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On the Wave Function of Coulson and Fischer: A Third Way in Quantum Chemistry

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Advances in the Theory of Atomic and Molecular Systems

Part of the book series: Progress in Theoretical Chemistry and Physics ((PTCP,volume 19))

Abstract

The wave function of Coulson and Fischer is examined within the context of recent developments in quantum chemistry. It is argued that the Coulson–Fischer ansatz establishes a ‘third way’ in quantum chemistry, which should not be confused with the traditional molecular orbital and valence bond formalisms. The Coulson–Fischer theory is compared with ‘modern’ valence bond approaches and also modern multireference correlation methods. Because of the non-orthogonality problem which arises when wave functions are constructed from arbitrary orbital products, the application of the Coulson–Fischer method to larger molecules necessitates the introduction of approximation schemes. It is shown that the use of hierarchical orthogonality restrictions has advantages, combining a picture of molecular electronic structure which is an accord with simple, but nevertheless empirical, ideas and concepts, with a level of computational complexity which renders practical applications to larger molecules tractable. An open collaborative virtual environment is proposed to foster further development.

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References

  1. S. Wilson, P. J. Grout, J. Maruani, G. Delgado-Barrio, P. Piecuch, eds., Frontiers in Quantum Systems in Chemistry and Physics, Progress in Theoretical Chemistry & Physics, 18, Springer (2008)

    Google Scholar 

  2. S. Wilson, I. Hubač. In: Frontiers in Quantum Systems in Chemistry and Physics, S. Wilson, P. J. Grout, J. Maruani, G. Delgado-Barrio, P. Piecuch, eds., p. 561, Springer (2008)

    Google Scholar 

  3. R. S. Mulliken, C. C. J. Roothaan, Proc. Nat. Acad. Sci. USA 45, 394 (1959)

    Article  CAS  Google Scholar 

  4. P. A. M. Dirac, Proc. Roy. Soc. A123, 714 (1929)

    Article  Google Scholar 

  5. S. F. Boys, Proc. Roy. Soc. A200, 542 (1950)

    Article  Google Scholar 

  6. R. McWeeny, Nature. 166, 21 (1950)

    Article  CAS  Google Scholar 

  7. S. Wilson, Chemistry by Computer, Plenum Press, New York (1986)

    Book  Google Scholar 

  8. G. A. Moore, Electronics 38, No. 8, April 19 (1965)

    Google Scholar 

  9. J. M. Roberts, Twentieth Century – A History of the World 1901 to present, p. 562, Allen Lane, London (1999)

    Google Scholar 

  10. W. J. Hehre, L. Radom, P. von Schleyer, J. A. Pople, Ab initio Molecular Orbital Theory, John Wiley, Chichester (1986)

    Google Scholar 

  11. L. A. Curtiss, K. Raghavachari, P. C. Redfern, V. Rassolov, J. A. Pople, J. Chem. Phys. 109, 7764 (1998)

    Article  CAS  Google Scholar 

  12. L. A. Curtiss, P. C. Redfern, K. Raghavachari, V. Rassolov, J. A. Pople, J. Chem. Phys. 110, 4703 (1999)

    Article  CAS  Google Scholar 

  13. J. A. Pople, Rev. Mod. Phys. 71, 1267 (1999)

    Article  CAS  Google Scholar 

  14. S. Wilson. In: Chemical Modelling – Applications and Theory, Specialist Periodical Report, A. Hinchliffe, ed., p. 208, Royal Society of Chemistry, London (2008)

    Google Scholar 

  15. M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert, M. S. Gordon, J. H. Jensen, S. Koseki, N. Matsunaga, K. A. Nguyen, S. Su, T. L. Windus, M. Dupuis, J. A. Montgomery, J. Comput. Chem. 14, 1347 (1993)

    Article  CAS  Google Scholar 

  16. M. S. Gordon, M. W. Schmidt. In: Theory and Applications of Computational Chemistry: the first forty years, C. E. Dykstra, G. Frenking, K. S. Kim, G. E. Scuseria, eds., p. 1167, Elsevier, Amsterdam (2005)

    Google Scholar 

  17. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery, Jr., T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez, J. A. Pople, Gaussian 03, Gaussian, Inc., Wallingford CT (2004)

    Google Scholar 

  18. C. A. Coulson, I. Fischer, Philos. Mag. 40. 386 (1949)

    Article  CAS  Google Scholar 

  19. W. Heitler, F. London, Zeits. für Physik 44, 455 (1927)

    Article  CAS  Google Scholar 

  20. F. London, Zeits. für Physik 46, 455 (1928)

    Article  CAS  Google Scholar 

  21. F. Hund, Zeits. für Physik 51, 759 (1928)

    Article  CAS  Google Scholar 

  22. F. Hund, Zeits. für Physik 73, 1 (1931)

    Google Scholar 

  23. F. Hund, Zeits. für Physik 74, 1 (1932)

    Article  CAS  Google Scholar 

  24. R. S. Mulliken, Phys. Rev. 32, 186 (1928)

    Article  CAS  Google Scholar 

  25. R. S. Mulliken, Phys. Rev. 32, 761 (1928)

    Article  CAS  Google Scholar 

  26. R. S. Mulliken, Phys. Rev. 33, 730 (1929)

    Article  CAS  Google Scholar 

  27. R. S. Mulliken, Phys. Rev. 41, 49 (1932)

    Article  CAS  Google Scholar 

  28. L. Pauling, Proc. Nat. Acad. Sci. USA 14, 359 (1928)

    Article  CAS  Google Scholar 

  29. L. Pauling, J. Am. Chem. Soc. 53, 1367 (1931)

    Article  CAS  Google Scholar 

  30. L. Pauling, J. Am. Chem. Soc. 53, 3225 (1931)

    Article  CAS  Google Scholar 

  31. L. Pauling, The Nature of the Chemical Bond, Cornell University Press, Ithaca, New York (1939)

    Google Scholar 

  32. J. C. Slater, Phys. Rev. 37, 481 (1931)

    Article  CAS  Google Scholar 

  33. J. C. Slater, Phys. Rev. 38, 1109 (1931)

    Article  CAS  Google Scholar 

  34. J. C. Slater, Phys. Rev. 41, 255 (1931)

    Article  Google Scholar 

  35. G. N. Lewis, J. Am. Chem. Soc. 38, 762 (1916)

    Article  CAS  Google Scholar 

  36. J. H. Van Vleck, A. Sherman, Rev. Mod. Phys. 7, 167 (1935)

    Article  Google Scholar 

  37. R. Hoffmann, S. Shaik, P. C. Hiberty, Accounts of Chemical Research 36, 750 (2003)

    Article  CAS  Google Scholar 

  38. S. S. Shaik, P. C. Hiberty, Helv. Chim. Acta. 86, 1063 (2003)

    Article  CAS  Google Scholar 

  39. P. Watson: A Terrible Beauty. The People and Ideas that Shaped the Modern Mind. A History, Weidenfeld & Nicolson, London (2000)

    Google Scholar 

  40. T. Hager: Force of Nature: The Life of Linus Pauling, p. 217, Simon & Schuster, New York (1995)

    Google Scholar 

  41. C. C. J. Roothaan, Rev. Mod. Phys. 23, 69 (1951)

    Article  CAS  Google Scholar 

  42. G. G. Hall, Proc. Roy. Soc. A 205, 541 (1951)

    Article  CAS  Google Scholar 

  43. J. M. Schulman, D. N. Kaufman, J. Chem. Phys. 53, 477 (1970)

    Article  CAS  Google Scholar 

  44. U. Kaldor, Phys. Rev. A 7, 427 (1973)

    Article  Google Scholar 

  45. S. Wilson, D. M. Silver, Phys. Rev. A 14, 1949 (1976)

    Article  CAS  Google Scholar 

  46. S. Wilson, Electron Correlation in Molecules, Dover, New York (2007)

    Google Scholar 

  47. S. Wang, Phys. Rev. 31, 579 (1928)

    Article  CAS  Google Scholar 

  48. S. Weinbaum, J. Chem. Phys. 1, 593 (1933)

    Article  CAS  Google Scholar 

  49. C. A. Coulson, Trans. Faraday Soc. 33, 1479 (1937)

    Article  CAS  Google Scholar 

  50. C. A. Coulson, Z. Luz, Monatshefte für Chemie 98, 62 (1967)

    Article  Google Scholar 

  51. R. McWeeny, Intern. J. Quantum Chem. 74, 87 (1999)

    Article  CAS  Google Scholar 

  52. P. B. Karadakov. In: Chemical Modelling Application and Theory, Specialist Periodical Report, A. Hinchliffe, ed., p. 312, Royal Society of Chemistry, London (2008)

    Google Scholar 

  53. G. A. Gallup, Valence Bond Methods – Theory and Applications, Cambridge University Press, Cambridge (2002)

    Book  Google Scholar 

  54. F. Weinhold, C. R. Landis, Valency and Bonding: A Natural Bond Orbital Donor-Acceptor Perspective, Cambridge University Press, Cambridge (2005)

    Book  Google Scholar 

  55. S. S. Shaik, P. C. Hiberty, A Chemist’s Guide to Valence Bond Theory, Wiley, New York (2007)

    Book  Google Scholar 

  56. S. Wilson, M. Raimondi, D. L. Cooper, eds., Quantum Theory of Chemical Bonding, Special Issue in Memory of Joseph Gerratt, International Journal of Quantum Chemistry, 74 (2) (1999)

    Google Scholar 

  57. D. L. Cooper, ed., Valence Bond Methods, Theoretical and Computational Chemistry, volume 10, Elsevier, Amsterdam (2002)

    Google Scholar 

  58. S. Wilson, P. F. Bernath, R. McWeeny, eds., Handbook of Molecular Physics and Quantum Chemistry, volume 2: Molecular Electronic Structure, John Wiley, Chichester (2003)

    Google Scholar 

  59. D. L. Cooper, P. B. Karadakov, T. Thorsteinsson, Modern Valence-Bond Description of Gas-Phase Pericyclic Reactions. In: Theoretical and Computational Chemistry, volume 10, p. 41, D. L. Cooper, ed., Elsevier, Amsterdam (2002)

    Google Scholar 

  60. H. Nakano, K. Sorakubo, K. Nakayama, K. Hirao, Complete Active Space Valence Bond (CASVB) Method and its Application to Chemical Reactions. In: Theoretical and Computational Chemistry, volume 10, p. 55, D. L. Cooper, ed., Elsevier, Amsterdam (2002)

    Google Scholar 

  61. J. H. Van Lenthe, F. Dijkstra, R. W. A. Havenith, TURTLE – A Gradient VBSCF Program. Theory and Studies of Aromaticity. In: Theoretical and Computational Chemistry, volume 10, p. 79, D. L. Cooper, ed., Elsevier, Amsterdam (2002)

    Google Scholar 

  62. W. Hiberty, Y. Mo, Z. Cao, Q. Zhang, A Spin-Free Approach for Valence Bond Theory and its Applications. In: Theoretical and Computational Chemistry, volume 10, p. 143, D. L. Cooper, ed., Elsevier, Amsterdam (2002)

    Google Scholar 

  63. P. C. Hiberty, S. Shaik, bovb – A Valence Bond Method Incorporating Static and Dynamic Electon Correlation Effects. In: Theoretical and Computational Chemistry, volume 10, p. 187, D. L. Cooper, ed., Elsevier, Amsterdam (2002)

    Google Scholar 

  64. J. J. W. McDouall, The Biorthogonal Valence Bond Method. In: Theoretical and Computational Chemistry, volume 10, p. 227, Ed: D. L. Cooper, Elsevier, Amsterdam (2002)

    Google Scholar 

  65. M. Sironi, M. Raimondi, R. Martinazzo, F. Gianturco, D. L. Cooper, Recent Developments of the SCVB Method. In: Theoretical and Computational Chemistry, volume 10, p. 261, D. L. Cooper, ed., Elsevier, Amsterdam (2002)

    Google Scholar 

  66. R. McWeeny, J. Li, Valence Bond Theory Using Symmetric Group Methods. In: Handbook of Molecular Physics and Quantum Chemistry, volume 2: Molecular Electronic Structure, chapter 10, p. 122, S. Wilson, P. F. Bernath, R. McWeeny (eds.) Wiley, Chichester (2003)

    Google Scholar 

  67. M. Sironi, D. L. Cooper, M. Raimondi, Valence Bond Theory: Determinantal Methods. In: Handbook of Molecular Physics and Quantum Chemistry, volume 2: Molecular Electronic Structure, chapter 11, p. 140, S. Wilson, P. F. Bernath, R. McWeeny, eds., John Wiley, Chichester (2003)

    Google Scholar 

  68. J. Gerratt, D. L. Cooper, P. Karaddakov, M. Raimondi, Spin-coupled Theory. In: Handbook of Molecular Physics and Quantum Chemistry, volume 2: Molecular Electronic Structure, chapter 12, p. 148, S. Wilson, P. F. Bernath, R. McWeeny, ed., John Wiley, Chichester (2003)

    Google Scholar 

  69. D. L. Cooper, Valence Bond Theory: Other Methods. In: Handbook of Molecular Physics and Quantum Chemistry, volume 2: Molecular Electronic Structure, chapter 13, p. 169, S. Wilson, P. F. Bernath, R. McWeeny, eds., John Wiley, Chichester (2003)

    Google Scholar 

  70. J. Gerratt, W. N. Lipscomb, Proc. Nat. Acad. Sci. 59, 332 (1968)

    Article  CAS  Google Scholar 

  71. J. Gerratt, W. N. Lipscomb, Intern. J. Quantum Chem. 74, 83 (1999)

    Article  CAS  Google Scholar 

  72. J. Gerratt, Adv. At. Mol. Phys. 7, 141 (1971)

    Article  Google Scholar 

  73. J. Gerratt, Specialist Periodical Reports: Theoretical Chemistry 1, 60 (1974)

    CAS  Google Scholar 

  74. S. Wilson, J. Gerratt, In: Proceedings of the src Atlas Symposium: Quantum Chemistry – The State of the Art, V. R. Saunders, J. Brown, eds., St. Catherine’s College, Oxford, p. 109, Atlas Computer Laboratory, Science Research Council, Chilton, Oxfordshire (1974)

    Google Scholar 

  75. N. C. Pyper, J. Gerratt. In: Proceedings of the src Atlas Symposium: Quantum Chemistry – The State of the Art, V. R. Saunders, J. Brown, eds., St. Catherine’s College, Oxford, p. 93, Atlas Computer Laboratory, Science Research Council, Chilton, Oxfordshire (1974)

    Google Scholar 

  76. S. Wilson, J. Gerratt, Molec. Phys. 30, 765 (1975)

    Article  CAS  Google Scholar 

  77. S. Wilson, J. Gerratt, Molec. Phys. 30, 777 (1975)

    Article  CAS  Google Scholar 

  78. S. Wilson, J. Gerratt, Molec. Phys. 30, 789 (1975)

    Article  CAS  Google Scholar 

  79. S. Wilson, A Self-Consistent Group Function Model for Molecular Wave Functions, doctoral dissertation, University of Bristol (1975)

    Google Scholar 

  80. N. C. Pyper, J. Gerratt, Proc. Roy. Soc. (London) A 355, 407 (1977)

    Article  Google Scholar 

  81. D. L. Cooper, J. Gerratt, M. Raimondi, Adv. Chem. Phys. 69, 319 (1987)

    CAS  Google Scholar 

  82. D. L. Cooper, J. Gerratt, M. Raimondi, Int. Rev. Phys. Chem. 7, 59 (1988)

    Article  CAS  Google Scholar 

  83. J. Gerratt, D. L. Cooper, M. Raimondi. In: Valence Bond and Chemical Structure, D. J. Klein, N. Trinajstic, eds., Elsevier, Amsterdam (1990)

    Google Scholar 

  84. D. L. Cooper, J. Gerratt, M. Raimondi, Chem. Rev. 91, 929 (1991)

    Article  CAS  Google Scholar 

  85. J. Gerratt, D. L. Cooper, P. B. Karadakov, M. Raimondi, Chem. Soc. Rev. 26, 87 (1997)

    Article  CAS  Google Scholar 

  86. P. B. Karadakov, Progr. Phys. Chem. 94, 2 (1998)

    Google Scholar 

  87. A. C. Hurley, J. E. Lennard-Jones, J. A. Pople, Proc. Roy. Soc. (London) A220, 446 (1953)

    Article  Google Scholar 

  88. A. C. Hurley, Proc. Roy. Soc. (London) A235, 224 (1956)

    Article  Google Scholar 

  89. W. J. Hunt, P. J. Hay, W. A. Goddard, J. Chem. Phys. 57, 738 (1972)

    Article  Google Scholar 

  90. A. C. Wahl, G. Das. In: Methods of electronic structure theory, H. F. Schaefer iii, ed., Plenum, New York (1977)

    Google Scholar 

  91. A. C. Wahl, G. Das, Adv. Quantum Chem. 5, 261 (1970)

    Article  CAS  Google Scholar 

  92. K. Ruedenberg, K. R. Sundbarg. In: Quantum Science, J. L. Calais, O. Goscinski, J. Linderberg, Y. Ohrn, eds., Plenum, New York (1976)

    Google Scholar 

  93. K. Ruedenberg, M. W. Schmidt, M. M. Gilbert, S. T. Elbert, Chem. Phys. 71, 41 (1982)

    Article  CAS  Google Scholar 

  94. B. O. Roos, P. R. Taylor, P. E. M. Siegbahn, Chem. Phys. 48, 157 (1980)

    Article  CAS  Google Scholar 

  95. I. Hubač, S. Wilson, Brillouin-Wigner methods for many-body systems, Progress in Theoretical Chemistry and Physics, Springer (in press)

    Google Scholar 

  96. W. Kolos, C. C. J. Roothaan, Rev. Mod. Phys. 32, 219 (1960)

    Article  CAS  Google Scholar 

  97. E. P. Wigner, Group Theory and its Application to the Quantum Mechanics of Atomic Spectra, Academic Press, New York (1959)

    Google Scholar 

  98. P. B. Karadakov, Spin Functions. In: Handbook of Molecular Physics and Quantum Chemistry, volume 2: Molecular Electronic Structure, chapter 3, p. 25, S. Wilson, P. F. Bernath, R. McWeeny, eds., John Wiley, Chichester (2003)

    Google Scholar 

  99. P. B. Karadakov, Spatial Wavefunctions, In: Handbook of Molecular Physics and Quantum Chemistry, volume 2: Molecular Electronic Structure, chapter 4, p. 33, S. Wilson, P. F. Bernath, R. McWeeny, eds., John Wiley, Chichester (2003)

    Google Scholar 

  100. I. G. Kaplan, The Pauli Principle, In: Handbook of Molecular Physics and Quantum Chemistry, volume 2: Molecular Electronic Structure, chapter 2, p. 15, S. Wilson, P. F. Bernath, R. McWeeny, eds., John Wiley, Chichester (2003)

    Google Scholar 

  101. H. A. Jahn, Phys. Rev. 96, 989 (1954)

    Article  Google Scholar 

  102. G. A. Gallup, Adv. Quantum Chem. 7, 113 (1973)

    Article  CAS  Google Scholar 

  103. G. A. Gallup, Adv. Quantum Chem. 16, 229 (1982)

    Article  CAS  Google Scholar 

  104. W. A. Goddard iii, Phys. Rev. 157, 73 (1967); ibid. 157, 81 (1967)

    Article  CAS  Google Scholar 

  105. W. A. Goddard iii, J. Chem. Phys. 48, 450 (1968); ibid. 48, 5377 (1968)

    Article  CAS  Google Scholar 

  106. S. J. McNicholas, F. R. Manby, Intern. J. Quantum Chem. 74, 97 (1999)

    Article  CAS  Google Scholar 

  107. S. Wilson, Intern. J. Quantum Chem. 74, 135 (1999)

    Article  CAS  Google Scholar 

  108. J. Barnes, P. Hut, Nature 324, 446 (1986)

    Article  Google Scholar 

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  1. Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, OX1 3QZ, Oxford, London, England

    Stephen Wilson

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  1. Department of Chemistry, Michigan State University, 48824, East Lansing, MI, USA

    Piotr Piecuch

  2. Laboratoire de Chimie Physique CNRS and UPMC, 11 Rue Pierre et Marie Curie, F-75005, Paris, France

    Jean Maruani

  3. Instituto de Física Fundamental, CSIC, Serrano 123, E-28006, Madrid, Spain

    Gerardo Delgado-Barrio

  4. Physical & Theoretical Chemistry Laboratry, University of Oxford, South Parks Road, OX1 3QZ, Oxford, UK

    Stephen Wilson

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Wilson, S. (2009). On the Wave Function of Coulson and Fischer: A Third Way in Quantum Chemistry. In: Piecuch, P., Maruani, J., Delgado-Barrio, G., Wilson, S. (eds) Advances in the Theory of Atomic and Molecular Systems. Progress in Theoretical Chemistry and Physics, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2596-8_13

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