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The Direct Configuration Interaction Method from Molecular Integrals

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Methods of Electronic Structure Theory

Part of the book series: Modern Theoretical Chemistry ((MTC,volume 3))

Abstract

In this paper we will address ourselves to some aspects of the problem of finding accurate solutions to the electronic Schrödinger equation by means of the configuration interaction (CI) method. This method is probably one of the most encouraging for general studies of molecular systems in their ground and excited states, and also for studies of energy surfaces for chemical reactions.

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References

  1. S. F. Boys, Electronic wave functions, I. A general method of calculation for the stationary states of any molecular system, Proc. R. Soc. London, Ser. A 200, 542–554 (1950).

    Article  CAS  Google Scholar 

  2. S. F. Boys, Electronic wave functions. II. A calculation for the ground state of the beryllium atom, Proc. R. Soc. London, Ser. A 201, 125–137 (1950).

    Article  CAS  Google Scholar 

  3. D. R. Hartree, W. Hartree, and B. Swirles, Self-consistent field, including exchange and superposition of configurations with some results for oxygen, Philos. Trans. R. Soc. London, Ser. A 238, 229–247 (1939).

    Article  Google Scholar 

  4. E. A. Hylleraas, Neue Berechnung der Energie des Heliums im Grundzustande, sowie des tiefsten Terms von Ortho-Helium, Z. Phys. 54, 347–366 (1929).

    Article  CAS  Google Scholar 

  5. A. P. Jucys, On the Hartree—Fock method in multi-configuration approximation, Adv. Chem. Phys. 14, 191–206 (1969) (atoms).

    Article  CAS  Google Scholar 

  6. G. Das and A. C. Wahl, Extended Hartree—Fock wavefunctions: Optimized valence configurations for H2 and Li2, optimized double configurations for F2, J. Chem. Phys. 44, 87–96 (1966) (diatomic molecules).

    Article  CAS  Google Scholar 

  7. T. L. Gilbert, Multiconfigurational self-consistent-field theory for localized orbitals. I. The orbital equation, Phys. Rev. A6, 580–600 (1972). A thorough discussion of the subject can also be found in Ref. 30.

    Article  Google Scholar 

  8. B. Roos, A new method for large scale CI calculations, Chem. Phys. Lett. 15, 153 (1972).

    Article  Google Scholar 

  9. B. Roos and P. Siegbahn, in : Chemical and Biochemical Reactivity, the Jerusalem Symposia on Quantum Chemistry and Biochemistry, VI, The Israel Academy of Sciences and Humanities, Jerusalem (1974).

    Google Scholar 

  10. J. Almlöf, B. Roos, and P. Siegbahn, the Program System Molecule, Reference Manual (to be published).

    Google Scholar 

  11. J. K. L. MacDonald, Successive approximations by the Rayleigh—Ritz variation method, Phys. Rev. 43, 830–833 (1933).

    Article  Google Scholar 

  12. H. J. Silverstone and O. Sinanoglu, Many-electron theory of nonclosed-shell atoms and molecules. I. Orbital wave function and perturbation theory, J. Chem. Phys. 44, 1899–1907 (1966);

    Article  CAS  Google Scholar 

  13. H. J. Silverstone and O. Sinanoglu, Many-electron theory of nonclosed-shell atoms and molecules. II. Variational theory, J. Chem. Phys. 44, 3608–3617 (1966).

    Article  CAS  Google Scholar 

  14. P.-O. Löwdin, Quantum theory of many-particle systems. I. Physical interpretations by means of density matrices, natural spin-orbitals, and convergence problems in the method of configurational interaction, Phys. Rev. 97, 1474–1489 (1955).

    Article  Google Scholar 

  15. A. J. Coleman, Structure of fermion density matrices, Rev. Mod. Phys. 35, 668–689 (1963).

    Article  Google Scholar 

  16. A. D. McLean and B. Liu, Classification of configurations and the determination of interacting and noninteracting spaces in configuration interaction, J. Chem. Phys. 58, 1066–1078 (1973).

    Article  CAS  Google Scholar 

  17. O. Sinanoďlu, Many-electron theory of atoms and molecules. I. Shells, electron pairs versus many-electron correlations, J. Chem. Phys. 36, 706 (1962).

    Article  Google Scholar 

  18. W. Meyer, PNO—CI studies of electron correlation effects. I. Configuration expansion by means of nonorthogonal orbitals, and application to the ground state and ionized states of methane, J. Chem. Phys. 58, 1017–1035 (1973).

    Article  CAS  Google Scholar 

  19. R. McWeeny and B. T. Sutcliffe, Methods of Molecular Quantum Mechanics, Academic Press, London (1969).

    Google Scholar 

  20. B. Liu and P. Siegbahn, An accurate three-dimensional potential surface for H3, to be published.

    Google Scholar 

  21. C. Bender, private communication.

    Google Scholar 

  22. R. K. Nesbet, Algorithm for diagonalization of large matrices, J. Chem. Phys. 43, 311–312 (1965).

    Article  CAS  Google Scholar 

  23. I. Shavitt, C. F. Bender, A. Pipano, and R. P. Hosteny, The iterative calculation of several of the lowest or highest eigenvalues and corresponding eigenvectors of very large symmetric matrices, J. Comput. Phys.11, 90–108 (1973).

    Article  Google Scholar 

  24. P.-O. Löwdin, Studies in perturbation theory IX. Upper bounds to energy eigenvalues in Schrödinger,s perturbation theory, J. Math. Phys. 6, 1341–1353 (1965).

    Article  Google Scholar 

  25. E. Brôndas and O. Goscinski, Variation-perturbation expansions and Padé-approximants to the energy, Phys. Rev. A 6, 552–560 (1970).

    Article  Google Scholar 

  26. O. Goscinski and E. Brändas, in : Theory of Electronic Shells of Atoms and Molecules, Report from the Vilnius International Symposium, 1969, Mintis, Vilnius (1971).

    Google Scholar 

  27. R. J. Bartlett and E. J. Brändas, Reduced partitioning procedure in configuration interaction studies. II. Excited states, J. Chem. Phys. 59, 2032–2042 (1973).

    Article  CAS  Google Scholar 

  28. E. R. Davidson, The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices, J. Comput. Phys. 17, 87–94 (1975).

    Article  Google Scholar 

  29. V. R. Saunders and I. H. Hillier, A “level-shifting” method for converging closed shell Hartree—Fock wave functions, Int. J. Quantum Chem. 7, 699–705 (1973).

    Article  Google Scholar 

  30. V. R. Saunders and M. F. Guest, in : Proceedings of SRC Atlas Symposium No. 4, “Quantum Chemistry—the State of the Art” (V. R. Saunders and J. Brown, eds.), Atlas Computer Laboratory, Chilton Didcot, Oxfordshire (1975).

    Google Scholar 

  31. J. Hinze, MC-SCF. I. The multi-configurational self-consistent-field method, J. Chem. Phys. 59, 6424–6432 (1973).

    Article  CAS  Google Scholar 

  32. P. S. Bagus, B. Liu, A. D. McLean, and M. Yoshimine,in: Wave Mechanics the First Fifty Years (W. C. Price, S. S. Chissik, and T. Ravensdale, eds.), pp. 88–98, Butterworth & Co., London (1973).

    Google Scholar 

  33. C. Edminston and M. Krauss, Pseudonatural orbitals as a basis for the superposition of configurations. I. Hthaythe, J. Chem. Phys. 45, 1833–1839 (1966).

    Article  Google Scholar 

  34. W. P. Reinhardt and J. D. Doll, Direct calculation of natural orbitals by many-body perturbation theory: Application to helium, J. Chem. Phys. 50, 2767–2768 (1969).

    Article  CAS  Google Scholar 

  35. P. Dejardin, E. Kochanski, A. Veillard, B. Roos, and P. Siegbahn, MC—SCF and CI calculations for the ammonia molecule, J. Chem. Phys. 59, 5546–5553 (1973).

    Article  CAS  Google Scholar 

  36. P. Bertoncini and A. C. Wahl, Ab initio calculation of the helium-helium 1Σ potential at intermediate and large separations, Phys. Rev. Lett. 25, 991–994 (1970).

    Article  CAS  Google Scholar 

  37. H. F. Schaefer, D. R. McLaughlin, F. E. Harris, and B. J. Alder, Calculation of the attractive He pair potential, Phys. Rev. Lett. 25, 988–990 (1970).

    Article  CAS  Google Scholar 

  38. M. Yoshimine, The use of direct access devices in problems requiring the reordering of long data lists, IBM Corp. Tech. Rep. RJ 555 (1973).

    Google Scholar 

  39. F. E. Harris and H. H. Michels, Open-shell valence configuration-interaction studies of diatomic and polyatomic molecules, Int. J. Quantum Chem. 1, S 329–338 (1967).

    Article  Google Scholar 

  40. H. F. Schaefer and F. E. Harris, Ab initio calculations on 62 low-lying states of the O2 molecule, J. Chem. Phys. 48, 4946–4955 (1968).

    Article  CAS  Google Scholar 

  41. P. Siegbahn. in : Proceedings of SRC Atlas Symposium No. 4, “Quantum Chemistry—the State of the Art” (V. R. Saunders and J. Brown, eds.), Atlas Computer Laboratory, Chilton Didcot, Oxfordshire (1975).

    Google Scholar 

  42. W. Meyer, in : Proceedings of SRC Atlas Symposium No. 4, “Quantum Chemistry—the State of the Art” (V. R. Saunders and J. Brown, eds.), Atlas Computer Laboratory, Chilton Didcot, Oxfordshire (1975).

    Google Scholar 

  43. W. Meyer, Ionization energies of water from PNO-CI calculations, Int. J. Quantum Chem. 5, S 341–348 (1971).

    Article  Google Scholar 

  44. G. H. F. Diercksen, W. P. Kraemer, and B. Roos, SCF-CI Studies of correlation effects on hydrogen bonding and ion hydration, The systems: H20, HH+ • H2O, Li+ • H2O, F- • H2O and H2O • H2O, Theor. Chim. Acta 36, 249–274 (1975).

    Article  CAS  Google Scholar 

  45. G. H. F. Diercksen, W. P. Kraemer, and B. Roos, SCF-CI studies of the equilibrium structure and proton transfer barrier in H3Othaythe, Theor. Chim. Acta 42, 77–82 (1976).

    Article  Google Scholar 

  46. A. Stϕgård, A. Strich, J. Almlöf, and B. Roos, Correlation effects on hydrogen-bond potentials. SCF-CI calculations for the systems HFthaythe and H3Othaythe, Chem. Phys. 8, 405–411 (1975).

    Article  Google Scholar 

  47. J. Kowalewski and B. Roos, Large configuration interaction calculations of nuclear spin-spin coupling constants. III. Vibrational effects in ammonia, Chem. Phys. 11, 123–128 (1975).

    Article  CAS  Google Scholar 

  48. K. Niblaeus, private communication.

    Google Scholar 

  49. K. Niblaeus, B. Roos, and P. Siegbahn, An UHF-CI study of the H3O radical, to be published.

    Google Scholar 

  50. P. K. Pearson, G. L. Blackman, H. F. Schaefer III, B. Roos, and U. Wahlgren, HNC molecule in interstellar space? Some pertinent theoretical calculations, Astrophys. J. 184, L19-L22 (1973).

    Article  Google Scholar 

  51. A. D. McLean and P. Siegbahn, to be published.

    Google Scholar 

  52. R. F. Hausman, Jr., S. D. Bloom, and C. F. Bender, A new technique for describing the electronic states of atoms and molecules—the vector method, Chem. Phys. Lett. 32, 483–488 (1975).

    Article  CAS  Google Scholar 

  53. The original tables published in Ref. 8 were unfortunately incorrect. The authors are grateful to Dr. N. C. Handy for pointing out a number of these errors.

    Google Scholar 

  54. F. B. van Duijneveldt, Gaussian basis sets for the atoms H-Ne for use in molecular calculations, IBM Research Report RJ 945 (1971).

    Google Scholar 

  55. B. Liu, Ab initio potential energy surface for linear H3, J. Chem. Phys. 58, 1925–1937 (1973).

    Article  CAS  Google Scholar 

  56. P. Siegbahn and H. F. Schaefer III, Potential energy surface for H + Li2 thaythe LiH + Li. I. Ground state surface from large scale configuration interaction, J. Chem. Phys. 62, 3488–3495 (1975).

    Article  CAS  Google Scholar 

  57. B. Liu and A. D. McLean, Accurate calculation of the attractive interaction of two ground state helium atoms, J. Chem. Phys. 59, 4557–4558 (1973).

    Article  CAS  Google Scholar 

  58. J. Kowalewski, B. Roos, P. Siegbahn, and R. Vestin, Large configuration interaction calculations of nuclear spin-spin coupling constants. I. HD molecule, Chem. Phys. 3, 70–77 (1974).

    Article  CAS  Google Scholar 

  59. J. Kowalewski, B. Roos, P. Siegbahn, and R. Vestin. Large configuration interaction calculations of nuclear spin-spin coupling constants. II. Some polyatomic molecules, Chem. Phys. 9, 29–39 (1975).

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Institute of Theoretical Physics, University of Stockholm, 113 46, Stockholm, Sweden

    Björn O. Roos & Per E. M. Siegbahn

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  1. Björn O. Roos
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  2. Per E. M. Siegbahn
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Editors and Affiliations

  1. University of California, Berkeley, USA

    Henry F. Schaefer III

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Roos, B.O., Siegbahn, P.E.M. (1977). The Direct Configuration Interaction Method from Molecular Integrals. In: Schaefer, H.F. (eds) Methods of Electronic Structure Theory. Modern Theoretical Chemistry, vol 3. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0887-5_7

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  • DOI: https://doi.org/10.1007/978-1-4757-0887-5_7

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-0889-9

  • Online ISBN: 978-1-4757-0887-5

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