Descriptions of exchange and correlation effects in inhomogeneous electron systems, Phys. Rev. B 20: 3136 (1979)

    Article  Google Scholar 

  61. J. F. Dobson and J. H. Rose, Orbital self-interaction in Hartree-Fock and density functional theories, J. Phys. C 15: L1183 (1982)

    Article  ADS  Google Scholar 

  62. G. C. Lie and E. Clementi, Study of the electronic structure of molecules XXI,XXII, J. Chem. Phys. 60: 1275, 1288 (1974)

    Article  ADS  Google Scholar 

  63. J. Lievin, J. Breulet, and G. Verhaegen, A method for molecular correlation energy calculations, Theoret. Chim. Acta 60: 339 (1981)

    Article  Google Scholar 

  64. R. Colle and O. Salvetti, Approximate calculation of the correlation energy for the closed and open shells, Theoret. Chim. Acta 53: 55 (1979)

    Article  Google Scholar 

  65. R. McWeeny, Present status of the correlation problem, in: “The New World of Quantum Chemistry”, B. Pullman and R. Parr, eds., Reidel, Dordrecht (1976)

    Google Scholar 

  66. J. W. Moskowitz, K. E. Schmidt, M. A. Lee, and M. H. Kalos, Monte-Carlo variational study of Be: a survey of correlated wave functions, J. Chem. Phys. 76: 1064 (1982)

    Article  ADS  Google Scholar 

  67. M. H. Ang, K. Yates, I. G. Csizmadia, and R. Daudel, Relationship of correlation energy and size, Int. J. Quantum Chem. 20: 793 (1980)

    Article  Google Scholar 

  68. A. Dalgarno, C. Boettcher, and G. A. Victor, Pseudopotential calculation of atomic interactions, Chem. Phys. Lett. 7: 265 (1970)

    Article  ADS  Google Scholar 

  69. J. Migdalek and W. E. Baylis, Core-polarization, relaxation, and relativistic effects in the first ionization potentials for some systems in Cu, Ag, and Au isoelectronic sequences, Can. J. Phys. 60: 1317 (1982)

    ADS  Google Scholar 

  70. P. Fuentealba, H. Preuss, H. Stoll, and L. v. Szentpâly, A proper account of core-polarization with pseudopotentials, Chem. Phys. Lett. 89: 418 (1982)

    Article  ADS  Google Scholar 

  71. W. Müller, J. Flesch, and W. Meyer, Treatment of inter-shell correlation effects in ab-initio calculations by use of core polarization potentials, J. Chem. Phys., submitted

    Google Scholar 

  72. J. Migdalek and W. E. Baylis, Electron affinities for halogens calculated in the relativistic Hartree-Fock approach with atomic polarization, Phys. Rev. A 26: 1839 (1982)

    Article  Google Scholar 

  73. A. Savin and P. Fuentealba, in preparation

    Google Scholar 

  74. J. K. O’Connell and N. F. Lane, Nonadjustable exchange-correlation model for electron scattering from closed-shell atoms and molecules, Phys. Rev. A 27: 1893 (1983)

    Article  Google Scholar 

  75. T. Ziegler, A. Rauk, and E. J. Baerends, On the calculation of multiplet energies by the Hartree-Fock-Slater method, Theoret. Chim. Acta 43: 261 (1977)

    Article  Google Scholar 

  76. U. von Barth, Local-density theory of multiplet structure, Phys. Rev. A 20: 1693 (1979)

    Article  Google Scholar 

  77. D. C. Langreth and M. J. Mehl, Beyond the local-density approximation in calculations of ground-state electronic properties, Phys. Rev. B 28: 1809 (1983)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Chemie, Universität Stuttgart, D-7000, Stuttgart 80, West Germany

    Hermann Stoll & Andreas Savin

Authors
  1. Hermann Stoll
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andreas Savin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute for Theoretical Physics, Johann Wolfgang Goethe University, Frankfurt/Main, Federal Republic of Germany

    Reiner M. Dreizler

  2. Department of Physics, University of Coimbra, Coimbra, Portugal

    João da Providência

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Plenum Press, New York

About this chapter

Cite this chapter

Stoll, H., Savin, A. (1985). Density Functionals for Correlation Energies of Atoms and Molecules. In: Dreizler, R.M., da Providência, J. (eds) Density Functional Methods In Physics. NATO ASI Series, vol 123. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0818-9_7

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-0818-9_7

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-0820-2

  • Online ISBN: 978-1-4757-0818-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation