Electron Correlation in Atoms

  • Karol Jankowski


A reliable description of the electronic structure of atoms and molecules has to be based on methods more accurate than the one-electron schemes, i.e., on methods accounting for electron correlation effects. Therefore, since the beginning of quantum mechanics, much effort has been invested in developing such methods. As a result, there exist a large variety of techniques taking into account correlation effects in many-electron systems. This methodological progress, together with the revolution in computer technology, have considerably enlarged the number of systems for which accurate theoretical results are available. Nevertheless, the theory of electron correlation effects is still being intensively developed.


Electron Correlation Atomic System Correlation Energy Pair Function Pair Energy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    O. Sinanoğlu and K. A. Brueckner, Three Approaches to Electron Correlation in Atoms, Yale University Press, New Haven (1970).Google Scholar
  2. 2.
    C. S. Sarma, Correlation energies in atoms, Phys. Rep. C 26, 1–67 (1976).Google Scholar
  3. 3.
    J. I. Musher, in: MPT International Review of Science. Theoretical Chemistry Volume (W. Byers-Brown, ed.), pp. 1–40, Butterworth, London (1972).Google Scholar
  4. 4.
    A. Hibbert, Developments in atomic structure calculations. Rep. Prog. Phys. 38, 1217–1338 (1975).Google Scholar
  5. 5.
    I. Lindgren and J. Morrison, Atomic Many-Body Theory, Springer-Verlag, Berlin (1982).Google Scholar
  6. 6.
    C. F. Froese-Fischer, The Hartree-Fock Method for Atoms, Wiley-Interscience, New York (1976).Google Scholar
  7. 7.
    N. H. March, Self-Consistent Fields in Atoms, Pergamon Press, Oxford (1975).Google Scholar
  8. 8.
    E. dementi and C. Roetti, Tables of automic functions, At. Data Nucl. Data Tables 14, 177–478 (1974).Google Scholar
  9. 9.
    P. O. Löwdin, Correlation problem in many-electron quantum mechanics, Adv. Chem. Phys. 2, 207–322 (1959).Google Scholar
  10. 10.
    C. A. Coulson and A. H. Neilson, Electron correlation in the ground state of helium, Proc. Phys. Soc. 78, 831–837 (1961).Google Scholar
  11. 11.
    I. Öksüz and O. Sinanoğlu, Theory of atomic structure including electron correlation II, Phys. Rev. 181, 54–65 (1969).Google Scholar
  12. 12.
    K. Jankowski and M. Polasik, An approximate method for the evaluation of electron correlation effects on atomic energy differences, J. Phys. B 17, 2393–2411 (1984).Google Scholar
  13. 13.
    K. Jankowski and M. Polasik, Differential correlation effects for states of the 3d n and 3d n 4s m configurations I, II, J. Phys. B 18, 2133-2146, 4383–4391 (1985).Google Scholar
  14. 14.
    P. Westhaus and O. Sinanoglu, Theory of atomic structure including electron correlation. III. Calculations of Multiplet Oscillator Strengths and Comparison with Experiments for C II, N I, N II, N III, O II, O III, O IV, F II, Ne II, and Na III, Phys. Rev. 183, 56–67 (1969).Google Scholar
  15. 15.
    A. J. Sadlej, Perturbation theory of electron correlation effects for atomic and molecular properties, J. Chem. Phys. 75, 320–321 (1981).Google Scholar
  16. 16.
    C. Froese-Fischer and J. S. Carley, The effect of electron correlation on the charge density at the iron nucleus, J. Phys. B 9, 29–35 (1976).Google Scholar
  17. 17.
    J. Hata and I. P. Grant, Tests of QED in two-electron ions: II. The 2 3 S-2 3 P 0,1,2 energies, J. Phys. B 16, 523–536 (1982).Google Scholar
  18. 18.
    B. P. Das, J. Andriessen, M. Vajed-Samii, S. N. Ray, and T. P. Das, First principle analysis of strength of parity nonconservation in atomic thallium by relativistic many-body theory, Phys. Rev. Lett. 49, 32–35 (1982).Google Scholar
  19. 19.
    S. Wilson, Electron Correlation in Molecules, Clarendon Press, Ocford (1984).Google Scholar
  20. 20.
    B. Jeziorski and W. Kołos, in: Molecular Interactions (H. Ratajczak and W. J. Orville-Thomas, eds.), Vol. 3, pp. 1–46, Wiley, Chichester (1982).Google Scholar
  21. 21.
    L. Åsbrink, Shielding efficiencies determined from atomic spectroscopy for use in semiempirical SCF MO calculations, Phys. Scr. 28, 394–420 (1983).Google Scholar
  22. 22.
    D. J. Newman, S. S. Bishton, M. M. Curtis, and C. D. Taylor, Configuration interaction and lanthanide crystal fields, J. Phys. C 4, 3234–3248 (1971).Google Scholar
  23. 23.
    G. G. Siu and D. J. Newman, Spin correlated intensities: A new parametrization, Lanthanide Actinide Res. 1, 163–168 (1986).Google Scholar
  24. 24.
    K. Jankowski, in: Rare Earth Spectroscopy (B. Jezowska-Trzebiatowska, J. Legendziewicz, and W. Strek, eds.), pp. 39–56, World Scientific, Singapore (1985).Google Scholar
  25. 25.
    U. Fano and G. Racah, Irreducible Tensor Sets, Academic, New York (1959).Google Scholar
  26. 26.
    L. C. Biedenharn and J. D. Louk, Angular Momentum in Quantum Physics. Theory and Application, Addison-Wesley, Reading, Massachusetts (1981).Google Scholar
  27. 27.
    J. Midtdal, Perturbation theory expansion through 21st order of the nonrelativistic energies of two-electron systems (2p)2 3 P and (1s)2 1 S, Phys. Rev. 138, A1010–1014 (1965).Google Scholar
  28. 28.
    K. Frankowski and C. L. Pekeris, Logarithmic terms in the wave functions of the ground state of two-electron atoms, Phys. Rev. 146, 46–49 (1966).Google Scholar
  29. 29.
    C. W. Bauschlicher, Jr., S. P. Walch, and S. R. Langhoff, The importance of atomic and molecular correlation on the bonding in transition metal compounds, Proceeding of the Strassbourg Symposium (September, 1985).Google Scholar
  30. 30.
    R. J. Bartlett, Many-body perturbation theory and coupled-cluster theory for electron correlation in molecules, Ann. Rev. Phys. Chem. 32, 359–401 (1981).Google Scholar
  31. 31.
    K. A. Brueckner, Many-body problem for strongly interacting particles. II. Linked cluster expansion, Phys. Rev. 100, 36–45 (1955).Google Scholar
  32. 32.
    H. Primas, in: Modern Quantum Chemistry (O. Sinanoğlu, ed.), Vol.2, pp. 45–74, Academic, New York (1965).Google Scholar
  33. 33.
    A. C. Hurley, J. Lennard-Jones, and J. A. Pople, The molecular orbital theory of chemical valency XVI. A theory of paired-electrons in polyatomic molecules, Proc. R. Soc. London A 220, 446–455 (1953).Google Scholar
  34. 34.
    W. Kutzelnigg, in: Methods of Electronic Structure Theory (H. F. Schaefer III, ed.), pp. 129–188, Plenum Press, New York (1977).Google Scholar
  35. 35.
    K. J. Miller and K. Ruedenberg, Electron correlation and separated-pair approximation. An application to berylliumlike atomic systems, J. Chem. Phys. 48, 3414–3443 (1968).Google Scholar
  36. K. J. Miller and K. Ruedenberg, Electron correlation and augmented separated-pair expansion, J. Chem. Phys. 48, 3444–3449 (1968).Google Scholar
  37. K. J. Miller and K. Ruedenberg, Electron correlation and augmented separated-pair expansion in berylliumlike atomic systems, J. Chem. Phys. 48, 3450–3450 (1968).Google Scholar
  38. 36.
    O. Sinanoğlu, Many-electron theory of atoms and molecules. I. Shells, electron pairs vs. many-electron correlations, J. Chem. Phys. 36, 706–717 (1961).Google Scholar
  39. 37.
    O. Sinanoğlu, Many-electron theory of atoms, molecules and their interactions, Adv. Chem. Phys. 6, 315–412 (1964).Google Scholar
  40. 38.
    I. öksüz and O. Sinanoğlu, Theory of atomic structure including electron correlation. I. Three kinds of correlation in ground and excited configurations, Phys. Rev. 181, 42–53 (1969).Google Scholar
  41. 39.
    O. Sinanoğlu, in: Topics in Current Physics (S. Bashkin, ed.), Vol. 1, pp. 111–146, Springer-Verlag, Berlin (1976).Google Scholar
  42. 40.
    O. Sinanoğlu and B. Skutnik, Electron correlation in excited states and term splittings in the carbon—I isoelectronic sequence, J. Chem. Phys. 61, 3670–3675 (1974).Google Scholar
  43. 41.
    W. L. Luken and O. Sinanoğlu, Non-closed-shell many-electron-theory atomic charge wavefunctions, At. Data Nucl. Data Tables 18, 525–585 (1976).Google Scholar
  44. 42.
    K. Jankowski and P. Malinowski, Application of symmetry-adapted pair functions in atomic structure calculations: A variational-perturbation treatment of the Ne atom, Phys. Rev. A 21, 45–65 (1980).Google Scholar
  45. 43.
    V. L. Donlan, Two-electron fractional parentage coefficients for the configurations 1n, J. Chem. Phys. 52, 3431–3438 (1970).Google Scholar
  46. 44.
    C. D. H. Chisholm, A. Dalgarno, and F. R. Innes, Tables of one-and two-particle coefficients of fractional parentage for configurations s λ s μ p q, Adv. At. Mol. Phys. 5, 297–335 (1969).Google Scholar
  47. 45.
    A. Kotchoubey and L. H. Thomas, Numerical calculations of the energy and wavefunction of the ground state of beryllium, J. Chem. Phys. 45, 3342–3349 (1966).Google Scholar
  48. 46.
    S. Huzinaga, Gaussian-type functions for polyatomic systems. I, J. Chem. Phys. 42, 1293–1302 (1965).Google Scholar
  49. 47.
    R. D. Bardo and K. Ruedenberg, Even tempered atomic orbitals. II. Economic deployment of Gaussian primitives in expanding atomic SCF orbitals, J. Chem. Phys. 59, 5956–5965 (1973).Google Scholar
  50. 48.
    T. A. Weber, J. H. Weare, and R. G. Parr, Extensions of the Hulthén orbital concept, J. Chem. Phys. 54, 1865–1871 (1971).Google Scholar
  51. 49.
    D. M. Bishop and J. C. Leclerc, Unconventional basis sets in quantum mechanical calculations, Mol. Phys. 24, 979–992 (1972).Google Scholar
  52. 50.
    C. P. Yue and R. L. Samorjai, Integral-transform-generated basis sets, J. Chem. Phys. 55, 4595–4600 (1971).Google Scholar
  53. 51.
    T. L. Gilbert and P. J. Bertoncini, Spline representations. I. Linear spline bases for atomic calculations, J. Chem. Phys. 61, 3026–3036 (1974).Google Scholar
  54. 52.
    H. J. Silverstone, D. P. Carroll, and D. M. Silver, Piecewise polynomial basis functions for configuration interaction and many-body theory calculations. The radal limit of helium, J. Chem. Phys. 68, 616–618 (1978).Google Scholar
  55. 53.
    E. Yurtsever and D. Shillady, Slater-transform-Preuss basis sets for He to Ne and energies for H2, LiH and HF, Chem. Phys. Lett. 43, 20–22 (1976).Google Scholar
  56. 54.
    E. A. Hylleraas, Neue Berechnung der Energie des Heliums in Grundzustande, sowie des tiefsten Terms von Ortho-Helium, Z. Phys. 54, 347–366 (1929).Google Scholar
  57. 55.
    T. Kato, On the eigenfunctions of many-particle systems in quantum mechanics, Commun. Pure Appl. Math. 10, 151–177 (1957).Google Scholar
  58. 56.
    C. L. Pekeris, Ground state of two-electron atoms, Phys. Rev. 112, 1649–1658 (1958).Google Scholar
  59. 57.
    T. Kinoshita, Ground state of the helium atom, Phys. Rev. 108, 1490–1502 (1957).Google Scholar
  60. 58.
    Y. öhrn and J. Nordling, On the calculation of some atomic integrals containing functions of r 12, r 13, and r 23, J. Chem. Phys. 39, 1864–1871 (1963).Google Scholar
  61. 59.
    W. A. Lester and M. Krauss, Gaussian correlation functions: Two-electron systems, J. Chem. Phys. 41, 1407–1413 (1964).Google Scholar
  62. 60.
    K.-C. Pan and H. F. King, Electron correlation in closed-shell systems. I. Perturbation theory using Gaussian-type geminals, J. Chem. Phys. 56, 4667–4688 (1972).Google Scholar
  63. 61.
    K. B. Wenzel, J. G. Zabolitzky, K. Szalewicz, B. Jeziorski, and H. J. Monkhorst, Atomic and molecular correlation energies with explicitly correlated Gaussian geminals V. Cartesian Gaussian geminals and the neon atom, J. Chem. Phys. 8, xxx–xxx (1986).Google Scholar
  64. 62.
    D. R. Hartree, W. Hartree, and B. Swirles, Self-consistent field, including exchange and superposition of configurations with some results for oxygen, Phil. Trans. R. Soc. London, A 238, 229–247 (1939).Google Scholar
  65. 63.
    A. P. Jucys, Fock equations in the multi-configuration approximation. Zh. Eksp. Teor. Fiz. 23, 129–139 (1952) (in Russian).Google Scholar
  66. 64.
    S. T. Epstein, The Variational Method in Quantum Chemistry, Academic, New York (1974).Google Scholar
  67. 65.
    B. Klahn and W. A. Bingel, The Convergence of Rayleigh-Ritz method in quantum chemistry. I. The criteria of convergence, Theoret. Chim. Acta 44, 9–26 (1977).Google Scholar
  68. B. Klahn and W. A. Bingel, II. Investigation of the convergence for special systems of Slater, Gauss and two-electron functions, Theoret. Chim. Acta 44, 27–43 (1977).Google Scholar
  69. 66.
    A. Bongers, A convergence theorem for Ritz approximations of eigenvalues with application to Cl-calculations, Chem. Phys. Lett. 49, 393–398 (1977).Google Scholar
  70. 67.
    C. F. Bunge and A. Bunge, Symmmetry eigenfunctions suitable for many-electron theories and calculations. I. Mainly atoms, Int. J. Quantum Chem. 7, 927–944 (1973).Google Scholar
  71. 68.
    I. Shavitt, in: Methods of Electronic Structure Theory (H. F. Schaefer III, ed.), pp. 189–275, Plenum Press, New York (1977).Google Scholar
  72. 69.
    H. P. Kelly, Many-body perturbation theory applied to atoms, Phys. Rev. 136, B896–B912 (1964).Google Scholar
  73. 70.
    S. Huzinaga and C. Arnau, Virtual orbitals in HF theory, Phys. Rev. A 1, 1285–1288 (1970).Google Scholar
  74. 71.
    K. Morokuma and S. Iwata, Extended Hartree-Fock theory for excited states, Chem. Phys. Lett. 16, 192–197 (1972).Google Scholar
  75. 72.
    G. de Alti, P. Decleva, and A. Lisini, Configuration interaction with X α orbitals. A CI and RSPT study of the ground and ionized states of the Be atom, Chem. Phys. Lett. 100, 371–374 (1983).Google Scholar
  76. 73.
    Y. M. Poon, Accurate basis sets for atomic configuration interaction calculations, Computer Phys. Commun. 29, 113–116 (1983).Google Scholar
  77. 74.
    K. Jankowski and A. Sokołpwski, Ab initio studies of electron correlation in rare-earth ions. I: Intrashell correlation for 4f 2 in Pr3+, J. Phys. B 14, 3345–3353 (1981).Google Scholar
  78. 75.
    W. L. Luken and B. A. B. Seiders, Interaction-optimized virtual orbitals. I. External double excitations, Chem. Phys. 92, 235–246 (1985).Google Scholar
  79. 76.
    P. O. Löwdin, Quantum theory of many-particle-systems I. Physical interpretation by means of density matrices, natural spin-orbitals and convergence problems in the method of configuration interaction, Phys. Rev. 97, 1474–1489 (1955).Google Scholar
  80. 77.
    E. R. Davidson, Reduced Density Matrices in Quantum Chemistry, Academic, New York (1976).Google Scholar
  81. 78.
    W. Meyer, in: Methods of Electronic Structure Theory (H. F. Schaefer III, ed.), pp. 413–446, Plenum Press, New York (1977).Google Scholar
  82. 79.
    R. Ahlrichs and F. Driessler, Direct determination of pair natural orbitals, Theor. Chim. Acta 36, 275–287 (1975).Google Scholar
  83. 80.
    W. Brening, Zweiteilchennäherungen des Mehrkörperproblems I, Nucl. Phys. 4, 363–374 (1957).Google Scholar
  84. 81.
    J. Paldus, in: Theoretical Chemistry: Advances and Perspectives (H. Eyring and D. Henderson, eds.), vol. 2, pp. 131–290, Academic, New York (1976).Google Scholar
  85. 82.
    P. E. M. Siegbahn, The externally contracted CI method applied to N2, Int. J. Quantum Chem. 23, 1869–1889 (1983).Google Scholar
  86. 83.
    R. J. Bartlett and G. D. Purvis, Many-body perturbation theory, coupled-pair many-electron theory, and the importance of quadruple excitations for the correlation problem, Int. J. Quantum Chem. 14, 561–581 (1978).Google Scholar
  87. 84.
    C. W. Bauschlicher, S. R. Langhoff, P. R. Taylor, and H. Partridge, A full CI treatment of Ne atom—A benchmark calculation performed on the NAS CRAY-2, Chem. Phys. Lett. 126, 436–440 (1986).Google Scholar
  88. 85.
    B. C. Shore, Method for calculating matrix elements between configurations with several open 1 shells, Phys. Rev. 139, A1042–A1048 (1965).Google Scholar
  89. 86.
    U. Fano, Interaction between configurations with several open shells, Phys. Rev. 140, A67–A75 (1965).Google Scholar
  90. 87.
    A. P. Jucys and A. J. Savukynas, Mathematical Foundations of the Atomic Theory, Mintis, Vilnius (1973).Google Scholar
  91. 88.
    F. Sasaki, Matrix elements in configuration interaction calculations, Int. J. Quantum Chem. 8, 605–617 (1974).Google Scholar
  92. 89.
    B. R. Judd, Operator Techniques in Atomic Spectroscopy, McGraw-Hill, New York (1963).Google Scholar
  93. 90.
    W. Duch and J. Karwowski, Symmetric group approximation to configuration interaction methods, Computer Phys. Rep. 2, 93–170 (1985).Google Scholar
  94. 91.
    B. O. Roos, A new method for large-scale CI calculations, Chem. Phys. Lett. 15, 153–159 (1972).Google Scholar
  95. 92.
    V. R. Saunders and J. H. van Lenthe, The direct CI method. A detailed analysis, Mol. Phys. 48, 923–954 (1983).Google Scholar
  96. 93.
    I. Shavitt, in: Lecture Notes in Chemistry, Vol. 22 (J. Hinze, ed.), pp. 50–98, Springer, Berlin (1981).Google Scholar
  97. 94.
    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, 529–534 (1950).Google Scholar
  98. S. F. Boys, II. A calculation for the ground state of the beryllium atom, Proc. R. Soc. London Ser. A 201, 125–137 (1950).Google Scholar
  99. 95.
    S. F. Boys, Electronic wave functions. IX. Calculations for the three lowest states of the beryllium atom, Proc. R. Soc. London Ser. A 200, 136–150 (1952).Google Scholar
  100. 96.
    R. E. Watson, Approximate wave functions for atomic Be, Phys. Rev. 119, 170–177 (1960).Google Scholar
  101. 97.
    C. F. Bunge, Accurate determination of the total energy of the Be ground state, Phys. Rev. A 14, 1965–1978 (1976).Google Scholar
  102. 98.
    F. Sasaki and M. Yoshimine, Configuration-interaction study of atoms. I. Correlation energies of B, C, N, O, F and Ne, Phys. Rev. A 9, 17–25 (1974).Google Scholar
  103. F. Sasaki and M. Yoshimine, II. Electron affinities of B, C, N, O, and F, Phys. Rev. A 9, 26–34 (1974).Google Scholar
  104. 99.
    A. Bunge, Electronic wave functions for atoms. III. Partition of degenerate spaces and ground state of C, J. Chem. Phys. 53, 20–28 (1970).Google Scholar
  105. 100.
    D. P. Carrol, H. J. Silverstone, and R. M. Metzger, Piecewise polynomial configuration interaction natural orbital study of 1s2 helium, J. Chem. Phys. 71, 4142–4163 (1979).Google Scholar
  106. 101.
    C. F. Bunge, The present limits of accuracy in atomic calculations of small systems, Phys. Scr. 21, 328–334 (1980).Google Scholar
  107. 102.
    B. H. Botch, T. H. Dunning, and J. F. Harrison, Valence correlation in the s 2 d n, sd n + 1, and d n+1 state of the first-row transition metal atoms, J. Chem. Phys. 75, 3466–3476 (1981).Google Scholar
  108. 103.
    C. W. Bauschlicher, S. P. Walch, and H. Partridge, On correlation in the first row transition metal atoms, J. Chem. Phys. 76, 1033–1039 (1982).Google Scholar
  109. 104.
    A. C. Wahl and G. Das, in: Methods of Electronic Structure Theory (H. F. Schaefer III, ed.), pp. 51–78, Plenum Press, New York (1977).Google Scholar
  110. 105.
    H. J. Werner and W. Meyer, A quadratically convergent multiconfiguration—self-consistent field method with simultaneous optimization of orbitals and CI coefficients, J. Chem. Phys. 73, 2342–2356 (1980).Google Scholar
  111. 106.
    B. O. Roos, P. R. Taylor, and P. E. M. Siegbahn, A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach, Chem. Phys. 48, 157–173 (1980).Google Scholar
  112. 107.
    B. O. Roos, in: Methods in Computational Molecular Physics (G. H. F. Diercksen and S. Wilson, eds.), pp. 161–187, Reidel, Dordrecht (1983).Google Scholar
  113. 108.
    P. E. M. Siegbahn, A new direct CI method for large scale CI expansions in a small orbital space, Chem. Phys. Lett. 109, 417–423 (1984).Google Scholar
  114. 109.
    C. F. Froese-Fischer and K. M. S. Saxena, Correlation study of Be 1s22s2 by a separatedpair numerical multiconfiguration Hartree-Fock procedure, Phys. Rev. A 9, 1498–1506 (1974).Google Scholar
  115. 110.
    D. H. Tycko, L. H. Thomas, and K. M. King, Numerical calculation of the wave function and energies of the 1 1 S and 2 3 S states of helium. Phys. Rev. 109, 369–374 (1958).Google Scholar
  116. 111.
    S. Larsson, Calculations on the 2 S ground state of the lithium atom using wave functions of Hylleraas type, Phys. Rev. 169, 49–54 (1968).Google Scholar
  117. 112.
    P.-O. Löwdin and L. Rédei, Combined use of the methods of superposition of configurations and correlation factor on the ground states of the helium-like ions, Phys. Rev. 114, 752–757 (1959).Google Scholar
  118. 113.
    J. S. Sims and S. Hagstrom, Combined configuration-interaction-Hylleraas-type wave-function study of the ground state of the beryllium atom, Phys. Rev. A 4, 908–916 (1971).Google Scholar
  119. J. S. Sims and S. Hagstrom, Combined CI-Hy studies of atomic states. II. Compact wave functions for the Be ground state, Int. J. Quantum. Chem. 9, 149–156 (1975).Google Scholar
  120. 114.
    J. S. Sims and S. A. Hagstrom. One-center r ij integrals over Slater-type orbitals, J. Chem. Phys. 55, 4699–4710 (1971).Google Scholar
  121. 115.
    J. Muszyńska, D. Papierowska, and W. Wożnicki, Variational calculations of the lowest 2 S and 2 P states of the Li atom, Chem. Phys. Lett. 76, 136–137 (1980).Google Scholar
  122. 116.
    D. C. Clary and N. C. Handy, CI-Hylleraas variational calculation on the ground state of the neon atom, Phys. Rev. A 5, 1607–1613 (1976).Google Scholar
  123. 117.
    C. A. Coulson and P. J. Haskins, On the relative accuracies of eigenvalue bounds, J. Phys. B 6, 1741–1750 (1973).Google Scholar
  124. 118.
    C. E. Dykstra, H. F. Schaefer, and W. Meyer, A theory of self-consistent electron pairs. Computational methods and preliminary applications, J. Chem. Phys. 65, 2740–2750 (1976).Google Scholar
  125. 119.
    O. Sinanoğlu, Theory of electron correlation in atoms and molecules, Proc. R. Soc. London Ser. A 260, 379–392 (1961).Google Scholar
  126. 120.
    J. O. Hirschfelder, W. Byers-Brown, and S. T. Epstein, Recent developments in perturbation theory, Adv. Quantum Chem. 1, 255–274 (1964).Google Scholar
  127. 121.
    C. Møller and M. S. Plessett, Note on the approximate treatment for many electron systems, Phys. Rev. 46, 618–622 (1934).Google Scholar
  128. 122.
    E. A. Hylleraas, Über den Grundterm der Zweielektronenprobleme von H, He, Li +, Be + + usw., Z. Phys. 65, 209–225 (1930).Google Scholar
  129. 123.
    P. Claverie, S. Diner, and J. P. Malrieu, The use of perturbation methods for the study of the effects of configuration interaction. I. Choice of the zeroth-order Hamiltonian, Int. J. Quantum. Chem. 1, 751–767 (1967).Google Scholar
  130. 124.
    T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin (1966).Google Scholar
  131. 125.
    R. Ahlrichs, Convergence of the 1/Z expansion, Phys. Rev. 5, 605–614 (1972).Google Scholar
  132. 126.
    D. Layzer, Z. Horak, M. N. Lewis, and D. P. Thomson, Second-order Z-dependent theory of many-electron atoms, Ann. Phys. (N.Y.) 29, 101–124 (1964).Google Scholar
  133. 127.
    J. Goldstone, Derivation of the Brueckner many-body theory, Proc. R. Soc. London Ser. A 239, 267–279 (1957).Google Scholar
  134. 128.
    P. W. Langhoff and A. J. Hernandez, On the Brueckner and Goldstone forms of the linked-cluster theorem, Int. J. Quantum Chem. (Symp.) 10, 337–351 (1976).Google Scholar
  135. 129.
    H. P. Kelly, Correlation effects in atoms, Phys. Rev. 131, 684–699 (1963).Google Scholar
  136. H. P. Kelly, Many-body perturbation theory applied to atoms, Phys. Rev. 144, 39–55 (1966).Google Scholar
  137. 130.
    K. F. Freed, Many-body theories of the electronic structure of atoms and molecules, Ann. Rev. Phys. Chem. 21, 313–346 (1972).Google Scholar
  138. 131.
    J. Paldus and J. Čižek, Time-independent diagrammatic approach to perturbation theory of fermion systems, Adv. Quantum Chem. 9, 105–197 (1975).Google Scholar
  139. 132.
    I. Hubač and P. Čarsky, Computational methods of correlation energy, Topics Current Chem. 75, 97–164 (1978).Google Scholar
  140. 133.
    S. Wilson, Diagrammatic many-body perturbation theory of atomic and molecular electronic structure, Computer Phys. Rep. 2, 389–480 (1985).Google Scholar
  141. 134.
    H. F. Monkhorst, B. Jeziorski, and F. E. Harris, Recursive scheme for order-by-order many-body perturbation theory, Phys. Rev. A 23, 1639–1644 (1981).Google Scholar
  142. 135.
    H. Kelly and Akiva Ron, Electron correlation energies in the neutral iron atom, Phys. Rev. A 4, 11–14 (1971).Google Scholar
  143. 136.
    T. Lee, N. C. Dutta, and T. P. Das, Correlation energy of the neon atom, Phys. Rev. A 4, 1410–1424 (1971).Google Scholar
  144. 137.
    E. Eggarter and T. P. Eggarter, Atomic correlation energies I. Rigorous evaluation of E (2) for He, Li and Be, J. Phys. B 11, 1157–1170 (1978)Google Scholar
  145. E. Eggarter and T. P. Eggarter, II. Converged E (2) values for Ne and Ne+, J. Phys. B 11, 2069–2075 (1978)Google Scholar
  146. E. Eggarter and T. P. Eggarter, III. Second order correlations to the Hartree-Fock ground state of B, C, N, O and F, J. Phys. B 11, 2969–2973 (1978).Google Scholar
  147. 138.
    J. A. Pople, J. S. Binkley, and R. Seeger, Theoretical models incorporating electron correlation, Int. J. Quantum Chem. Symp. 10, 1–19 (1976).Google Scholar
  148. 139.
    S. Wilson and D. M. Silver, Algebraic approximation in many-body perturbation theory, Phys. Rev. A 14, 1949–1960 (1976).Google Scholar
  149. 140.
    M. Urban, I. Hubač, V. Kellö, and Jozef Noga, The fourth order diagrammatic MP-RSPT calculations of the correlation energy of ten electron systems, J. Chem. Phys. 72, 3378–3385 (1980).Google Scholar
  150. 141.
    V. V. Tolmachev, The Field-Theoretic Form of the Perturbation Theory for Many-Electron Problem in Atoms and Molecules, Rotaprint, Tartu (1963) (in Russian).Google Scholar
  151. 142.
    U. I. Safronova and V. V. Tolmachev, The numerical calculation of the contribution from Feynman diagrams for the ground state energy of two-electronic atomic systems, Lit. Fiz. Sb. 4, 13–23 (1964).Google Scholar
  152. 143.
    E. P. Ivanova and U. I. Safronova, Perturbation theory in calculations of atomic energy levels, J. Phys. B 8, 1591–1602 (1975).Google Scholar
  153. 144.
    S. Wilson, Many-body perturbation theory using a bare-nucleus reference function: A model study, J. Phys. B 17, 505–518 (1984).Google Scholar
  154. 145.
    A. B. Bolotin, I. B. Levinson, and V. V. Tolmachev, Angular integration of Feynman diagrams in field perturbation theory of atoms, Lit. Fiz. Sb. 4, 25–33 (1964).Google Scholar
  155. 146.
    A. P. Jucys, I. B. Levinson, and V. V. Vanagas, Mathematical Apparatus of the Theory of Angular Momentum, Israel Program for Scientific Translations, Jerusalem (1962).Google Scholar
  156. 147.
    D. Mukherjee and D. Bhattacharya, Spin-adaptation in many-body perturbation theory, Mol. Phys. 34, 773–792 (1977).Google Scholar
  157. 148.
    O. Sinanoğlu, Perturbation theory of many-electron atoms and molecules, Phys. Rev. 122, 493–499 (1961).Google Scholar
  158. 149.
    C. D. H. Chisholm and A. Dalgarno, An expansion method for calculating atomic properties VII. The correlation energies of the lithium sequence, Proc. R. Soc. London Ser. A 290, 264–271 (1966).Google Scholar
  159. 150.
    M. A. Robb, in: Computational Techniques in Quantum Chemistry and Molecular Physics (G. Diercksen et al., eds.), pp. 435–503, D. Reidel, Dordrecht (1975).Google Scholar
  160. 151.
    K. Jankowski, P. Malinowski, A. Sokolowski, I. Lindgren, and A.-M. Mårtensson-Pendrill, Electron correlation effects in the 4f 14 shell, Int. J. Quantum Chem. 27, 665–675 (1985).Google Scholar
  161. 152.
    V. McKoy and N. W. Winter, Numerical solution of quantum-mechanical pair equations, J. Chem. Phys. 48, 5514–5523 (1968).Google Scholar
  162. 153.
    A. M. Mårtensson, An iterative, numeric procedure to obtain pair functions applied to two-electron systems, J. Phys. B 12, 3995–4012 (1979).Google Scholar
  163. 154.
    H. C. Bolton and H. I. Scoins, Eigenvalue problems treated by finite-difference methods. II. Two-dimensional Schrödinger equations, Proc. Cambridge Philos. Soc. 53, 150–161 (1956).Google Scholar
  164. 155.
    I. Lindgren and S. Salmonson, A numerical coupled-cluster procedure applied to the closed-shell atoms Be and Ne, Phys. Scr. 21, 335–342 (1980).Google Scholar
  165. 156.
    F. Y. Hajj, Eigenvalue of the two-dimensional Schrödinger equation, J. Phys. B 15, 683–692 (1982).Google Scholar
  166. 157.
    J. I. Musher and J. M. Schulman, Perturbation-theoretic approach to atoms and molecules, Phys. Rev. 173, 93–107 (1968).Google Scholar
  167. 158.
    B. C. Webster and R. F. Steward, First order pair functions for the beryllium isoelectronic sequence, Theor. Chim. Acta 27, 355–366 (1972).Google Scholar
  168. 159.
    J. Morrison, Many-body calculations for heavy atoms. III. Pair correlations, J. Phys. B 6, 2205–2212 (1973).Google Scholar
  169. 160.
    C. W. Scherr and R. E. Knight, Two-electron atoms. III. A sixth-order perturbation study of the 1 1 S ground state, Rev. Mod. Phys. 35, 436–442 (1963).Google Scholar
  170. 161.
    K. Aashamar, G. Lyslo, and J. Midtdal, Variation perturbation theory study of some excited states of two-electron atoms, J. Chem. Phys. 52, 3324–3336 (1970).Google Scholar
  171. 162.
    C. D. H. Chisholm, A. Dalgarno, and F. R. Innes, Correlation energies of the lithium sequence, Phys. Rev. 167, 60–62 (1968).Google Scholar
  172. 163.
    R. E. Knight, Correlation energies of some states of 3–10 electron atoms, Phys. Rev. 183, 45–51 (1969).Google Scholar
  173. 164.
    F. W. Byron and C. J. Joachain, Correlation effects in atoms. III. Four-electron systems, Phys. Rev. 157, 7–23 (1967).Google Scholar
  174. 165.
    K. Jankowski, D. Rutkowska, and A. Rutkowski, Application of symmetry-adapted pair functions in atomic structure calculations. II. Third-order correlation energy of the neon atom, Phys. Rev. A 26, 2378–2394 (1982).Google Scholar
  175. 166.
    K. Szalewicz, B. Jeziorski, H. J. Monkhorst, and J. G. Zabolitzky, A new functional for variational calculation of atomic and molecular second-order correlation energies, Chem. Phys. Lett. 91, 169–172 (1982).Google Scholar
  176. 167.
    K. Szalewicz, J. G. Zabolitzky, B. Jeziorski, and H. J. Monkhorst, Atomic and molecular correlation energies with explicitly correlated Gaussian geminals. IV. A simplified treatment of strong orthogonality in MBPT and coupled cluster calculations, J. Chem. Phys. 81, 2723–2735 (1984).Google Scholar
  177. 168.
    C. Schwartz, Importance of angular correlations between atomic electrons, Phys. Rev. 126, 1015–1019 (1962).Google Scholar
  178. 169.
    K. Jankowski, P. Malinowski, and M. Polasik, Second-order correlation energies of Mg and Ar, J. Phys. B 12, 3157–3170 (1979).Google Scholar
  179. 170.
    K. Jankowski, D. Rutkowska, and A. Rutkowski, Accurate third-order correlation energies for closed-shell systems: II. Two-and four-electron systems, J. Phys. B 15, 4063–4077 (1982).Google Scholar
  180. 171.
    K. Jankowski, P. Malinowski, and M. Polasik, Second-order electron correlation energies for some 3d 10 and 3d 104s 2 ions, J. Chem. Phys. 82, 841–847 (1985).Google Scholar
  181. 172.
    K. Jankowski, P. Malinowski, and M. Polasik, Transferability of the partial-wave increments to the second-order pair correlation energies for atoms, J. Phys. B 13, 3909–3919 (1980).Google Scholar
  182. 173.
    E. Clementi, Correlation energy in atomic systems. III. Configurations with 3d and 4s electrons, J. Chem. Phys. 42, 2783–2787 (1965).Google Scholar
  183. 174.
    K. Jankowski, D. Rutkowska, and A. Rutkowski, Accurate third-order correlation energies for closed-shell systems: I. Ten-electron systems, J. Phys. B 15, 1137–1159 (1982).Google Scholar
  184. 175.
    D. Rutkowska, A. Rutkowski, and K. Jankowski, Accuracy of first-order wavefunctions for ten-electron atomic systems, Chem. Phys. Lett. 105, 370–373 (1984).Google Scholar
  185. 176.
    J. O. Hirschfelder and P. R. Certain, Degenerate RS perturbation theory, J. Chem. Phys. 60, 1118–1137 (1974).Google Scholar
  186. 177.
    D. J. Klein, Degenerate perturbation theory, J. Chem. Phys. 61, 786–798 (1974).Google Scholar
  187. 178.
    B. Brandow, in: New Horizons of Quantum Chemistry (P.-O. Löwdin and B. Pullman, eds.), pp. 15–29, D. Reidel, Dordrecht (1983).Google Scholar
  188. 179.
    V. Kvasnicka, Application of diagrammatic quasidegenerate RSPT in quantum molecular physics, Adv. Chem. Phys. 36, 345–412 (1977).Google Scholar
  189. 180.
    J. H. van Vleck, On σ-type doubling and electron spin in the spectra of diatomic molecules, Phys. Rev. 33, 467–506 (1929).Google Scholar
  190. 181.
    C. Bloch, Sur la théorie des perturbations des états liés, Nucl. Phys. 6, 329–347 (1958).Google Scholar
  191. 182.
    B. H. Brandow, Linked-cluster expansion for the nuclear many-body problem, Rev. Mod. Phys. 39, 771–828 (1967).Google Scholar
  192. 183.
    I. Lindgren, The Rayleigh-Schrödinger perturbation and linked-diagram theorem for a multi-configurational model space, J. Phys. B 7, 2441–2470 (1974).Google Scholar
  193. 184.
    T. H. Schucan and H. A. Weidenmüller, The effective interaction in nuclei and its perturbation expansion: An algebraic approach, Ann. Phys. (N.Y.) 73, 108–135 (1972).Google Scholar
  194. 185.
    G. Hose and U. Kaldor, Diagrammatic and many-body perturbation theory for general model spaces, J. Phys. B 12, 3827–3855 (1979).Google Scholar
  195. 186.
    S. Salomonson, I. Lindgren, and A.-M. Mårtenson, Numerical many-body perturbation calculations on Be-like systems using a multiconfigurational model space, Phys. Scr. 21, 351–356 (1980).Google Scholar
  196. 187.
    H. Sun, K. F. Freed, and M. F. Herman, Ab initio effective valence shell Hamiltonian for the neutral and ionic valence states of N, O, F, Si, P, and S, J. Chem. Phys. 72, 4158–4173 (1980).Google Scholar
  197. 188.
    Y. S. Lee and K. F. Freed, Electron correlation effects on the structure of all 3d n4s m valence states of Ti, V, and Cr and their ions as studied by quasidegenerate many-body perturbation theory, J. Chem. Phys. 11, 1984–2001 (1982).Google Scholar
  198. 189.
    M. G. Sheppard and K. F. Freed, Third-order quasidegenerate many-body perturbation theory calculations for valence state correlation energies of nitrogen and oxygen atoms and their ions, Int. J. Quantum Chem. Symp. 15, 21–31 (1981).Google Scholar
  199. 190.
    J. Morrison and S. Salomonson, Many-body perturbation theory of the effective electron-electron interactions for open-shell atoms, Phys. Scr. 21, 343–350 (1980).Google Scholar
  200. 191.
    P. Westhaus and E. G. Bradford, Effective valence shell interactions in carbon, nitrogen, and oxygen atoms, J. Chem. Phys. 63, 5416–5427 (1975).Google Scholar
  201. 192.
    W. Kutzelnigg and S. Koch, Quantum chemistry in Fock space. II. Effective Hamiltonians in Fock space, J. Chem. Phys. 79, 4315–4335 (1983).Google Scholar
  202. 193.
    S. Koch, Effektive Hamiltonoperatoren im Fockraum, Ph.D. thesis, Bochum (1984).Google Scholar
  203. 194.
    G. Hose and U. Kaldor, General-model-space many-body perturbation theory: The (2s2p)1,3 P states in the Be isoelectronic sequence, Phys. Rev. A 30, 2932–2935 (1984).Google Scholar
  204. 195.
    R. K. Nesbet, Electronic correlation in atoms and molecules, Adv. Chem. Phys. 9, 321–363 (1965).Google Scholar
  205. 196.
    K. F. Freed, Many-body approch to electron correlation in atoms and molecules, Phys. Rev. 173, 1–24 (1968).Google Scholar
  206. 197.
    R. K. Nesbet, Atomic Bethe-Goldstone equations. III. Correlation energies of ground states of Be, B, C, N, O, F, and Ne, Phys. Rev. 175, 2–9 (1968).Google Scholar
  207. 198.
    T. L. Barr and E. R. Davidson, Nature of the configuration-interaction method in ab initio calculations. I. Ne ground state. Phys. Rev. A 1, 644–658 (1970).Google Scholar
  208. 199.
    R. K. Nesbet, Atomic Bethe-Goldstone equations. IV. Valence-shell correlation energies of ground states of Na, Mg, Al, Si, P, S, Cl, and Ar, Phys. Rev. A 3, 87–94 (1971).Google Scholar
  209. 200.
    A. W. Weiss, Symmetry-adapted pair correlations in Ne, F, Ne +, and F, Phys. Rev. A 3, 126–129 (1971).Google Scholar
  210. 201.
    M. A. Marchetti, M. Krauss, and A. W. Weiss, Symmetry-adapted pair correlations in O and O, Phys. Rev. A 5, 2387–2390 (1972).Google Scholar
  211. 202.
    J. W. Viers, F. E. Harris, and H. F. Schaeffer. III. Pair correlations and atomic structure of neon, Phys. Rev. A 1, 24–27 (1970).Google Scholar
  212. 203.
    C. M. Moser and R. K. Nesbet, Atomic Bethe-Goldstone calculations of term splittings, ionization potentials and electron affinities for B, C, N, O, F, and Ne, II. Configurational excitations, Phys. Rev. A 6, 1710–1714 (1972).Google Scholar
  213. 204.
    J. Hubbard, The description of collective motion in terms of many-body perturbation theory, Proc. R. Soc. London Ser. A 240, 539–560 (1957).Google Scholar
  214. 205.
    F. Coester and H. Kümmel, Short-range corrrelations in nuclear wave functions, Nucl. Phys. 17, 477–485 (1960).Google Scholar
  215. 206.
    J. Čižek, On the correlation problem in atomic and molecular systems. Calculation of wavefunction components in Ursell-type expansion using quantum-field theoretical methods, J. Chem. Phys. 45, 4256–4266 (1966).Google Scholar
  216. 207.
    A. C. Hurley, Electron Correlation in Small Molecules, Academic, New York (1976).Google Scholar
  217. 208.
    J. Paldus and J. Čižek, in: Energy, Structure, and Reactivity (D. W. Smith and W. B. McRae, eds.), pp. 198–209, Wiley, New York (1973).Google Scholar
  218. 209.
    J. Paldus, Correlation problems in atomic and molecular systems. V. Spin-adapted coupled cluster many-electron theory, J. Chem. Phys. 67, 303–318 (1977).Google Scholar
  219. 210.
    J. A. Pople, R. Krishnan, H. B. Schlegel, and J. S. Binkley, Electron correlation theories and their application to the study of simple reaction potential surfaces, Int. J. Quantum Chem. 14, 545–560 (1978).Google Scholar
  220. 211.
    R. A. Chiles and C. E. Dykstra, An electron pair operator approach to coupled-cluster wave-functions. Application to He2, Be2, and Mg2 and comparison with CEPA methods, J. Chem. Phys. 74, 4544–4556 (1981).Google Scholar
  221. 212.
    A. P. Jucys and A. A. Bandzaitis, The Theory of Angular Momentum in Quantum Mechanics, Mintis, Vilnius (1964) (in Russian).Google Scholar
  222. 213.
    E. El Baz and B. Castel, Graphical Methods of Spin Algebras in Atomic, Nuclear and Particle Physics, M. Dekker, New York (1972).Google Scholar
  223. 214.
    B. G. Adams and J. Paldus, Symmetry-adapted coupled-pair approach to the many-electron correlation problem. I. LS-adapted theory for closed-shell atoms, Phys. Rev. A 24, 2302–2315 (1981).Google Scholar
  224. 215.
    R. J. Bartlett and G. P. Purvis III, Molecular applications of coupled cluster and many-body perturbation methods, Phys. Scr. 21, 255–265 (1980).Google Scholar
  225. 216.
    B. G. Adams, K. Jankowski, and J. Paldus, Symmetry-adapted coupled-pair approach to the many-electron correlation problem. II. Application to the Be atom, Phys. Rev. A 24, 2316–2329 (1981).Google Scholar
  226. 217.
    B. Jeziorski, H. J. Monkhorst, K. Szalewicz, and J. G. Zabolitzky, Atomic and molecular correlation energies with explicity correlated Gaussian geminals. III. Coupled cluster treatment for He, Be, H2 and LiH, J. Chem. Phys. 81, 368–389 (1984).Google Scholar
  227. 218.
    C. M. Rohlfing and R. L. Martin, On correlation treatments of the nickel atom, Chem. Phys. Lett. 115, 104–107 (1985).Google Scholar
  228. 219.
    E. A. Salter, L. Adamowicz, and R. Bartlett, Coupled cluster and MBPT study of nickel states, Chem. Phys. Lett. 122, 23–28 (1985).Google Scholar
  229. 220.
    F. Coester, in: Boulder Lectures of Theoretical Physics (K. T. Mahanthappa and W. E. Brittin, eds.), vol. 11B, pp. 157–186, Gordon and Breach, New York (1969).Google Scholar
  230. 221.
    J. Paldus, in: New Horizons of Quantum Chemistry (P. O. Löwdin and B. Pullman, eds.), pp. 31–60, D. Reidel, Dordrecht (1983).Google Scholar
  231. 222.
    R. J. Bartlett, C. E. Dykstra, and J. Paldus, in: Advanced Theories and Computational Approaches to the Electronic Structure of Molecules (C. E. Dykstra, ed.), pp. 127–159, D. Reidel, Dordrecht (1984).Google Scholar
  232. 223.
    J. Paldus, J. Čižek, M. Saute, and A. Laforgue, Correlation problems in atomic and molecular systems. VI. Coupled-cluster approach to open-shell systems, Phys. Rev. A. 17, 805–815 (1978).Google Scholar
  233. 224.
    K. Hirao and H. Nakatsuji, Cluster expansion of the wavefunction. Symmetry-adapted-cluster (SAC) theory for excited states, Chem. Phys. Lett. 79, 292–298 (1981).Google Scholar
  234. 225.
    I. Lindgren, A. coupled-cluster approach to the many-body perturbation theory for open-shell systems, Int. J. Quantum Chem. Symp. 12, 33–58 (1978).Google Scholar
  235. 226.
    A. Haque and D. Mukherjee, Application of cluster expansion techniques to open-shells: Calculation of difference energies, J. Chem. Phys. 80, 5058–5069 (1984).Google Scholar
  236. 227.
    A. Banerjee and J. Simons, The coupled-cluster method with a multiconfiguration reference state, Int. J. Quantum Chem. 19, 207–216 (1981).Google Scholar
  237. 228.
    A. Banerjee and J. Simons, Applications of multiconfigurational coupled-cluster theory, J. Chem. Phys. 76, 4548–4559 (1982).Google Scholar
  238. 229.
    A. Haque and U. Kaldor, Open-shell coupled-cluster theory applied to atomic and molecular systems, Chem. Phys. Lett. 117, 347–351 (1985).Google Scholar
  239. 230.
    B. Jeziorski and H. J. Monkhorst, Coupled-cluster method for multideterminantal reference states, Phys. Rev. A 24, 1668–1681 (1981).Google Scholar
  240. 231.
    W. Meyer, PNO-CI studies of electron correlation effects. I. Configuration expansion by means of nonorthogonal orbitals, and applicatio to the ground state and ionized states of methan, J. Chem. Phys. 58, 1017–1035 (1973).Google Scholar
  241. 232.
    B. G. Adams, K. Jankowski, and J. Paldus, Symmetry-adapted coupled-pair approach to the many-electron correlation problem. III. Approximate coupled-pair approaches for the Be atom, Phys. Rev. A. 24, 2330–2338 (1981).Google Scholar
  242. 233.
    R. Ahlrichs, in: Methods in Computational Molecular Physics (G. H. F. Diercksen and S. Wilson, eds.), pp. 209–226, D. Reidel, Dordrecht (1983).Google Scholar
  243. 234.
    H. P. Kelly and A. M. Sessler, Correlation effects in many-fermion systems: Multiple-particle excitation expansion, Phys. Rev. 132, 2091–2095 (1963).Google Scholar
  244. 235.
    R. Ahlrichs, F. Driessler, H. Lischka, V. Staemmler, and W. Kutzelnigg, PNO-CI (pair natural orbital configuration interaction) and CEPA-PNO (coupled-electron pair approximation with pair natural orbitals) calculation of molecular systems. II. The molecules BeH2, BH, BH3, CH4, CH 3, NH3 (planar and pyramidal), H2O, OH3 +, HF and the Ne atom, J. Chem. Phys. 62, 1235–1247 (1975).Google Scholar
  245. 236.
    G. B. Bacskay, The calculation of ionization energies by perturbation, configuration interaction and approximate coupled pair techniques and comparison with Green’s function methods for Ne, H2O and N2, Chem. Phys. 48, 21–38 (1980).Google Scholar
  246. 237.
    K. Jankowski and J. Paldus, Applicability of coupled-pair theories to quasidegenerate electronic states: A model study, Int. J. Quantum Chem. 17, 1243–1269 (1980).Google Scholar
  247. 238.
    R. Ahlrichs, P. Scharf, and C. Ehrhardt, The coupled pair functional (CPF). A size consistent modification of the CI(SD) based on an energy functional. J. Chem. Phys. 82, 890–898 (1985).Google Scholar
  248. 239.
    S. Shankar and P. T. Narasimhan, Linear coupled-cluster method. I. Exchange-correlation effects in atoms, Phys. Rev. A 29, 52–57 (1984).Google Scholar
  249. 240.
    E. R. Davidson, in: The World of Quantum Chemistry (R. Daudel and B. Pullman, eds.), pp. 17–30, D. Reidel, Dordrecht (1974).Google Scholar
  250. 241.
    R. Ahlrichs, Many-body perturbation calculations and coupled electron-pair models, Comp. Phys. Commun. 17, 31–45 (1979).Google Scholar
  251. 242.
    P. Bruna, S. D. Peyerimhoff, and R. J. Buenker, The ground state of the CN+ ion: A multi-reference CI study, Chem. Phys. Lett. 72, 278–284 (1980).Google Scholar
  252. 243.
    K. Jankowski, L. Meissner, and J. Wasilewski, Davidson-type correlations for quasidegenerate states, Int. J. Quantum Chem. 28, 931–942 (1985).Google Scholar
  253. 244.
    I. Hubac, V. Kvasnicka, and A. Holubec, Application of many-body Rayleigh-Schrödinger perturbation theory to calculation of ionization potentials and electron affinities, Chem. Phys. Lett. 23, 381–385 (1973).Google Scholar
  254. 245.
    I. Hubac and M. Urban, Calculation of vertical ionization potentials of H2O and Ne by many-body Rayleigh-Schrödinger perturbation theory, Theor. Chim. Acta 45, 185–195 (1977).Google Scholar
  255. 246.
    L. S. Cederbaum and K. Schönhammer, Electron affinities by a variation-perturbation approach, Phys. Rev. A 15, 833–842 (1977).Google Scholar
  256. 247.
    D. Sinha, S. Mukhopadhyay, and D. Mukherjee, A note on the direct calculation of excitation energies by quasi-degenerate MBPT and coupled-cluster theory, Chem. Phys. Lett. 129, 369–374 (1986).Google Scholar
  257. 248.
    U. Kaldor and A. Haque, Open-shell coupled-cluster method: Direct calculation of excitation energies, Chem. Phys. Lett. 128, 45–48 (1986).Google Scholar
  258. 249.
    H. Reitz and W. Kutzelnigg, Direct calculation of energy differences by a common unitary transformation of two model states, with application to ionization potentials, Chem. Phys. Lett. 66, 111–115 (1979).Google Scholar
  259. 250.
    E. Dalgaard and H. J. Monkhorst, Some aspects of the time-dependent coupled-cluster approach to dynamic response functions, Phys. Rev. A 28, 1217–1222 (1983).Google Scholar
  260. 251.
    H. Sekino and R. J. Bartlett, A linear response, coupled-cluster theory for excitation energy, Int. J. Quantum Chem. Symp. 18, 255–265 (1984).Google Scholar
  261. 252.
    P. Roman, Advanced Quantum Theory, Addison-Wesley, Reading, Massachusetts (1965).Google Scholar
  262. 253.
    A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems, McGraw-Hill, New York (1971).Google Scholar
  263. 254.
    Gy. Csanak, H. S. Taylor, and R. Yaris, Green’s function technique in atomic and molecular physics, Adv. At. Mol. Phys. 7, 287–361 (1971).Google Scholar
  264. 255.
    J. Linderberg and Y. Öhrn, Propagators in Quantum Chemistry, Academic, London (1973).Google Scholar
  265. 256.
    W. P. Reinhardt and J. D. Doll, Direct calculation of natural orbitals by many-body perturbation theory: Applications to helium, J. Chem. Phys. 50, 2767–2768 (1969).Google Scholar
  266. 257.
    J. D. Doll and W. P. Reinhardt, Many-body Green’s functions for finite nonuniform systems: Application to closed shell atoms, J. Chem. Phys. 57, 1169–1184 (1972).Google Scholar
  267. 258.
    P. W. Langhoff and A. J. Hernandez, Green’s function calculations of ground-state correlation energies, Chem. Phys. Lett. 49, 361–366 (1977).Google Scholar
  268. 259.
    M. W. Ribarsky, General structure of excitations in many-body systems: Applications to atoms, Phys. Rev. A 12, 1739–1750 (1975).Google Scholar
  269. 260.
    D. H. Kobe, Field theoretic approach to atomic helium, Adv. Quantum Chem. 4, 109–145 (1968).Google Scholar
  270. 261.
    B. S. Yarlagadda, G. Csanak, H. S. Taylor, B. Schneider, and R. Yaris, Application of many-body Green’s functions to the scattering and bound-state properties of helium, Phys. Rev. A 7, 146–154 (1973).Google Scholar
  271. 262.
    O. Goscinski and B. Lukman, Moment-conserving decoupling of Green functions via Padé approximants, Chem. Phys. Lett. 7, 573–576 (1970).Google Scholar
  272. 263.
    J. Oddershede and P. Jørgensen, An order analysis of the particle-hole propagator, J. Chem. Phys. 66, 1541–1556 (1977).Google Scholar
  273. 264.
    G. D. Purvis and Y. Öhrn, Atomic and molecular electronic spectra and properties from the electron propagator, J. Chem. Phys. 60, 4063–4069 (1974).Google Scholar
  274. 265.
    L. T. Redmon, G. Purvis, and Y. Öhrn, Higher-order decoupling of the electron propagator, J. Chem. Phys. 63, 5011–5017 (1975).Google Scholar
  275. 266.
    L. S. Cederbaum and W. Domcke, Theoretical aspects of ionization potentials and photoelectron spectroscopy: A Green’s function approach, Adv. Chem. Phys. 36, 205–344 (1977).Google Scholar
  276. 267.
    J. Paldus and J. Čižek, Green’s function approach to the direct perturbation calculation of the excitation energies of closed shell fermion systems, J. Chem. Phys. 60, 149–163 (1974).Google Scholar
  277. 268.
    W. P. Reinhardt and J. B. Schmith, Application of the many-body Green’s function formalism to the lithium atom, J. Chem. Phys. 58, 2148–2152 (1973).Google Scholar
  278. 269.
    H. Yamakawa, T. Aoyama, and I. Ichikawa, Calculations of vertical ionization potential using the one-body Green’s function: Ne, Mg, and H2O, Chem. Phys. Lett. 41, 269–274 (1977).Google Scholar
  279. 270.
    W. von Niessen, G. H. F. Diercksen, and L. S. Cederbaum, On the accuracy of ionization potentials calculated by Green’s functions, J. Chem. Phys. 67, 4124–4131 (1977).Google Scholar
  280. 271.
    O. Walter and J. Schirmer, The two-particle Tamm-Dancoff approximation (2ph-TDA) for atoms, J. Phys. B 14, 3805–3826 (1981).Google Scholar
  281. 272.
    K. F. Freed, M. H. Herman, and D. L. Yeager, Critical comparison between equation of motion-Green’s function methods and configuration interaction methods: Analysis of methods and applications, Phys. Scr. 21, 242–250 (1980).Google Scholar
  282. 273.
    M. F. Herman, K. F. Freed, and D. L. Yeager, Analysis and evaluation of ionization potentials, electron affinities, and excitation energies by the equation of motion-Green’s function method, Adv. Chem. Phys. 48, 1–69 (1981).Google Scholar
  283. 274.
    C. W. McCurdy, T. N. Rescigno, D. L. Yeager, and V. McKoy, in: Methods of Electronic Structure Theory (H. F. Schaefer III, ed.), pp. 339–386, Plenum Press, New York (1977).Google Scholar
  284. 275.
    J. Oddershede, Polarization propagator calculations, Adv. Quantum Chem. 11, 275–352 (1978).Google Scholar
  285. 276.
    D. J. Rowe, Equation-of-motion method and the extended shell model, Rev. Mod. Phys. 40, 153–166 (1968).Google Scholar
  286. 277.
    T.-I. Shibuya and V. McKoy, Higher random-phase approximation as an approximation to the equations of motion, Phys. Rev. A 2, 2208–2218 (1970).Google Scholar
  287. 278.
    P. L. Altick and A. E. Glassgold, Correlation effects in atomic structure using the random-phase approximation, Phys. Rev. 133, A632–A646 (1964).Google Scholar
  288. 279.
    D. L. Yeager and K. F. Freed, Analysis of third order contributions to equation of motion-Green’s function excitation energies: Application to N2, Chem. Phys. 22, 415–433 (1977).Google Scholar
  289. 280.
    M. F. Herman, K. F. Freed, D. L. Yeager, and B. Liu, Critical test of equation-of-motion-Green’s function method. II. Comparison with configuration interaction results, J. Chem. Phys. 72, 611–620 (1980).Google Scholar
  290. 281.
    G. P. Purvis and Y. Öhrn, The transition state, the electron propagator, and the equation of motion method, J. Chem. Phys. 65, 917–922 (1976).Google Scholar
  291. 282.
    T. Szondy, Determination of wave function of molecular systems by the method of moments. I, Act. Phys. Hung. 17, 303–313 (1964).Google Scholar
  292. 283.
    C. Schwartz, Numerical tecniques in matric mechanics, J. Comput. Phys. 2, 90–113 (1967).Google Scholar
  293. 284.
    K. Jankowski, D. Rutkowska, and A. Rutkowski, An investigation of the reliability of the Galerkin-Petrov method. III. Excited states and nonlinear parameters, Theor. Chim. Acta 48, 119–125 (1978).Google Scholar
  294. 285.
    S. F. Boys, Some bilinear convergence characteristics of the solutions of dissymmetric secular equations, Proc. R. Soc. London Scr. A. 309, 195–208 (1969).Google Scholar
  295. 286.
    S. F. Boys and N. C. Handy, A condition to remove the indeterminancy in interelectronic correlation functions, Proc. R. Soc. London Scr. A 309, 209–220 (1969).Google Scholar
  296. S. F. Boys and N. C. Handy, The determination of energies and wavefunctions with full electronic correlation, Proc. R. Soc. London Scr. A 310, 43–61 (1969). A calculation for the energies and wavefunctions for states of neon with full electronic correlation accuracy, ibid. 310, 63-78 (1969).Google Scholar
  297. 287.
    N. C. Handy, Energies and expectation values for Be by the transcorrelated method, J. Chem. Phys. 51, 3205–3212 (1969).Google Scholar
  298. 288.
    M. W. C. Dharma-wardana and F. Grimaldi, Correlated electronic wave functions: Correlated and transcorrelated wave functions, Phys. Rev. A 13, 1702–1712 (1976).Google Scholar
  299. 289.
    G. G. Hall and C. J. Miller, The factorized wave function, Phys. Rev. A 18, 889–894 (1978).Google Scholar
  300. 290.
    J. M. Norbeck and R. McWeeny, The use of biorthogonal sets in valence bond calculations, Chem. Phys. Lett. 34, 206–210 (1975).Google Scholar
  301. 291.
    P. W. Payne, Configuration interaction in a basis of biorthogonal states, J. Chem. Phys. 77, 5630–5638 (1982).Google Scholar
  302. 292.
    I. Røeggen, Antisymmetric product of geminals in the context of the method of moments, Int. J. Quantum Chem. 19, 319–335 (1981).Google Scholar
  303. I. Røeggen, Electron correlation described by extended geminal models: the EXGEM2 and EXGEM3 models, Int. J. Quant. Chem. 22, 149–168 (1982).Google Scholar
  304. 293.
    L. Szasz, I. Berrios-Pagan and G. McGinn, Density-functional formalism, Z. Naturforsch. 30a, 1516–1534 (1975).Google Scholar
  305. 294.
    P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136, B864–B871 (1964).Google Scholar
  306. 295.
    W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140, A1133–1138 (1965).Google Scholar
  307. 296.
    O. Gunnarsson and B. I. Lundqvist, Exchange and correlation in atoms, molecules and solids by the spin-density-functional formalism, Phys. Rev. B 13, 4274–4298 (1976).Google Scholar
  308. 297.
    O. Gunnarsson and R. O. Jones, Density functional calculations for atoms, molecules and clusters, Phys. Scr. 21, 394–401 (1980).Google Scholar
  309. 298.
    O. Gunnarsson and Jones, Total energy differences: Source of error in the local approximations, Phys. Rev. B 31, 7588–7602 (1985).Google Scholar
  310. 299.
    S. Ossicini and C. M. Bertoni, Density-functional calculation of atomic structure with nonlocal exchange and correlation, Phys. Rev. A 31, 3550–3556 (1985).Google Scholar
  311. 300.
    J. G. Harrison, Density functional calculations for atoms in the first transition series, J. Chem. Phys. 79, 2265–2269 (1983).Google Scholar
  312. 301.
    S. K. Ghosh and B. M. Deb, Densities, density-functionals and electron fluids, Phys. Rep. 92, 1–44 (1982).Google Scholar
  313. 302.
    J. C. Stoddart and N. H. March, Density functional theory of magnetic instabilities in metals, Ann. Phys. (N.Y.) 64, 174–210 (1971).Google Scholar
  314. 303.
    J. P. Perdow, Orbital functionals for exchange and correlation: Self interaction correction to the local density approximation, Chem. Phys. Lett. 64, 127–130 (1979).Google Scholar
  315. 304.
    B. Y. Tong and L. J. Sham, Application of a self-consistent scheme including exchange and correlation effects to atoms, Phys. Rev. 144, 1–4 (1966).Google Scholar
  316. 305.
    H. Stoll, C. M. E. Pavlidou, and H. Preuss, On the calculation of correlation energies in the spin-density functional formalism, Theor. Chim. Acta 149, 143–149 (1978).Google Scholar
  317. 306.
    U. von Barth, Local-density theory of multiplet structure, Phys. Rev. A 20, 1693–1703 (1979).Google Scholar
  318. 307.
    F. H. Wood, Atomic multiplet structures obtained from Hartree-Fock statistical exchange and local spin density approximations, J. Phys. B 13, 1–14 (1980).Google Scholar
  319. 308.
    O. Gunnarsson and R. O. Jones, Extension of the LSD approximation in density functional calculations, J. Chem. Phys. 72, 5357–5362 (1980).Google Scholar
  320. 309.
    R. O. Jones, Energy differences using an accurate local density functional, J. Chem. Phys. 76, 3098–3101 (1982).Google Scholar
  321. 310.
    J. G. Harrison, An improved self-interaction-corrected local spin density functional for atoms, J. Chem. Phys. 78, 4562–4566 (1983).Google Scholar
  322. 311.
    A. Frost, R. E. Kellog, and E. C. Curtis, Local-energy method in electronic energy calculations, Rev. Mod. Phys. 32, 313–317 (1960).Google Scholar
  323. 312.
    B. M. Gimarc and A. A. Frost, Energy of the lithium atom by the least-squares local energy method, J. Chem. Phys. 39, 1698–1702 (1963).Google Scholar
  324. 313.
    R. E. Stanton and R. L. Taylor, Mathematical properties of Frost’s local-energy method, J. Chem. Phys. 45, 565–571 (1966).Google Scholar
  325. 314.
    S. Ehrenson and G. D. Harp, Importance of sampling in local energy calculations on H2, Int. J. Quantum Chem. 7, 1099–1116 (1976).Google Scholar
  326. 315.
    D. K. Harriss and I. G. Solev, On the solution of the least-squares local energy variance minimization equations, Int. J. Quantum Chem. 9, 975–980 (1975).Google Scholar
  327. 316.
    H. Conroy, Molecular Schrödinger equation. II. Monte Carlo evaluation of integrals, J. Chem. Phys. 41, 1331–1335 (1964).Google Scholar
  328. H. Conroy, III. Calculation of ground-state energies by extrapolation, J. Chem. Phys. 41, 1336–1340 (1964); IV. Results for one-and two-electron systems, ibid. 41, 1341-1351 (1964).Google Scholar
  329. 317.
    J. Goodisman, Minimization of the width as an alternative to the conventional variation method, J. Chem. Phys. 45, 3659–3667 (1966).Google Scholar
  330. 318.
    N. C. Handy, On the minimization of the variance of the transcorrelated hamiltonian, Mol. Phys. 21, 817–828 (1971).Google Scholar
  331. 319.
    M. Rosina and C. Garrod, The variational calculations of reduced density matrices, J. Comput. Phys. 18, 300–310 (1975).Google Scholar
  332. 320.
    C. Garrod and M. A. Fusco, A density matrix variational calculation for atomic Be, Int. J. Quantum Chem. 10, 495–510 (1976).Google Scholar
  333. 321.
    C. Valdemoro, Spin-adapted reduced Hamiltonian. I. Elementary excitations, Phys. Rev. A 31, 2114–2122 (1985).Google Scholar
  334. C. Valdemoro, II. Total energy and reduced density matrices, Phys. Rev. A 31, 2123–2130 (1985).Google Scholar
  335. 322.
    K. Dietz, O. Lechtenfeld, and G. Weymans, Optimized mean-fields for atoms. I. Mean-field methods for the description of N-fermion systems, J. Phys. B 15, 4301–4314 (1982)Google Scholar
  336. K. Dietz, O. Lechtenfeld, and G. Weymans, II. Numerical studies, J. Phys. B 15, 4315–4330 (1982); III. g-Hartree many-body calculations for small Z atoms, ibid. 17, 2987-3002 (1984).Google Scholar
  337. 323.
    C. Valdemoro, L. Lain, F. Breitia, A. Ortiz de Zarate, and F. Castano, Direct approximation to the reduced density matrices: Calculation of the isoelectronic sequence of berryllium up to argon, Phys. Rev. A 33, 1525–1531 (1984).Google Scholar
  338. 324.
    J. N. Bardsley, Pseudopotentials in atomic and molecular physics, Case Stud. At. Phys. 4, 299–368 (1974).Google Scholar
  339. 325.
    J. Berthelat and Ph. Durand, Recent progress of pseudo-potential methods in quantum chemistry, Gaz. Chim. Ital. 108, 225–236 (1978).Google Scholar
  340. 326.
    M. Krauss and W. J. Stevens, Effective potentials in molecular quantum chemistry, Ann. Rev. Phys. Chem. 35, 357–385 (1984).Google Scholar
  341. 327.
    H. Preuss, H. Stoll, U. Weding, and T. Krüger, Combinations of pseudopotentials and density functionals. Int. J. Quantum Chem. 19, 113–130 (1981).Google Scholar
  342. 328.
    B. Pittel and W. H. E. Schwartz, Correlation energies from pseudo-potential calculations, Chem. Phys. Lett. 46, 121–124 (1977).Google Scholar
  343. 329.
    M. Szulkin and J. Karwowski, The effect of core polarization on oscillator strengths and on the localization of energy levels in sodium, Act. Phys. Polon. A 54, 231–235 (1978).Google Scholar
  344. 330.
    G. H. Jeung, J. P. Malrieu, and J. P. Daudey, Inclusion of core-valence correlation effects in pseudo-potential calculations. I. Alkali atoms and diatoms, J. Chem. Phys. 77, 3571–3577 (1982).Google Scholar
  345. 331.
    W. Müller, J. Flesch, and W. Meyer, Treatment of intershell correlation effects in ab initio calculations by use of core polarization potentials. Method and application to alkali and alkaline earth atoms. J. Chem. Phys. 80, 3297–3310 (1984).Google Scholar
  346. 332.
    W. J. Stevens, A. M. Karo, and J. R. Hiskes, MCSCF pseudopotential calculations for the alkali hydrides and their anions, J. Chem. Phys. 74, 3989–3998 (1981).Google Scholar
  347. 333.
    W. J. Stevens, D. D. Konowalow, and L. B. Ratcliff, Electronic structure and spectra of the lowest five 1Σ+ and 3Σ+ states, and three 1Π, 3Π, 1Δ, and 3Δ states of NaK, J. Chem. Phys. 80, 1215–1224 (1984).Google Scholar
  348. 334.
    B. C. Laskowski, S. P. Walch, and P. A. Christiansen, Ab initio calculation of the X 1Σ state of CsH, J. Chem. Phys. 78, 6824–6832 (1983).Google Scholar
  349. 335.
    S. Topiol, A. Zunger, and M. A. Ratner, The use of pseudopotentials within local-density formalism calculations for atoms: some results for the first row, Chem. Phys. Lett. 49, 367–373 (1977).Google Scholar
  350. 336.
    B. R. Judd, Complex atomic spectra, Rep. Progr. Phys. 48, 907–980 (1985).Google Scholar
  351. 337.
    J. E. Hansen and A. J. J. Raassen, A structure of fitted and calculated parameter values in III, IV, V and VI spectra of the iron group elements, Physica 111C, 76–101 (1981).Google Scholar
  352. 338.
    J. C. Slater, Quantum Theory of Atomic Structure, McGraw-Hill, New York (1960).Google Scholar
  353. 339.
    R. F. Bacher and S. Goudsmit, Atomic energy relations. I, Phys. Rev. 46, 948–969 (1934).Google Scholar
  354. 340.
    K. Rajnak and B. G. Wybourne, Configuration interactions effects in 1N configurations, Phys. Rev. 132, 280–290 (1963).Google Scholar
  355. 341.
    G. Racah and J. Stein, Effective electrostatic interactions in 1N configurations, Phys. Rev. 156, 58–64 (1967).Google Scholar
  356. 342.
    G. Racah, Group theory and spectroscopy, Erg. Exact Naturw. 37, 28–84 (1965).Google Scholar
  357. 343.
    J. E. Hansen, B. R. Judd, G. M. S. Lister, and W. Persson, Observation of four-body effects in atomic spectra, J. Phys. B 18, L725–L730 (1985).Google Scholar
  358. 344.
    B. R. Judd, J. E. Hansen, and A. J. J. Raassen, Parametric fits in the atomic d shell, J. Phys. B 15, 1457–1472 (1982).Google Scholar
  359. 345.
    J. C. Morrison and K. Rajnak, Many-body calculations for the heavy atoms, Phys. Rev. A 4, 536–542 (1971).Google Scholar
  360. 346.
    E. Clementi, Correlation energy for atomic systems, J. Chem. Phys. 38, 2248–2256 (1963).Google Scholar
  361. E. Clementi, II. Isoelectronic series with 11 to 18 electrons, J. Chem. Phys. 39, 175–179 (1963); IV. Degeneracy effects, J. Chem. Phys. 44, 3050-3053 1966).Google Scholar
  362. 347.
    L. C. Allen, E. Clementi, and H. M. Gladney, Pair correlation energies, Rev. Mod. Phys. 35, 465–473 (1963).Google Scholar
  363. 348.
    T. Anno and Y. Sakai, Pair correlation energies as derived from the analysis of semiempirical values of correlation energies of atoms, J. Chem. Phys. 57, 1636–1647 (1972).Google Scholar
  364. T. Anno and Y. Sakai, Erratum, J. Chem. Phys. 63, 5509–5509 (1975).Google Scholar
  365. 349.
    F. Bernardi, P. G. Mezey, and I. G. Csizmadia, A relationship between correlation energies and sizes: The series of beryllium and neon-like ions, Can. J. Chem. 55, 2417–2419 (1977).Google Scholar
  366. 350.
    M. H. Ang, K. Yates, I. G. Csizmadia, and R. Daudel, Relationship of correlation energy and size, Int. J. Quantum Chem. 20, 793–806 (1981).Google Scholar
  367. 351.
    A. J. Sadlej, Molecular electric polarizabilities. Electric-field-variant (EFV) Gaussian basis set for polarizability calculations, Chem. Phys. Lett. 47, 50–54 (1977).Google Scholar
  368. 352.
    C. Froese-Fischer, Correlation effects important for accurate oscillator strengths, J. Phys. B 7, L91–L96 (1974).Google Scholar
  369. 353.
    G. T. Daborn, W. I. Ferguson, and N. C. Handy, The calculation of second-order molecular properties the configuration interaction level of accurary, Chem. Phys. 50, 255–263 (1980).Google Scholar
  370. 354.
    I. Lindgren, Effective operators in the atomic hyperfine interactions, Rep. Progr. Phys. 47, 345–398 (1984).Google Scholar

Copyright information

© Springer Science+Business Media New York 1987

Authors and Affiliations

  • Karol Jankowski
    • 1
  1. 1.Institute of PhysicsNicholas Copernicus UniversityToruńPoland

Personalised recommendations