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Pair Correlation Theories

  • Chapter
Methods of Electronic Structure Theory

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

Abstract

In the simplest possible description of an n-electron system, one one-electron function (spin-orbital) is associated with each electron and the n -electron wave function is a Slater determinant built up from these spin-orbitals. The one-to-one correspondence between electrons and spin-orbitals gives an acceptable first-order description only for closed-shell and certain open-shell states. A one-electron theory that is applicable in general to open-shell states as well is characterized by assigning sets of electrons to sets of degenerate spin-orbitals, where the number of electrons within one set can be equal to or smaller than the dimension of the irreducible representation spanned by the degenerate set of spin-orbitals. An example is the well-known characterization of an atomic state by its configuration,(1) e.g., for the carbon ground state 1s22s22p2, without specifying the ms and ml values. (For a general discussion of closed- and open-shell states in the framework of rigorous quantum mechanics, see Refs. 2 and 3.)

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References

  1. E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra, Cambridge University Press, New York (1951).

    Google Scholar 

  2. W. Kutzelnigg and V. H. Smith, Jr., Open- and closed-shell states in few-particle quantum mechanics. I. Definitions, Int. J. Quantum Chem. 2, 531–552 (1968).

    Article  CAS  Google Scholar 

  3. V. H. Smith, Jr., and W. Kutzelnigg, Open- and closed-shell states in few-particle quantum mechanics. II. Classification of atomic states, Int. J. Quantum Chem. 2, 553–562 (1968).

    Article  CAS  Google Scholar 

  4. E. Steiner, Theory of correlated wave functions. II. The symmetry properties of atomic correlated wave functions, J. Chem. Phys. 45, 328–337 (1966).

    Article  CAS  Google Scholar 

  5. O. Sinanoglu, Many-electron theory of atoms and molecules. I. Shells, electron pairs versus many-electron correlation, J. Chem. Phys. 36, 706–717 (1962);

    Article  CAS  Google Scholar 

  6. O. Sinanoglu, Many-electron theory of atoms and molecules. II, J. Chem. Phys. 36, 3198–3208 (1962);

    Article  CAS  Google Scholar 

  7. O. Sinanoglu, Many-electron theory of atoms, molecules, and their interactions, Adv. Chem. Phys. 6, 315–412 (1964).

    Article  CAS  Google Scholar 

  8. E. P. Wigner and F. Seitz, Constitution of metallic sodium I, II, Phys. Rev. 43, 804–810 (1933);

    Article  CAS  Google Scholar 

  9. E. P. Wigner and F. Seitz, Constitution of metallic sodium I, II, Phys. Rev. 46, 509–524 (1934).

    Article  CAS  Google Scholar 

  10. N. R. Kestner and O. Sinanoglu, Intermolecular-potential-energy curves; theory and calculations on the helium—helium potential, J. Chem. Phys. 45, 194–207 (1966).

    Article  CAS  Google Scholar 

  11. A. C. Hurley, J. E. Lennard-Jones, and J. A. Pople, The molecular orbitals theory of chemical valency. XVI. A theory of paired electrons in polyatomic molecules, Proc. R. Soc. London, Ser. A 220, 446–455 (1953).

    Article  CAS  Google Scholar 

  12. J. M. Parks and R. G. Parr, Theory of separated electron pairs, J. Chem. Phys. 28, 335–345 (1958).

    Article  CAS  Google Scholar 

  13. R. McWeeny, The density matrix in many-electron quantum mechanics. I. Generalized product functions. Factorization and physical interpretation of the density matrix, Proc. R. Soc. London Ser. A 253, 242–259 (1959).

    Article  CAS  Google Scholar 

  14. W. Kutzelnigg, Direct determination of natural orbitals and natural expansion coefficients of many-electron wave functions. I. Natural orbitals in the geminal product approximation, J. Chem. Phys. 40, 3640–3647 (1964).

    Article  CAS  Google Scholar 

  15. R. Ahlrichs and W. Kutzelnigg, Direct calculation of approximate natural orbitals and natural expansion coefficients of atomic and molecular electronic wave functions. II. Decoupling of the pair equations and calculation of the pair correlation energies for the Be and LiH ground states, J. Chem. Phys. 48, 1819–1832 (1968).

    Article  CAS  Google Scholar 

  16. W. Kutzelnigg, Electron correlation and electron pair theories, Fortschr. Chem. Forsch. 41, 31–73 (1973).

    CAS  Google Scholar 

  17. E. L. Mehler, K. Ruedenberg, and D. M. Silver, Electron correlation and the separated pair approximation in diatomic molecules. II. Lithium hydride and boron hydride, J. Chem. Phys., 52, 1181–1205 (1970).

    Article  CAS  Google Scholar 

  18. M. Krauss and A. W. Weiss, Pair correlation in closed-shell systems, J. Chem. Phys. 40, 80–85 (1964).

    Article  CAS  Google Scholar 

  19. H. Primas, in: Modern Quantum Chemistry (O. Sinanoglu, ed.), Vol. 2, pp. 45–74, Academic Press, New York (1965).

    Google Scholar 

  20. H. D. Ursell, The evaluation of Gibb’s phase integral for imperfect gases, Proc. Cambridge Philos. Soc. 23, 685–697 (1927).

    Article  CAS  Google Scholar 

  21. J. E. Mayer, The statistical mechanics of condensing systems. I., J. Chem. Phys. 5, 67–73 (1937).

    Article  CAS  Google Scholar 

  22. B. Kahn and G. E. Uhlenbeck, Theory of condensation, Physica 5, 399–416 (1938).

    Article  CAS  Google Scholar 

  23. R. Brout and P. Caruthers, Lectures on the Many-Electron Problem, Gordon and Breach, New York (1969).

    Google Scholar 

  24. F. Coester, Bound states of a many-particle system, Nucl. Phys. 7, 421–424 (1958).

    Article  Google Scholar 

  25. R. K. Nesbet, Brueckner’s theory and the method of superposition of configurations, Phys. Rev. 109, 1632–1638 (1958).

    Article  CAS  Google Scholar 

  26. W. Brenig, Zweiteilchennäherungen des Mehrkörperproblems. I. Nucl. Phys. 4, 363–374 (1957).

    Article  Google Scholar 

  27. F. Coester and H. Kümmel, Short range correlations in nuclear wave functions, Nucl. Phys. 17, 477–485 (1960).

    Article  CAS  Google Scholar 

  28. H. Kümmel, Compound pair states in imperfect Fermi gases, Nucl. Phys. 22, 177–183 (1961).

    Article  Google Scholar 

  29. J. da Providencia, Linked graph expansion for the logarithm of the norm of many-body wave functions, Nucl. Phys. 44, 572–578 (1963);

    Article  Google Scholar 

  30. J. da Providencia, Cluster expansion of operator averages for systems of many particles, Nucl. Phys. 46, 401–412 (1963).

    Article  Google Scholar 

  31. K. Kumar, Validity of the two-particle approximation in the many-body problem, Nucl. Phys. 21, 99–105 (1960).

    Article  CAS  Google Scholar 

  32. R. K. Nesbet, Electronic correlation in atoms and molecules, Adv. Chem. Phys. 9, 321–363 (1965).

    Article  Google Scholar 

  33. P.-O. Löwdin, Studies in perturbation theory. V. Some aspects on the exact self-consistent field theory, J. Math. Phys. 3, 1171–1184 (1962).

    Article  Google Scholar 

  34. W. Kutzelnigg and V. H. Smith,Jr., On different criteria for the best independent-particlemodel approximation, J. Chem. Phys. 41, 896–897 (1964).

    Article  CAS  Google Scholar 

  35. R. A. Krumhout, Exact energy self-consistent field, Phys. Rev. 107, 215–219 (1957).

    Article  Google Scholar 

  36. H. Kümmel and J. Q. Zabolitzky, Fully self-consistent Brueckner—Hartree—Fock and renormalized Brueckner—Hartree—Fock calculation for 4He and 160, Phys. Rev. C 7, 547–552 (1973).

    Article  Google Scholar 

  37. J. Cižek, 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);

    Article  Google Scholar 

  38. J. Cižek, On the use of the cluster expansion and the technique of diagrams in calculations of correlation effects in atoms and molecules, Adv. Chem. Phys. 14, 35–89 (1969).

    Article  Google Scholar 

  39. J. Čižek, J. Paldus, and L. šroubkova, Cluster expansion analysis for delocalized systems, Int. J. Quantum Chem. 3, 149–167 (1969).

    Article  Google Scholar 

  40. J. Čižek and J. Paldus, Correlation problems in atomic and molecular systems. III. Rederivation of the coupled-pair many-electron theory using the traditional quantum chemical methods, Int. J. Quantum Chem. 5, 359–379 (1971).

    Article  Google Scholar 

  41. J. Paldus, J. Čižek, and I. Shavitt, Correlation problems in atomic and molecular system. IV. Extended coupled-pair many-electron theory and its application to the borane molecule, Phys. Rev. A 5, 50–67 (1972).

    Google Scholar 

  42. H. Kümmel, Theory of many-body wave functions with correlations, Nucl. Phys. A 176, 205–218 (1971).

    Google Scholar 

  43. H. Kümmel and H. Lüihrmann, Equations for linked clusters and the energy variational principle, Nucl. Phys. A 191, 525–534 (1972);

    Article  Google Scholar 

  44. H. Kümmel and H. Lüihrmann, Equation for linked clusters and Brueckner— Bethe theory, Nucl. Phys. A 194, 225–236 (1972).

    Article  Google Scholar 

  45. H. P. Kelly and A. M. Sessler, Correlation effects in many Fermion systems. Multiple-particle excitation expansion, Phys. Rev. 132, 2091–2095 (1963).

    Article  CAS  Google Scholar 

  46. H. P. Kelly, Correlation effects in many Fermion systems. II. Linked clusters, Phys. Rev. 134A, 1450–1453 (1964).

    Article  Google Scholar 

  47. R. Brout, Variational methods and the nuclear many-body problem, Phys. Rev.111, 1324–1333 (1958).

    Article  Google Scholar 

  48. B. H. Brandow, Compact-cluster expansion for the nuclear many-body problem, Phys. Rev. 152, 863–882 (1966);

    Article  CAS  Google Scholar 

  49. B. H. Brandow, Linked cluster expansion for the nuclear many-body problem, Rev. Mod. Phys. 39, 771–828 (1967).

    Article  CAS  Google Scholar 

  50. K. A. Brueckner, Two-body forces and nuclear saturation. III. Details of the structure of the nucleus, Phys. Rev. 97, 1353–1366;(1955)

    Article  CAS  Google Scholar 

  51. K. A. Brueckner, Many-body problem for strongly interacting particles. II. Linked cluster expansion, Phys. Rev.100, 36–45 (1955).

    Article  CAS  Google Scholar 

  52. H. A. Bethe, Nuclear many-body problem, Phys. Rev. 103, 1353–1390 (1956).

    Article  CAS  Google Scholar 

  53. J. D. Thouless, The Quantum Mechanics of Many-Body Systems, Academic Press, New York (1961).

    Google Scholar 

  54. R. Ahlrichs, Convergence of the 1/Z expansion, Phys. Rev. A 5, 605–614 (1972).

    Google Scholar 

  55. D. Layzer, Z. Horak, M. N. Lewis, and D. P. Thompson, Second-order Z-dependent theory of many-electron atoms, Ann. Phys. 29, 101–124 (1964).

    Article  CAS  Google Scholar 

  56. J. Linderberg and H. Shull, Electronic correlation energy in 3- and 4-electron atoms, J. Mol. Spectrosc. 5, 1–16 (1960).

    Article  CAS  Google Scholar 

  57. M. Cohen and A. Dalgarno, The Hartree energies of the helium sequence, Proc. Phys. Soc. London Ser. A 77, 165 (1961).

    Article  Google Scholar 

  58. S. T. Epstein, Hartree—Fock Hamiltonians and separable nonlocal potentials, J. Chem. Phys. 41, 1045–1046 (1964).

    Article  Google Scholar 

  59. S. T. Epstein, in : Perturbation Theory and Its Applications in Quantum Mechanics (C. H. Wilcox, ed.), pp. 49–56, Wiley, New York (1966).

    Google Scholar 

  60. E. Steiner, Theory of correlated wavefunctions. III. Alternative initial approximations, J. Chem. Phys. 46, 1717–1736 (1967).

    Article  CAS  Google Scholar 

  61. C. MØller and M. S. Plessett, Note on the approximation treatment for many-electron systems, Phys. Rev. 46, 618–622 (1934).

    Article  Google Scholar 

  62. P. S. Epstein, The Stark effect from the point of view of Schrödinger’s quantum theory, Phys. Rev. 28, 695–710 (1926).

    Article  Google Scholar 

  63. R. K. Nesbet, Configuration interaction in orbital theories, Proc. R. Soc. London Ser. A 230, 312–321 (1955).

    Article  CAS  Google Scholar 

  64. 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).

    CAS  Google Scholar 

  65. O. Sinanoglu, Theory of electron correlation in atoms and molecules, Proc. R. Soc. London Ser. A 260, 379–392 (1961).

    Article  CAS  Google Scholar 

  66. E. Schmidt, Zur Theorie der linearen und nichtlinearen Integralgleichungen. I. Teil: Entwicklung willküirlicher Funktionen nach Systemen vorgeschriebener, Math. Ann. 63, 433–476 (1907).

    Article  Google Scholar 

  67. M. Golomb, in : On Numerical Approximation (R. E. Langer, ed.), pp. 275–327, Wisconsin University Press, Madison (1958).

    Google Scholar 

  68. D. C. Carlson and J. H. Keller, Eigenvalues of density matrices, Phys. Rev. 121, 659–661 (1961).

    Article  Google Scholar 

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

    Article  Google Scholar 

  70. P.-O. Löwdin and H. Shull, Natural orbitals in the quantum theory of two-electron systems, Phys. Rev. 101, 1730–1739 (1956).

    Article  Google Scholar 

  71. W. Kutzelnigg, Solution of the two-electron problem in quantum mechanics by direct determination of the natural orbitals. I. Theory, Theor. Chim. Acta 1, 327–342 (1963).

    Article  CAS  Google Scholar 

  72. W. A. Bingel and W. Kutzelnigg, Symmetry properties of reduced density matrices and natural p-states, Adv. Quantum Chem. 5, 201–218 (1970).

    Article  CAS  Google Scholar 

  73. R. Ahlrichs, W. Kutzelnigg, and W. A. Bingel, Solution of the two-electron problem in quantum mechanics by direct calculation of the natural orbitals. III. Refined treatment of the helium atom and the helium-like ions. IV. Application to the ground state of the hydrogen molecule in a one-center expansion, Theor. Chim. Acta 5, 289–304, 305–311 (1966).

    Article  CAS  Google Scholar 

  74. W. Kutzelnigg, in: Selected Topics in Molecular Physics (E. Clementi, ed.), pp. 91–102, Verlag Chemie, Weinheim (1972).

    Google Scholar 

  75. R. Ahlrichs and F. Driessler, Direct determination of pair natural orbitals. A new method to solve the multiconfiguration Hartree—Fock problem for two-electron wave functions, Theor. Chim. Acta 36, 275–287 (1975).

    Article  CAS  Google Scholar 

  76. P. W. Langhoff, Separation theorem for first-order pair-correlation equations, Int. J. Quantum Chem. 7S, 443–448 (1973).

    Article  CAS  Google Scholar 

  77. R. McWeeny and E. Steiner, The theory of pair-correlated wave functions, Adv. Quantum Chem. 2, 93–117 (1965).

    Article  CAS  Google Scholar 

  78. J. P. Malrieu, Cancellation occurring in the calculation of transition energies by a perturbation development of configuration interaction matrices, J. Chem. Phys. 47, 4555–4558 (1967).

    Article  Google Scholar 

  79. H. P. Kelly, Correlation effects in atoms, Phys. Rev. 131, 684–699 (1963);

    Article  Google Scholar 

  80. H. P. Kelly, Many-body perturbation theory applied to open-shell atoms, Phys. Rev. 136B, 896–912 (1964);

    Article  CAS  Google Scholar 

  81. H. P. Kelly, Many-body perturbation theory applied to atoms, Phys. Rev. 144, 39–55 (1966);

    Article  CAS  Google Scholar 

  82. H. P. Kelly, Frequencydependent polarizability of hydrogen calculated by many-body theory, Phys. Rev. A 1, 274–279 (1970);

    Article  Google Scholar 

  83. H. P. Kelly, Applications of many-body diagram techniques in atomic physics, Adv. Chem. Phys. 14, 129–190 (1969).

    Article  CAS  Google Scholar 

  84. H. P. Kelly, in : Perturbation Theory and Its Application in Quantum Mechanics (C. H. Wilcox, ed.), pp. 215–241, Wiley, New York (1966).

    Google Scholar 

  85. J. Goldstone, Derivation of the Brueckner many-body theory, Proc. R. Soc. London, Ser. A 239, 267–279 (1957).

    Article  CAS  Google Scholar 

  86. S. K. Ma and K. A. Brueckner, Correlation energy of an electron gas with a slowly varying high density, Phys. Rev. 165, 18–31 (1968).

    Article  Google Scholar 

  87. K. A. Brueckner and W. Wada, Nuclear saturation and two-body-forces. Self-consistent solution and the effects of the exclusion principle, Phys. Rev. 103, 1008–1016 (1956).

    Article  CAS  Google Scholar 

  88. K. A. Brueckner, J. L. Gammel, and H. Weitzner, Theory of finite nuclei, Phys. Rev. 110, 431–445 (1958).

    Article  CAS  Google Scholar 

  89. H. A. Bethe and J. Goldstone, Effect of a repulsive core in the theory of complex nuclei, Proc. R. Soc. London Ser. A 238, 551–567 (1957).

    Article  CAS  Google Scholar 

  90. L. C. Gomes, J. D. Walecka, and V. F. Weisskopf, Properties of nuclear matter, Ann. Phys. 3, 241–274 (1958).

    Article  CAS  Google Scholar 

  91. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Theory of superconductivity, Phys. Rev. 108, 1175–1204 (1957).

    Article  CAS  Google Scholar 

  92. N. Bogoljubov, A new method in the theory of superconductivity. I, Soviet Phys. JETP 7, 41–46 (1958).

    Google Scholar 

  93. M. A. Robb, Application of many-body perturbation methods in a discrete orbital basis, Chem. Phys. Lett. 20, 274–277 (1973).

    Article  CAS  Google Scholar 

  94. R. J. Bartlett and D. M. Silver, Many-body perturbation theory applied to electron pair correlation energies. I. Closed-shell first-row diatomic hydrides, J. Chem. Phys. 62, 3258–3268 (1975).

    Article  CAS  Google Scholar 

  95. M. A. Robb, Pair functions and diagrammatic perturbation theory, in : Computational Tech-niques in Quantum Chemistry and Molecular Physics (G. H. F. Diercksen et al., eds.), pp. 435–503, D. Reidel, Dordrecht, Holland (1975).

    Chapter  Google Scholar 

  96. K. F. Freed, Many-body theories of the electronic structure of atoms and molecules, Annu. Rev. Phys. Chem. 22, 313–346 (1971).

    Article  CAS  Google Scholar 

  97. S. Diner, J. P. Malrieu, P. Claverie, and F. Jordan, Fully localized bond orbitals and the correlation problem, Chem. Phys. Lett. 2, 319–323 (1968).

    Article  CAS  Google Scholar 

  98. S. Diner, J. P. Malrieu, and P. Claverie, Localized bond orbitals and the correlation problem. I. Perturbation calculation of ground-state energy, Theor. Chim. Acta 13, 1–17 (1969).

    Article  CAS  Google Scholar 

  99. J. P. Malrieu, P. Claverie, and S. Diner, Localized bond orbitals and the correlation problem. II. Application to πr-electron systems, Theor. Chim. Acta 13, 18–45 (1969).

    Article  CAS  Google Scholar 

  100. S. Diner, J. P. Malrieu, F. Jordan, and M. Gilbert, Localized bond orbitals and the correlation problem. III. Energy up to the third-order in the zero-differential overlap approximation. Application to πr-electron systems, Theor. Chim. Acta 15, 100–110 (1969).

    Article  CAS  Google Scholar 

  101. F. Jordani, M. Gilbert, J. P. Malrieu, and V. Pincelli, Localized bond orbitals and the correlation problem. IV. Stability of the perturbation energies with respect to bond hybridization and polarity, Theor. Chim. Acta 15, 211–224 (1969).

    Article  Google Scholar 

  102. C. F. Bender and E. R. Davidson, Correlation energy and molecular properties of hydrogen fluoride, J. Chem. Phys. 47, 360–366 (1967).

    Article  CAS  Google Scholar 

  103. T. L. Barr and E. R. Davidson, Nature of the configuration-interaction method of ab initio calculations. I. Neon ground state, Phys. Rev. A1, 644–658 (1970).

    Article  CAS  Google Scholar 

  104. R. K. Nesbet, T. L. Barr, and E. R. Davidson, Correlation energy of the neon atom, Chem. Phys. Lett. 4, 203–204 (1969).

    Article  CAS  Google Scholar 

  105. A. Weiss, Symmetry-adapted pair correlations in Ne, F , Ne+, and F, Phys. Rev. A 3, 126 (1971).

    Article  Google Scholar 

  106. C. M. Moser and R. K. Nesbet, Atomic Bethe—Goldstone calculations of term splittings, ionization potentials, and electron affinities for B, C, N, 0, F, and Ne. II. Configurational excitations, Phys. Rev. A 6, 1710–1715 (1972).

    Article  CAS  Google Scholar 

  107. J. W. Viers, F. E. Harris, and H. F. Schaeffer III, Pair correlations and the electronic structure of neon, Phys. Rev. A 1, 24–27 (1970).

    Article  Google Scholar 

  108. D. A. Micha, Many-body contributions to atomic correlation energies, Phys. Rev. A1, 755–764 (1970).

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  110. 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 

  111. W. Meyer, PNO-CI and CEPA studies of electron correlation effects. II. Potential curves and dipole moment functions of the OH radical, Theor. Chim. Acta 35, 277–292 (1974).

    Article  CAS  Google Scholar 

  112. R. Ahlrichs, 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) calculations of molecular systems. I. Outline of the method for closed-shell states, J. Chem. Phys. 62, 1225–1234 (1975).

    Article  CAS  Google Scholar 

  113. 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) calculations of molecular systems. II. The molecules BeH2, BH, BH3, CH4, CH3 , NH3 (planar and pyramidal), H2O, OH3, HF, and the Ne atom, J. Chem. Phys. 62, 1235–1247 (1975).

    Article  CAS  Google Scholar 

  114. R. Ahlrichs, F. Keil, H. Lischka, W. Kutzelnigg, and V. Staemmler, PNO-CI (pair natural orbital configuration interaction) and CEPA-PNO (coupled electron pair approximation with pair natural orbitals) calculations of molecular systems. III. The molecules MgH2, A1H3, SiH4, PH3 (planar and pyramidal), H2S, HC1 and the Ar atom, J. Chem. Phys. 63, 455–463 (1975).

    Article  CAS  Google Scholar 

  115. R. Ahlrichs, H. Lischka, B. Zurawski, and W. Kutzelnigg, PNO-CI (pair natural orbital configuration interaction) and CEPA-PNO (coupled electron pair approximation with pair natural orbitals) calculations of molecular systems. IV. The molecules N2, F2, C2H2, C2H4, and C2H6 J. Chem. Phys. 63, 4685–4694 (1975).

    Article  CAS  Google Scholar 

  116. K. F. Freed, Many-body approach to electron correlation in atoms and molecules, Phys. Rev. 173, 1–24 (1968).

    Article  CAS  Google Scholar 

  117. L. Szasz, Über die Berechnung der Korrelationsenergie der Atomelektronen, Z. Naturforsch. 15a, 909–926 (1960);

    Google Scholar 

  118. L. Szasz, Atomic many-body problem. I. General theory of correlated wave functions, Phys. Rev. 126, 169–181 (1962);

    Article  CAS  Google Scholar 

  119. L. Szasz, Formulation of the quantum-mechanical many-body problem in terms of one- and two-particle functions, Phys. Rev. 132, 936–947 (1963);

    Article  Google Scholar 

  120. L. Szasz, Pseudopotential theory of atoms and molecules. I. A new method for the calculation of correlated pair functions, J. Chem. Phys. 49, 679–691 (1968).

    Article  CAS  Google Scholar 

  121. H. J. Silverstone and O. Sinanoglu, Many-electron theory of nonclosed-shell atoms and molecules. I. Orbital wavefunction and perturbation theory. II. Variational theory, J. Chem. Phys. 44, 1899–1907, 3608–3617 (1966).

    Article  CAS  Google Scholar 

  122. V. Staemmler and M. Jungen, Application of the independent electron pair approach to the calculation of excitation energies, ionization potentials, and electron affinities of first row atoms, Theor. Chim. Acta 38, 303 (1975).

    Article  CAS  Google Scholar 

  123. W. Meyer, A recent CI method based on pseudonatural orbitals, this volume, Chapter 11.

    Google Scholar 

  124. B. Roos, A new method for large-scale CI calculations, Chem. Phys. Lett. 15, 153–159 (1972).

    Article  Google Scholar 

  125. P. Siegbahn and B. Roos, this volume, Chapter 7.

    Google Scholar 

  126. H. F. Schaefer III, Ab initio potential curve for the X3/g-state of 02, J. Chem. Phys. 54, 2207–2211 (1971).

    Article  CAS  Google Scholar 

  127. R. K. Nesbet, Atomic Bethe-Goldstone equations, Adv. Chem. Phys. 14, 1–34 (1969).

    Article  CAS  Google Scholar 

  128. G. A. van der Velde and W. C. Nieuwpoort, Generalized Bethe-Goldstone calculations on molecules, Chem. Phys. Lett. 13, 409–412 (1972).

    Article  Google Scholar 

  129. G. A. van der Velde, Thesis, Groningen (1974).

    Google Scholar 

  130. E. L. Mehler, Independent pair-potential correlated wave functions, Int. J. Quantum Chem. S7, 437–442 (1973);

    Article  CAS  Google Scholar 

  131. E. L. Mehler, Orbital correlation effects: The independent pair-potential approximation with application to the ground state and first ionized state of boron hydrides, Theor. Chim. Acta 35, 17–32 (1974).

    Article  CAS  Google Scholar 

  132. H. Primas, Generalized perturbation theory for quantum mechanical manyparticle problems, Helv. Phys. Acta 34, 331–351 (1961).

    CAS  Google Scholar 

  133. R. J. Yaris, Linked cluster theorem and unitarily, J. Chem. Phys. 41, 2419–2421 (1964);

    Article  CAS  Google Scholar 

  134. R. J. Yaris, Cluster expansion and the unitary group, J. Chem. Phys. 42, 3019–3024 (1965).

    Article  CAS  Google Scholar 

  135. B. Levy and G. Berthier, Generalized Brillouin theorem for multiconfiguration S.C.F. theories, Int. J. Quantum Chem. 2, 307–314 (1968).

    Article  CAS  Google Scholar 

  136. F. Maeder and W. Kutzelnigg, Ab initio calculation of van der Waals constants (C6, C8, C10) for two-valence-electron atoms, including correlation effects, Chem. Phys. Lett. 37, 285 (1976).

    Article  CAS  Google Scholar 

  137. H. Margenau and N. R. Kestner, Theory of Intermolecular Forces, Pergamon, New York (1969/71).

    Google Scholar 

  138. N. R. Kestner, Chem. Phys. 3, 193 (1974).

    Article  Google Scholar 

  139. W. Meyer, private communication.

    Google Scholar 

  140. 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 

  141. E. Steiner, Theory of correlated wavefunctions. IV. A “configuration interaction plus perturbation” approach, J. Chem. Phys. 46, 1727–1735 (1967).

    Article  CAS  Google Scholar 

  142. K. Roby, On the theory of electron correlation in atoms and molecules. II. General cluster expansion theory and the general correlated wave function method, Int. J. Quantum Chem. 6, 101–123 (1972).

    Article  CAS  Google Scholar 

  143. E. R. Davidson and C. F. Bender, Correlation energy calculations and unitary transformations for LiH, J. Chem. Phys. 49, 465–466 (1968).

    Article  CAS  Google Scholar 

  144. W. Kutzelnigg in : Localization and Delocalization in Quantum Chemistry (O. Chalvet et al., ed.), pp. 143–153, D. Reidel Dordrecht, Holland (1975).

    Chapter  Google Scholar 

  145. I. Lindgren, The Rayleigh-Schrödinger perturbation and the linked-diagram theorem for a multiconfigurational model space, J. Phys. B 7, 2441 (1974).

    Article  CAS  Google Scholar 

  146. W. Kutzelnigg, Note on perturbation theory of electron correlation, Chem. Phys. Lett. 35, 283–285 (1975).

    Article  CAS  Google Scholar 

  147. R. F. Hausman, 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 (1975).

    Article  CAS  Google Scholar 

  148. J. H. van Vleck, Sigma-type doubling and electron spin, Phys. Rev. 33, 467–490 (1929).

    Article  CAS  Google Scholar 

  149. H. J. Werner and W. Meyer, Finite perturbation calculations for the static dipole polarizabilities of the first row atoms, Phys. Rev. 13A, 13–16 (1976).

    Article  CAS  Google Scholar 

  150. J. S. Binkley and J. A. Pople, Møller–Plessett theory for atomic ground state energies, Int. J. Quantum Chem. 9, 229–236 (1975);J. A. Pople, J. S. Binkley, and R. Seeger, Theoretical models incorporating electron correlation, Int. J. Quantum Chem., to be published.

    Article  CAS  Google Scholar 

  151. W. Meyer, Theory of self-consistent pairs. An iterative method for correlated many-electron wavefunctions, J. Chem. Phys. 64, 2901–2907 (1976).

    Article  CAS  Google Scholar 

  152. J. da Providencia and C. M. Shakin, Some aspects of short-range correlations in nuclei, Ann. Phys. 30, 95–118 (1964).

    Article  Google Scholar 

  153. W. Meyer and P. Rosmus, PNO-CI and CEPA studies of electron correlation. III. Spectroscopic constants and dipole moment functions for the ground states of the first-row and second-row diatomic hydrides, J. Chem. Phys. 63, 2356–2375 (1975).

    Article  CAS  Google Scholar 

  154. H. J. Werner and W. Meyer, PNO-CI and PNO-CEPA studies of correlation effects. V. Static dipole polarizabilities of small molecules, Mol. Phys. 31, 855–872 (1976).

    Article  CAS  Google Scholar 

  155. F. Keil and R. Ahlrichs, Theoretical study of SN2 reactions. Ab initio computation on HF and CI level, J. Am. Chem. Soc. 98, 4787–4793 (1976).

    Article  CAS  Google Scholar 

  156. K. Hoheisel and W. Kutzelnigg, Ab initio calculation including electron correlation of the structure and binding energy of BH5 and B2H7 - , J. Am. Chem. Soc. 97, 6970–6975 (1975).

    Article  CAS  Google Scholar 

  157. F. Keil and W. Kutzelnigg, The chemical bond in phosphoranes. Comparative ab initio study of PH3F2 and the hypothetical molecules NH3F2 and PH5, J.Am. Chem. Soc. 97, 3623–3632 (1975).

    Article  CAS  Google Scholar 

  158. R. Ahlrichs, Theoretical study of the H5 system, Theor. Chim. Acta 39, 149–160 (1975).

    Article  CAS  Google Scholar 

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  1. Ruhr-Universität, D463, Bochum, Germany

    Werner Kutzelnigg (Lehrstuhl für Theoretische Chemie)

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  1. University of California, Berkeley, USA

    Henry F. Schaefer III

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Kutzelnigg, W. (1977). Pair Correlation Theories. 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_5

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