Natural resonance theory: I. General formalism

Journal of Computational Chemistry

Volumn 19, Issue 6, 1998, Pages 593-609

  Glendening, E D ^a,b   Weinhold, F ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b INDIANA STATE UNIVERSITY   (United States)

Author keywords

Natural bond orbitals; Natural resonance theory; Resonance theory

Indexed keywords

EID: 1642469600     PISSN: 01928651     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1096-987X(19980430)19:6<593::AID-JCC3>3.0.CO;2-M     Document Type: Article

References (71)

1. L. Pauling, Proc. R. Soc. London, A356, 433 (1993).
2. L. Pauling and G. W. Wheland, J. Chem. Phys., 1, 362 (1933); G. W. Wheland and L. Pauling, J. Am. Chem. Soc., 57, 2086 (1935); see also reference 12.
3. L. Pauling and G. W. Wheland, J. Chem. Phys., 1, 362 (1933); G. W. Wheland and L. Pauling, J. Am. Chem. Soc., 57, 2086 (1935); see also reference 12.
4. L. Pauling, Nature of the Chemical Bond, 3rd ed., Cornell University Press, Ithaca, NY, 1960.
5. G. W. Wheland, The Theory of Resonance and its Applications to Organic Chemistry, Wiley, New York, 1955.
6. Pauling himself acknowledged the need for a more quantitative formulation of resonance theory. For example, he states (reference 3, p. 569, in a section entitled "The Further Development and Application of the Concept of Resonance") that "The applications of the idea of resonance that have been made during the last thirty years are in the main qualitative in nature. This represents only the first step, which should be followed by more refined treatments with quantitative significance."
7. Reference 3, p. 232.
8. L. Pauling, L. O. Brockway, and J. Y. Beach, J. Am. Chem. Soc., 57, 2705 (1935).
9. Pauling (reference 3, pp. 219-220) states that "The theory of resonance is essentially a chemical theory (an empirical theory, obtained largely by induction from the results of chemical experiments). Classical structure theory was developed purely from chemical facts, without any help from physics. The theory of resonance was also well on its way toward formulation before quantum mechanics was discovered."
10. J. W. Armit and R. Robinson, J. Chem. Soc., 121, 827 (1922); J. Allen, A. E. Oxford, and J. C. Smith, J. Chem. Soc., 129, 401 (1926); R. Robinson, Outline of an Electrochemical [Electronic] Theory of the Course of Organic Reactions; Institute of Chemistry of Great Britain and Ireland, London, 1932.
11. J. W. Armit and R. Robinson, J. Chem. Soc., 121, 827 (1922); J. Allen, A. E. Oxford, and J. C. Smith, J. Chem. Soc., 129, 401 (1926); R. Robinson, Outline of an Electrochemical [Electronic] Theory of the Course of Organic Reactions; Institute of Chemistry of Great Britain and Ireland, London, 1932.
12. J. W. Armit and R. Robinson, J. Chem. Soc., 121, 827 (1922); J. Allen, A. E. Oxford, and J. C. Smith, J. Chem. Soc., 129, 401 (1926); R. Robinson, Outline of an Electrochemical [Electronic] Theory of the Course of Organic Reactions; Institute of Chemistry of Great Britain and Ireland, London, 1932.
13. C. K. Ingold, J. Chem. Soc., 121, 1133 (1922); C. K. Ingold and E. H. Ingold, J. Chem. Soc., 129, 1310 (1926); C. K. Ingold, J. Chem. Soc., 1933, 1120 (1933).
14. C. K. Ingold, J. Chem. Soc., 121, 1133 (1922); C. K. Ingold and E. H. Ingold, J. Chem. Soc., 129, 1310 (1926); C. K. Ingold, J. Chem. Soc., 1933, 1120 (1933).
15. C. K. Ingold, J. Chem. Soc., 121, 1133 (1922); C. K. Ingold and E. H. Ingold, J. Chem. Soc., 129, 1310 (1926); C. K. Ingold, J. Chem. Soc., 1933, 1120 (1933).
16. For additional discussion of the historical background of resonance theory, we A. R. Todd and J. W. Cornforth, Biogr. Mem. Fellows R. Soc. London, 22, 415 (1977) and references 1 and 3 (p. 184).
17. W. Heitler and F. London, Z. Phys., 44, 455 (1927); J. C. Slater, Phys. Rev., 37, 481 (1931), 38, 1109 (1931); L. Pauling, J. Am. Chem. Soc., 53, 1367 (1931), 53, 3225 (1932), 54, 998, 3570, (1932).
18. W. Heitler and F. London, Z. Phys., 44, 455 (1927); J. C. Slater, Phys. Rev., 37, 481 (1931), 38, 1109 (1931); L. Pauling, J. Am. Chem. Soc., 53, 1367 (1931), 53, 3225 (1932), 54, 998, 3570, (1932).
19. W. Heitler and F. London, Z. Phys., 44, 455 (1927); J. C. Slater, Phys. Rev., 37, 481 (1931), 38, 1109 (1931); L. Pauling, J. Am. Chem. Soc., 53, 1367 (1931), 53, 3225 (1932), 54, 998, 3570, (1932).
20. W. Heitler and F. London, Z. Phys., 44, 455 (1927); J. C. Slater, Phys. Rev., 37, 481 (1931), 38, 1109 (1931); L. Pauling, J. Am. Chem. Soc., 53, 1367 (1931), 53, 3225 (1932), 54, 998, 3570, (1932).
21. W. Heitler and F. London, Z. Phys., 44, 455 (1927); J. C. Slater, Phys. Rev., 37, 481 (1931), 38, 1109 (1931); L. Pauling, J. Am. Chem. Soc., 53, 1367 (1931), 53, 3225 (1932), 54, 998, 3570, (1932).
22. W. Heitler and F. London, Z. Phys., 44, 455 (1927); J. C. Slater, Phys. Rev., 37, 481 (1931), 38, 1109 (1931); L. Pauling, J. Am. Chem. Soc., 53, 1367 (1931), 53, 3225 (1932), 54, 998, 3570, (1932).
23. A useful historical overview of VB/resonance concepts and applications is given by D. J. Klein and N. Trinajstic, J. Chem. Ed., 67, 633 (1990). For representative works pertaining to (a) projecting VB-type structures from MO or MO-CI wave functions or density matrices, (b) VB-mixing descriptions of reactivity and properties, (c) classical or self-consistent VB computational methods, or (d) graph-theoretic methods, see: (a) M. Craig and R. S. Berry, J. Am. Chem. Soc., 89, 2801 (1967); P. C. Hiberty and C. Leforestier, J. Am. Chem. Soc., 100, 2012 (1978); P. C. Hiberty and G. Ohanessian, Int. J. Quant. Chem., 27, 259 (1978); P. C. Hiberty, Int. J. Quant. Chem., 19, 259 (1981); S. S. Shaik, J. Am. Chem. Soc., 103, 3692 (1981); P. C. Hiberty and G. Ohanessian, J. Am. Chem. Soc,. 104, 66 (1982); P. C. Hiberty, G. Ohanessian, and F. Delbecq, J. Am. Chem. Soc., 107, 3095 (1985); R. M. Parrondo, P. Karafiloglou, and E. Sánchez Marcos, Int. J. Quantum Chem., 52, 1127 (1994). (b) S. S. Shaik, H. B. Schlegel, and S. T. Wolfe, Theoretical Aspects of Physical Organic Chemistry, Wiley, New York, 1992; A. Pross, Theoretical and Physical Principles of Organic Reactivity, Wiley, New York, 1995; N. D. Epiotis, Lecture Notes in Chemistry, Vol. 34, American Chemical Society, New York, 1983; F. Bernardi and M. A. Robb, J. Am. Chem. Soc., 106, 54 (1984); Y. Apeloig and D. Arad, J. Am. Chem. Soc., 108, 3241 (1986); P. W. Anderson, Science, 235, 1196 (1987); F. Bernardi, A. Bottoni, M. Olivucci, A. Venturini, and M. A. Robb, J. Chem. Soc. Faraday Trans., 90, 1617 (1994). (c) G. A. Gallup, R. L. Vance, J. R. Collins, and J. M. Norbeck, Adv. Quantum Chem., 16, 229 (1982); D. L. Cooper, J. Gerratt, and M. Raimondi, Nature, 323, 699 (1986), Adv. Chem. Phys., 69, 319 (1987); F. W. Bobrowitz and W. A. Goddard, in H. F. Schaefer (ed.), Methods of Electronic Structure Theory, Vol. 3, Plenum, New York, 1977, p. 72; A. F. Voter and W. A. Goddard, J. Am. Chem. Soc., 108, 2830 (1986); J. H. Van Lanthe, J. Verbeek, and P. Pulay, Mol. Phys., 73, 1159 (1991). (d) S. J. Cyvin and I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons, Springer, Berlin, 1988.
24. A useful historical overview of VB/resonance concepts and applications is given by D. J. Klein and N. Trinajstic, J. Chem. Ed., 67, 633 (1990). For representative works pertaining to (a) projecting VB-type structures from MO or MO-CI wave functions or density matrices, (b) VB-mixing descriptions of reactivity and properties, (c) classical or self-consistent VB computational methods, or (d) graph-theoretic methods, see: (a) M. Craig and R. S. Berry, J. Am. Chem. Soc., 89, 2801 (1967); P. C. Hiberty and C. Leforestier, J. Am. Chem. Soc., 100, 2012 (1978); P. C. Hiberty and G. Ohanessian, Int. J. Quant. Chem., 27, 259 (1978); P. C. Hiberty, Int. J. Quant. Chem., 19, 259 (1981); S. S. Shaik, J. Am. Chem. Soc., 103, 3692 (1981); P. C. Hiberty and G. Ohanessian, J. Am. Chem. Soc,. 104, 66 (1982); P. C. Hiberty, G. Ohanessian, and F. Delbecq, J. Am. Chem. Soc., 107, 3095 (1985); R. M. Parrondo, P. Karafiloglou, and E. Sánchez Marcos, Int. J. Quantum Chem., 52, 1127 (1994). (b) S. S. Shaik, H. B. Schlegel, and S. T. Wolfe, Theoretical Aspects of Physical Organic Chemistry, Wiley, New York, 1992; A. Pross, Theoretical and Physical Principles of Organic Reactivity, Wiley, New York, 1995; N. D. Epiotis, Lecture Notes in Chemistry, Vol. 34, American Chemical Society, New York, 1983; F. Bernardi and M. A. Robb, J. Am. Chem. Soc., 106, 54 (1984); Y. Apeloig and D. Arad, J. Am. Chem. Soc., 108, 3241 (1986); P. W. Anderson, Science, 235, 1196 (1987); F. Bernardi, A. Bottoni, M. Olivucci, A. Venturini, and M. A. Robb, J. Chem. Soc. Faraday Trans., 90, 1617 (1994). (c) G. A. Gallup, R. L. Vance, J. R. Collins, and J. M. Norbeck, Adv. Quantum Chem., 16, 229 (1982); D. L. Cooper, J. Gerratt, and M. Raimondi, Nature, 323, 699 (1986), Adv. Chem. Phys., 69, 319 (1987); F. W. Bobrowitz and W. A. Goddard, in H. F. Schaefer (ed.), Methods of Electronic Structure Theory, Vol. 3, Plenum, New York, 1977, p. 72; A. F. Voter and W. A. Goddard, J. Am. Chem. Soc., 108, 2830 (1986); J. H. Van Lanthe, J. Verbeek, and P. Pulay, Mol. Phys., 73, 1159 (1991). (d) S. J. Cyvin and I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons, Springer, Berlin, 1988.
25. A useful historical overview of VB/resonance concepts and applications is given by D. J. Klein and N. Trinajstic, J. Chem. Ed., 67, 633 (1990). For representative works pertaining to (a) projecting VB-type structures from MO or MO-CI wave functions or density matrices, (b) VB-mixing descriptions of reactivity and properties, (c) classical or self-consistent VB computational methods, or (d) graph-theoretic methods, see: (a) M. Craig and R. S. Berry, J. Am. Chem. Soc., 89, 2801 (1967); P. C. Hiberty and C. Leforestier, J. Am. Chem. Soc., 100, 2012 (1978); P. C. Hiberty and G. Ohanessian, Int. J. Quant. Chem., 27, 259 (1978); P. C. Hiberty, Int. J. Quant. Chem., 19, 259 (1981); S. S. Shaik, J. Am. Chem. Soc., 103, 3692 (1981); P. C. Hiberty and G. Ohanessian, J. Am. Chem. Soc,. 104, 66 (1982); P. C. Hiberty, G. Ohanessian, and F. Delbecq, J. Am. Chem. Soc., 107, 3095 (1985); R. M. Parrondo, P. Karafiloglou, and E. Sánchez Marcos, Int. J. Quantum Chem., 52, 1127 (1994). (b) S. S. Shaik, H. B. Schlegel, and S. T. Wolfe, Theoretical Aspects of Physical Organic Chemistry, Wiley, New York, 1992; A. Pross, Theoretical and Physical Principles of Organic Reactivity, Wiley, New York, 1995; N. D. Epiotis, Lecture Notes in Chemistry, Vol. 34, American Chemical Society, New York, 1983; F. Bernardi and M. A. Robb, J. Am. Chem. Soc., 106, 54 (1984); Y. Apeloig and D. Arad, J. Am. Chem. Soc., 108, 3241 (1986); P. W. Anderson, Science, 235, 1196 (1987); F. Bernardi, A. Bottoni, M. Olivucci, A. Venturini, and M. A. Robb, J. Chem. Soc. Faraday Trans., 90, 1617 (1994). (c) G. A. Gallup, R. L. Vance, J. R. Collins, and J. M. Norbeck, Adv. Quantum Chem., 16, 229 (1982); D. L. Cooper, J. Gerratt, and M. Raimondi, Nature, 323, 699 (1986), Adv. Chem. Phys., 69, 319 (1987); F. W. Bobrowitz and W. A. Goddard, in H. F. Schaefer (ed.), Methods of Electronic Structure Theory, Vol. 3, Plenum, New York, 1977, p. 72; A. F. Voter and W. A. Goddard, J. Am. Chem. Soc., 108, 2830 (1986); J. H. Van Lanthe, J. Verbeek, and P. Pulay, Mol. Phys., 73, 1159 (1991). (d) S. J. Cyvin and I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons, Springer, Berlin, 1988.
26. A useful historical overview of VB/resonance concepts and applications is given by D. J. Klein and N. Trinajstic, J. Chem. Ed., 67, 633 (1990). For representative works pertaining to (a) projecting VB-type structures from MO or MO-CI wave functions or density matrices, (b) VB-mixing descriptions of reactivity and properties, (c) classical or self-consistent VB computational methods, or (d) graph-theoretic methods, see: (a) M. Craig and R. S. Berry, J. Am. Chem. Soc., 89, 2801 (1967); P. C. Hiberty and C. Leforestier, J. Am. Chem. Soc., 100, 2012 (1978); P. C. Hiberty and G. Ohanessian, Int. J. Quant. Chem., 27, 259 (1978); P. C. Hiberty, Int. J. Quant. Chem., 19, 259 (1981); S. S. Shaik, J. Am. Chem. Soc., 103, 3692 (1981); P. C. Hiberty and G. Ohanessian, J. Am. Chem. Soc,. 104, 66 (1982); P. C. Hiberty, G. Ohanessian, and F. Delbecq, J. Am. Chem. Soc., 107, 3095 (1985); R. M. Parrondo, P. Karafiloglou, and E. Sánchez Marcos, Int. J. Quantum Chem., 52, 1127 (1994). (b) S. S. Shaik, H. B. Schlegel, and S. T. Wolfe, Theoretical Aspects of Physical Organic Chemistry, Wiley, New York, 1992; A. Pross, Theoretical and Physical Principles of Organic Reactivity, Wiley, New York, 1995; N. D. Epiotis, Lecture Notes in Chemistry, Vol. 34, American Chemical Society, New York, 1983; F. Bernardi and M. A. Robb, J. Am. Chem. Soc., 106, 54 (1984); Y. Apeloig and D. Arad, J. Am. Chem. Soc., 108, 3241 (1986); P. W. Anderson, Science, 235, 1196 (1987); F. Bernardi, A. Bottoni, M. Olivucci, A. Venturini, and M. A. Robb, J. Chem. Soc. Faraday Trans., 90, 1617 (1994). (c) G. A. Gallup, R. L. Vance, J. R. Collins, and J. M. Norbeck, Adv. Quantum Chem., 16, 229 (1982); D. L. Cooper, J. Gerratt, and M. Raimondi, Nature, 323, 699 (1986), Adv. Chem. Phys., 69, 319 (1987); F. W. Bobrowitz and W. A. Goddard, in H. F. Schaefer (ed.), Methods of Electronic Structure Theory, Vol. 3, Plenum, New York, 1977, p. 72; A. F. Voter and W. A. Goddard, J. Am. Chem. Soc., 108, 2830 (1986); J. H. Van Lanthe, J. Verbeek, and P. Pulay, Mol. Phys., 73, 1159 (1991). (d) S. J. Cyvin and I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons, Springer, Berlin, 1988.
27. A useful historical overview of VB/resonance concepts and applications is given by D. J. Klein and N. Trinajstic, J. Chem. Ed., 67, 633 (1990). For representative works pertaining to (a) projecting VB-type structures from MO or MO-CI wave functions or density matrices, (b) VB-mixing descriptions of reactivity and properties, (c) classical or self-consistent VB computational methods, or (d) graph-theoretic methods, see: (a) M. Craig and R. S. Berry, J. Am. Chem. Soc., 89, 2801 (1967); P. C. Hiberty and C. Leforestier, J. Am. Chem. Soc., 100, 2012 (1978); P. C. Hiberty and G. Ohanessian, Int. J. Quant. Chem., 27, 259 (1978); P. C. Hiberty, Int. J. Quant. Chem., 19, 259 (1981); S. S. Shaik, J. Am. Chem. Soc., 103, 3692 (1981); P. C. Hiberty and G. Ohanessian, J. Am. Chem. Soc,. 104, 66 (1982); P. C. Hiberty, G. Ohanessian, and F. Delbecq, J. Am. Chem. Soc., 107, 3095 (1985); R. M. Parrondo, P. Karafiloglou, and E. Sánchez Marcos, Int. J. Quantum Chem., 52, 1127 (1994). (b) S. S. Shaik, H. B. Schlegel, and S. T. Wolfe, Theoretical Aspects of Physical Organic Chemistry, Wiley, New York, 1992; A. Pross, Theoretical and Physical Principles of Organic Reactivity, Wiley, New York, 1995; N. D. Epiotis, Lecture Notes in Chemistry, Vol. 34, American Chemical Society, New York, 1983; F. Bernardi and M. A. Robb, J. Am. Chem. Soc., 106, 54 (1984); Y. Apeloig and D. Arad, J. Am. Chem. Soc., 108, 3241 (1986); P. W. Anderson, Science, 235, 1196 (1987); F. Bernardi, A. Bottoni, M. Olivucci, A. Venturini, and M. A. Robb, J. Chem. Soc. Faraday Trans., 90, 1617 (1994). (c) G. A. Gallup, R. L. Vance, J. R. Collins, and J. M. Norbeck, Adv. Quantum Chem., 16, 229 (1982); D. L. Cooper, J. Gerratt, and M. Raimondi, Nature, 323, 699 (1986), Adv. Chem. Phys., 69, 319 (1987); F. W. Bobrowitz and W. A. Goddard, in H. F. Schaefer (ed.), Methods of Electronic Structure Theory, Vol. 3, Plenum, New York, 1977, p. 72; A. F. Voter and W. A. Goddard, J. Am. Chem. Soc., 108, 2830 (1986); J. H. Van Lanthe, J. Verbeek, and P. Pulay, Mol. Phys., 73, 1159 (1991). (d) S. J. Cyvin and I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons, Springer, Berlin, 1988.
28. A useful historical overview of VB/resonance concepts and applications is given by D. J. Klein and N. Trinajstic, J. Chem. Ed., 67, 633 (1990). For representative works pertaining to (a) projecting VB-type structures from MO or MO-CI wave functions or density matrices, (b) VB-mixing descriptions of reactivity and properties, (c) classical or self-consistent VB computational methods, or (d) graph-theoretic methods, see: (a) M. Craig and R. S. Berry, J. Am. Chem. Soc., 89, 2801 (1967); P. C. Hiberty and C. Leforestier, J. Am. Chem. Soc., 100, 2012 (1978); P. C. Hiberty and G. Ohanessian, Int. J. Quant. Chem., 27, 259 (1978); P. C. Hiberty, Int. J. Quant. Chem., 19, 259 (1981); S. S. Shaik, J. Am. Chem. Soc., 103, 3692 (1981); P. C. Hiberty and G. Ohanessian, J. Am. Chem. Soc,. 104, 66 (1982); P. C. Hiberty, G. Ohanessian, and F. Delbecq, J. Am. Chem. Soc., 107, 3095 (1985); R. M. Parrondo, P. Karafiloglou, and E. Sánchez Marcos, Int. J. Quantum Chem., 52, 1127 (1994). (b) S. S. Shaik, H. B. Schlegel, and S. T. Wolfe, Theoretical Aspects of Physical Organic Chemistry, Wiley, New York, 1992; A. Pross, Theoretical and Physical Principles of Organic Reactivity, Wiley, New York, 1995; N. D. Epiotis, Lecture Notes in Chemistry, Vol. 34, American Chemical Society, New York, 1983; F. Bernardi and M. A. Robb, J. Am. Chem. Soc., 106, 54 (1984); Y. Apeloig and D. Arad, J. Am. Chem. Soc., 108, 3241 (1986); P. W. Anderson, Science, 235, 1196 (1987); F. Bernardi, A. Bottoni, M. Olivucci, A. Venturini, and M. A. Robb, J. Chem. Soc. Faraday Trans., 90, 1617 (1994). (c) G. A. Gallup, R. L. Vance, J. R. Collins, and J. M. Norbeck, Adv. Quantum Chem., 16, 229 (1982); D. L. Cooper, J. Gerratt, and M. Raimondi, Nature, 323, 699 (1986), Adv. Chem. Phys., 69, 319 (1987); F. W. Bobrowitz and W. A. Goddard, in H. F. Schaefer (ed.), Methods of Electronic Structure Theory, Vol. 3, Plenum, New York, 1977, p. 72; A. F. Voter and W. A. Goddard, J. Am. Chem. Soc., 108, 2830 (1986); J. H. Van Lanthe, J. Verbeek, and P. Pulay, Mol. Phys., 73, 1159 (1991). (d) S. J. Cyvin and I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons, Springer, Berlin, 1988.
29. A useful historical overview of VB/resonance concepts and applications is given by D. J. Klein and N. Trinajstic, J. Chem. Ed., 67, 633 (1990). For representative works pertaining to (a) projecting VB-type structures from MO or MO-CI wave functions or density matrices, (b) VB-mixing descriptions of reactivity and properties, (c) classical or self-consistent VB computational methods, or (d) graph-theoretic methods, see: (a) M. Craig and R. S. Berry, J. Am. Chem. Soc., 89, 2801 (1967); P. C. Hiberty and C. Leforestier, J. Am. Chem. Soc., 100, 2012 (1978); P. C. Hiberty and G. Ohanessian, Int. J. Quant. Chem., 27, 259 (1978); P. C. Hiberty, Int. J. Quant. Chem., 19, 259 (1981); S. S. Shaik, J. Am. Chem. Soc., 103, 3692 (1981); P. C. Hiberty and G. Ohanessian, J. Am. Chem. Soc,. 104, 66 (1982); P. C. Hiberty, G. Ohanessian, and F. Delbecq, J. Am. Chem. Soc., 107, 3095 (1985); R. M. Parrondo, P. Karafiloglou, and E. Sánchez Marcos, Int. J. Quantum Chem., 52, 1127 (1994). (b) S. S. Shaik, H. B. Schlegel, and S. T. Wolfe, Theoretical Aspects of Physical Organic Chemistry, Wiley, New York, 1992; A. Pross, Theoretical and Physical Principles of Organic Reactivity, Wiley, New York, 1995; N. D. Epiotis, Lecture Notes in Chemistry, Vol. 34, American Chemical Society, New York, 1983; F. Bernardi and M. A. Robb, J. Am. Chem. Soc., 106, 54 (1984); Y. Apeloig and D. Arad, J. Am. Chem. Soc., 108, 3241 (1986); P. W. Anderson, Science, 235, 1196 (1987); F. Bernardi, A. Bottoni, M. Olivucci, A. Venturini, and M. A. Robb, J. Chem. Soc. Faraday Trans., 90, 1617 (1994). (c) G. A. Gallup, R. L. Vance, J. R. Collins, and J. M. Norbeck, Adv. Quantum Chem., 16, 229 (1982); D. L. Cooper, J. Gerratt, and M. Raimondi, Nature, 323, 699 (1986), Adv. Chem. Phys., 69, 319 (1987); F. W. Bobrowitz and W. A. Goddard, in H. F. Schaefer (ed.), Methods of Electronic Structure Theory, Vol. 3, Plenum, New York, 1977, p. 72; A. F. Voter and W. A. Goddard, J. Am. Chem. Soc., 108, 2830 (1986); J. H. Van Lanthe, J. Verbeek, and P. Pulay, Mol. Phys., 73, 1159 (1991). (d) S. J. Cyvin and I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons, Springer, Berlin, 1988.
30. A useful historical overview of VB/resonance concepts and applications is given by D. J. Klein and N. Trinajstic, J. Chem. Ed., 67, 633 (1990). For representative works pertaining to (a) projecting VB-type structures from MO or MO-CI wave functions or density matrices, (b) VB-mixing descriptions of reactivity and properties, (c) classical or self-consistent VB computational methods, or (d) graph-theoretic methods, see: (a) M. Craig and R. S. Berry, J. Am. Chem. Soc., 89, 2801 (1967); P. C. Hiberty and C. Leforestier, J. Am. Chem. Soc., 100, 2012 (1978); P. C. Hiberty and G. Ohanessian, Int. J. Quant. Chem., 27, 259 (1978); P. C. Hiberty, Int. J. Quant. Chem., 19, 259 (1981); S. S. Shaik, J. Am. Chem. Soc., 103, 3692 (1981); P. C. Hiberty and G. Ohanessian, J. Am. Chem. Soc,. 104, 66 (1982); P. C. Hiberty, G. Ohanessian, and F. Delbecq, J. Am. Chem. Soc., 107, 3095 (1985); R. M. Parrondo, P. Karafiloglou, and E. Sánchez Marcos, Int. J. Quantum Chem., 52, 1127 (1994). (b) S. S. Shaik, H. B. Schlegel, and S. T. Wolfe, Theoretical Aspects of Physical Organic Chemistry, Wiley, New York, 1992; A. Pross, Theoretical and Physical Principles of Organic Reactivity, Wiley, New York, 1995; N. D. Epiotis, Lecture Notes in Chemistry, Vol. 34, American Chemical Society, New York, 1983; F. Bernardi and M. A. Robb, J. Am. Chem. Soc., 106, 54 (1984); Y. Apeloig and D. Arad, J. Am. Chem. Soc., 108, 3241 (1986); P. W. Anderson, Science, 235, 1196 (1987); F. Bernardi, A. Bottoni, M. Olivucci, A. Venturini, and M. A. Robb, J. Chem. Soc. Faraday Trans., 90, 1617 (1994). (c) G. A. Gallup, R. L. Vance, J. R. Collins, and J. M. Norbeck, Adv. Quantum Chem., 16, 229 (1982); D. L. Cooper, J. Gerratt, and M. Raimondi, Nature, 323, 699 (1986), Adv. Chem. Phys., 69, 319 (1987); F. W. Bobrowitz and W. A. Goddard, in H. F. Schaefer (ed.), Methods of Electronic Structure Theory, Vol. 3, Plenum, New York, 1977, p. 72; A. F. Voter and W. A. Goddard, J. Am. Chem. Soc., 108, 2830 (1986); J. H. Van Lanthe, J. Verbeek, and P. Pulay, Mol. Phys., 73, 1159 (1991). (d) S. J. Cyvin and I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons, Springer, Berlin, 1988.
31. A useful historical overview of VB/resonance concepts and applications is given by D. J. Klein and N. Trinajstic, J. Chem. Ed., 67, 633 (1990). For representative works pertaining to (a) projecting VB-type structures from MO or MO-CI wave functions or density matrices, (b) VB-mixing descriptions of reactivity and properties, (c) classical or self-consistent VB computational methods, or (d) graph-theoretic methods, see: (a) M. Craig and R. S. Berry, J. Am. Chem. Soc., 89, 2801 (1967); P. C. Hiberty and C. Leforestier, J. Am. Chem. Soc., 100, 2012 (1978); P. C. Hiberty and G. Ohanessian, Int. J. Quant. Chem., 27, 259 (1978); P. C. Hiberty, Int. J. Quant. Chem., 19, 259 (1981); S. S. Shaik, J. Am. Chem. Soc., 103, 3692 (1981); P. C. Hiberty and G. Ohanessian, J. Am. Chem. Soc,. 104, 66 (1982); P. C. Hiberty, G. Ohanessian, and F. Delbecq, J. Am. Chem. Soc., 107, 3095 (1985); R. M. Parrondo, P. Karafiloglou, and E. Sánchez Marcos, Int. J. Quantum Chem., 52, 1127 (1994). (b) S. S. Shaik, H. B. Schlegel, and S. T. Wolfe, Theoretical Aspects of Physical Organic Chemistry, Wiley, New York, 1992; A. Pross, Theoretical and Physical Principles of Organic Reactivity, Wiley, New York, 1995; N. D. Epiotis, Lecture Notes in Chemistry, Vol. 34, American Chemical Society, New York, 1983; F. Bernardi and M. A. Robb, J. Am. Chem. Soc., 106, 54 (1984); Y. Apeloig and D. Arad, J. Am. Chem. Soc., 108, 3241 (1986); P. W. Anderson, Science, 235, 1196 (1987); F. Bernardi, A. Bottoni, M. Olivucci, A. Venturini, and M. A. Robb, J. Chem. Soc. Faraday Trans., 90, 1617 (1994). (c) G. A. Gallup, R. L. Vance, J. R. Collins, and J. M. Norbeck, Adv. Quantum Chem., 16, 229 (1982); D. L. Cooper, J. Gerratt, and M. Raimondi, Nature, 323, 699 (1986), Adv. Chem. Phys., 69, 319 (1987); F. W. Bobrowitz and W. A. Goddard, in H. F. Schaefer (ed.), Methods of Electronic Structure Theory, Vol. 3, Plenum, New York, 1977, p. 72; A. F. Voter and W. A. Goddard, J. Am. Chem. Soc., 108, 2830 (1986); J. H. Van Lanthe, J. Verbeek, and P. Pulay, Mol. Phys., 73, 1159 (1991). (d) S. J. Cyvin and I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons, Springer, Berlin, 1988.
32. A useful historical overview of VB/resonance concepts and applications is given by D. J. Klein and N. Trinajstic, J. Chem. Ed., 67, 633 (1990). For representative works pertaining to (a) projecting VB-type structures from MO or MO-CI wave functions or density matrices, (b) VB-mixing descriptions of reactivity and properties, (c) classical or self-consistent VB computational methods, or (d) graph-theoretic methods, see: (a) M. Craig and R. S. Berry, J. Am. Chem. Soc., 89, 2801 (1967); P. C. Hiberty and C. Leforestier, J. Am. Chem. Soc., 100, 2012 (1978); P. C. Hiberty and G. Ohanessian, Int. J. Quant. Chem., 27, 259 (1978); P. C. Hiberty, Int. J. Quant. Chem., 19, 259 (1981); S. S. Shaik, J. Am. Chem. Soc., 103, 3692 (1981); P. C. Hiberty and G. Ohanessian, J. Am. Chem. Soc,. 104, 66 (1982); P. C. Hiberty, G. Ohanessian, and F. Delbecq, J. Am. Chem. Soc., 107, 3095 (1985); R. M. Parrondo, P. Karafiloglou, and E. Sánchez Marcos, Int. J. Quantum Chem., 52, 1127 (1994). (b) S. S. Shaik, H. B. Schlegel, and S. T. Wolfe, Theoretical Aspects of Physical Organic Chemistry, Wiley, New York, 1992; A. Pross, Theoretical and Physical Principles of Organic Reactivity, Wiley, New York, 1995; N. D. Epiotis, Lecture Notes in Chemistry, Vol. 34, American Chemical Society, New York, 1983; F. Bernardi and M. A. Robb, J. Am. Chem. Soc., 106, 54 (1984); Y. Apeloig and D. Arad, J. Am. Chem. Soc., 108, 3241 (1986); P. W. Anderson, Science, 235, 1196 (1987); F. Bernardi, A. Bottoni, M. Olivucci, A. Venturini, and M. A. Robb, J. Chem. Soc. Faraday Trans., 90, 1617 (1994). (c) G. A. Gallup, R. L. Vance, J. R. Collins, and J. M. Norbeck, Adv. Quantum Chem., 16, 229 (1982); D. L. Cooper, J. Gerratt, and M. Raimondi, Nature, 323, 699 (1986), Adv. Chem. Phys., 69, 319 (1987); F. W. Bobrowitz and W. A. Goddard, in H. F. Schaefer (ed.), Methods of Electronic Structure Theory, Vol. 3, Plenum, New York, 1977, p. 72; A. F. Voter and W. A. Goddard, J. Am. Chem. Soc., 108, 2830 (1986); J. H. Van Lanthe, J. Verbeek, and P. Pulay, Mol. Phys., 73, 1159 (1991). (d) S. J. Cyvin and I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons, Springer, Berlin, 1988.
33. A useful historical overview of VB/resonance concepts and applications is given by D. J. Klein and N. Trinajstic, J. Chem. Ed., 67, 633 (1990). For representative works pertaining to (a) projecting VB-type structures from MO or MO-CI wave functions or density matrices, (b) VB-mixing descriptions of reactivity and properties, (c) classical or self-consistent VB computational methods, or (d) graph-theoretic methods, see: (a) M. Craig and R. S. Berry, J. Am. Chem. Soc., 89, 2801 (1967); P. C. Hiberty and C. Leforestier, J. Am. Chem. Soc., 100, 2012 (1978); P. C. Hiberty and G. Ohanessian, Int. J. Quant. Chem., 27, 259 (1978); P. C. Hiberty, Int. J. Quant. Chem., 19, 259 (1981); S. S. Shaik, J. Am. Chem. Soc., 103, 3692 (1981); P. C. Hiberty and G. Ohanessian, J. Am. Chem. Soc,. 104, 66 (1982); P. C. Hiberty, G. Ohanessian, and F. Delbecq, J. Am. Chem. Soc., 107, 3095 (1985); R. M. Parrondo, P. Karafiloglou, and E. Sánchez Marcos, Int. J. Quantum Chem., 52, 1127 (1994). (b) S. S. Shaik, H. B. Schlegel, and S. T. Wolfe, Theoretical Aspects of Physical Organic Chemistry, Wiley, New York, 1992; A. Pross, Theoretical and Physical Principles of Organic Reactivity, Wiley, New York, 1995; N. D. Epiotis, Lecture Notes in Chemistry, Vol. 34, American Chemical Society, New York, 1983; F. Bernardi and M. A. Robb, J. Am. Chem. Soc., 106, 54 (1984); Y. Apeloig and D. Arad, J. Am. Chem. Soc., 108, 3241 (1986); P. W. Anderson, Science, 235, 1196 (1987); F. Bernardi, A. Bottoni, M. Olivucci, A. Venturini, and M. A. Robb, J. Chem. Soc. Faraday Trans., 90, 1617 (1994). (c) G. A. Gallup, R. L. Vance, J. R. Collins, and J. M. Norbeck, Adv. Quantum Chem., 16, 229 (1982); D. L. Cooper, J. Gerratt, and M. Raimondi, Nature, 323, 699 (1986), Adv. Chem. Phys., 69, 319 (1987); F. W. Bobrowitz and W. A. Goddard, in H. F. Schaefer (ed.), Methods of Electronic Structure Theory, Vol. 3, Plenum, New York, 1977, p. 72; A. F. Voter and W. A. Goddard, J. Am. Chem. Soc., 108, 2830 (1986); J. H. Van Lanthe, J. Verbeek, and P. Pulay, Mol. Phys., 73, 1159 (1991). (d) S. J. Cyvin and I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons, Springer, Berlin, 1988.
34. A useful historical overview of VB/resonance concepts and applications is given by D. J. Klein and N. Trinajstic, J. Chem. Ed., 67, 633 (1990). For representative works pertaining to (a) projecting VB-type structures from MO or MO-CI wave functions or density matrices, (b) VB-mixing descriptions of reactivity and properties, (c) classical or self-consistent VB computational methods, or (d) graph-theoretic methods, see: (a) M. Craig and R. S. Berry, J. Am. Chem. Soc., 89, 2801 (1967); P. C. Hiberty and C. Leforestier, J. Am. Chem. Soc., 100, 2012 (1978); P. C. Hiberty and G. Ohanessian, Int. J. Quant. Chem., 27, 259 (1978); P. C. Hiberty, Int. J. Quant. Chem., 19, 259 (1981); S. S. Shaik, J. Am. Chem. Soc., 103, 3692 (1981); P. C. Hiberty and G. Ohanessian, J. Am. Chem. Soc,. 104, 66 (1982); P. C. Hiberty, G. Ohanessian, and F. Delbecq, J. Am. Chem. Soc., 107, 3095 (1985); R. M. Parrondo, P. Karafiloglou, and E. Sánchez Marcos, Int. J. Quantum Chem., 52, 1127 (1994). (b) S. S. Shaik, H. B. Schlegel, and S. T. Wolfe, Theoretical Aspects of Physical Organic Chemistry, Wiley, New York, 1992; A. Pross, Theoretical and Physical Principles of Organic Reactivity, Wiley, New York, 1995; N. D. Epiotis, Lecture Notes in Chemistry, Vol. 34, American Chemical Society, New York, 1983; F. Bernardi and M. A. Robb, J. Am. Chem. Soc., 106, 54 (1984); Y. Apeloig and D. Arad, J. Am. Chem. Soc., 108, 3241 (1986); P. W. Anderson, Science, 235, 1196 (1987); F. Bernardi, A. Bottoni, M. Olivucci, A. Venturini, and M. A. Robb, J. Chem. Soc. Faraday Trans., 90, 1617 (1994). (c) G. A. Gallup, R. L. Vance, J. R. Collins, and J. M. Norbeck, Adv. Quantum Chem., 16, 229 (1982); D. L. Cooper, J. Gerratt, and M. Raimondi, Nature, 323, 699 (1986), Adv. Chem. Phys., 69, 319 (1987); F. W. Bobrowitz and W. A. Goddard, in H. F. Schaefer (ed.), Methods of Electronic Structure Theory, Vol. 3, Plenum, New York, 1977, p. 72; A. F. Voter and W. A. Goddard, J. Am. Chem. Soc., 108, 2830 (1986); J. H. Van Lanthe, J. Verbeek, and P. Pulay, Mol. Phys., 73, 1159 (1991). (d) S. J. Cyvin and I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons, Springer, Berlin, 1988.
35. A useful historical overview of VB/resonance concepts and applications is given by D. J. Klein and N. Trinajstic, J. Chem. Ed., 67, 633 (1990). For representative works pertaining to (a) projecting VB-type structures from MO or MO-CI wave functions or density matrices, (b) VB-mixing descriptions of reactivity and properties, (c) classical or self-consistent VB computational methods, or (d) graph-theoretic methods, see: (a) M. Craig and R. S. Berry, J. Am. Chem. Soc., 89, 2801 (1967); P. C. Hiberty and C. Leforestier, J. Am. Chem. Soc., 100, 2012 (1978); P. C. Hiberty and G. Ohanessian, Int. J. Quant. Chem., 27, 259 (1978); P. C. Hiberty, Int. J. Quant. Chem., 19, 259 (1981); S. S. Shaik, J. Am. Chem. Soc., 103, 3692 (1981); P. C. Hiberty and G. Ohanessian, J. Am. Chem. Soc,. 104, 66 (1982); P. C. Hiberty, G. Ohanessian, and F. Delbecq, J. Am. Chem. Soc., 107, 3095 (1985); R. M. Parrondo, P. Karafiloglou, and E. Sánchez Marcos, Int. J. Quantum Chem., 52, 1127 (1994). (b) S. S. Shaik, H. B. Schlegel, and S. T. Wolfe, Theoretical Aspects of Physical Organic Chemistry, Wiley, New York, 1992; A. Pross, Theoretical and Physical Principles of Organic Reactivity, Wiley, New York, 1995; N. D. Epiotis, Lecture Notes in Chemistry, Vol. 34, American Chemical Society, New York, 1983; F. Bernardi and M. A. Robb, J. Am. Chem. Soc., 106, 54 (1984); Y. Apeloig and D. Arad, J. Am. Chem. Soc., 108, 3241 (1986); P. W. Anderson, Science, 235, 1196 (1987); F. Bernardi, A. Bottoni, M. Olivucci, A. Venturini, and M. A. Robb, J. Chem. Soc. Faraday Trans., 90, 1617 (1994). (c) G. A. Gallup, R. L. Vance, J. R. Collins, and J. M. Norbeck, Adv. Quantum Chem., 16, 229 (1982); D. L. Cooper, J. Gerratt, and M. Raimondi, Nature, 323, 699 (1986), Adv. Chem. Phys., 69, 319 (1987); F. W. Bobrowitz and W. A. Goddard, in H. F. Schaefer (ed.), Methods of Electronic Structure Theory, Vol. 3, Plenum, New York, 1977, p. 72; A. F. Voter and W. A. Goddard, J. Am. Chem. Soc., 108, 2830 (1986); J. H. Van Lanthe, J. Verbeek, and P. Pulay, Mol. Phys., 73, 1159 (1991). (d) S. J. Cyvin and I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons, Springer, Berlin, 1988.
36. A useful historical overview of VB/resonance concepts and applications is given by D. J. Klein and N. Trinajstic, J. Chem. Ed., 67, 633 (1990). For representative works pertaining to (a) projecting VB-type structures from MO or MO-CI wave functions or density matrices, (b) VB-mixing descriptions of reactivity and properties, (c) classical or self-consistent VB computational methods, or (d) graph-theoretic methods, see: (a) M. Craig and R. S. Berry, J. Am. Chem. Soc., 89, 2801 (1967); P. C. Hiberty and C. Leforestier, J. Am. Chem. Soc., 100, 2012 (1978); P. C. Hiberty and G. Ohanessian, Int. J. Quant. Chem., 27, 259 (1978); P. C. Hiberty, Int. J. Quant. Chem., 19, 259 (1981); S. S. Shaik, J. Am. Chem. Soc., 103, 3692 (1981); P. C. Hiberty and G. Ohanessian, J. Am. Chem. Soc,. 104, 66 (1982); P. C. Hiberty, G. Ohanessian, and F. Delbecq, J. Am. Chem. Soc., 107, 3095 (1985); R. M. Parrondo, P. Karafiloglou, and E. Sánchez Marcos, Int. J. Quantum Chem., 52, 1127 (1994). (b) S. S. Shaik, H. B. Schlegel, and S. T. Wolfe, Theoretical Aspects of Physical Organic Chemistry, Wiley, New York, 1992; A. Pross, Theoretical and Physical Principles of Organic Reactivity, Wiley, New York, 1995; N. D. Epiotis, Lecture Notes in Chemistry, Vol. 34, American Chemical Society, New York, 1983; F. Bernardi and M. A. Robb, J. Am. Chem. Soc., 106, 54 (1984); Y. Apeloig and D. Arad, J. Am. Chem. Soc., 108, 3241 (1986); P. W. Anderson, Science, 235, 1196 (1987); F. Bernardi, A. Bottoni, M. Olivucci, A. Venturini, and M. A. Robb, J. Chem. Soc. Faraday Trans., 90, 1617 (1994). (c) G. A. Gallup, R. L. Vance, J. R. Collins, and J. M. Norbeck, Adv. Quantum Chem., 16, 229 (1982); D. L. Cooper, J. Gerratt, and M. Raimondi, Nature, 323, 699 (1986), Adv. Chem. Phys., 69, 319 (1987); F. W. Bobrowitz and W. A. Goddard, in H. F. Schaefer (ed.), Methods of Electronic Structure Theory, Vol. 3, Plenum, New York, 1977, p. 72; A. F. Voter and W. A. Goddard, J. Am. Chem. Soc., 108, 2830 (1986); J. H. Van Lanthe, J. Verbeek, and P. Pulay, Mol. Phys., 73, 1159 (1991). (d) S. J. Cyvin and I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons, Springer, Berlin, 1988.
37. A useful historical overview of VB/resonance concepts and applications is given by D. J. Klein and N. Trinajstic, J. Chem. Ed., 67, 633 (1990). For representative works pertaining to (a) projecting VB-type structures from MO or MO-CI wave functions or density matrices, (b) VB-mixing descriptions of reactivity and properties, (c) classical or self-consistent VB computational methods, or (d) graph-theoretic methods, see: (a) M. Craig and R. S. Berry, J. Am. Chem. Soc., 89, 2801 (1967); P. C. Hiberty and C. Leforestier, J. Am. Chem. Soc., 100, 2012 (1978); P. C. Hiberty and G. Ohanessian, Int. J. Quant. Chem., 27, 259 (1978); P. C. Hiberty, Int. J. Quant. Chem., 19, 259 (1981); S. S. Shaik, J. Am. Chem. Soc., 103, 3692 (1981); P. C. Hiberty and G. Ohanessian, J. Am. Chem. Soc,. 104, 66 (1982); P. C. Hiberty, G. Ohanessian, and F. Delbecq, J. Am. Chem. Soc., 107, 3095 (1985); R. M. Parrondo, P. Karafiloglou, and E. Sánchez Marcos, Int. J. Quantum Chem., 52, 1127 (1994). (b) S. S. Shaik, H. B. Schlegel, and S. T. Wolfe, Theoretical Aspects of Physical Organic Chemistry, Wiley, New York, 1992; A. Pross, Theoretical and Physical Principles of Organic Reactivity, Wiley, New York, 1995; N. D. Epiotis, Lecture Notes in Chemistry, Vol. 34, American Chemical Society, New York, 1983; F. Bernardi and M. A. Robb, J. Am. Chem. Soc., 106, 54 (1984); Y. Apeloig and D. Arad, J. Am. Chem. Soc., 108, 3241 (1986); P. W. Anderson, Science, 235, 1196 (1987); F. Bernardi, A. Bottoni, M. Olivucci, A. Venturini, and M. A. Robb, J. Chem. Soc. Faraday Trans., 90, 1617 (1994). (c) G. A. Gallup, R. L. Vance, J. R. Collins, and J. M. Norbeck, Adv. Quantum Chem., 16, 229 (1982); D. L. Cooper, J. Gerratt, and M. Raimondi, Nature, 323, 699 (1986), Adv. Chem. Phys., 69, 319 (1987); F. W. Bobrowitz and W. A. Goddard, in H. F. Schaefer (ed.), Methods of Electronic Structure Theory, Vol. 3, Plenum, New York, 1977, p. 72; A. F. Voter and W. A. Goddard, J. Am. Chem. Soc., 108, 2830 (1986); J. H. Van Lanthe, J. Verbeek, and P. Pulay, Mol. Phys., 73, 1159 (1991). (d) S. J. Cyvin and I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons, Springer, Berlin, 1988.
38. A useful historical overview of VB/resonance concepts and applications is given by D. J. Klein and N. Trinajstic, J. Chem. Ed., 67, 633 (1990). For representative works pertaining to (a) projecting VB-type structures from MO or MO-CI wave functions or density matrices, (b) VB-mixing descriptions of reactivity and properties, (c) classical or self-consistent VB computational methods, or (d) graph-theoretic methods, see: (a) M. Craig and R. S. Berry, J. Am. Chem. Soc., 89, 2801 (1967); P. C. Hiberty and C. Leforestier, J. Am. Chem. Soc., 100, 2012 (1978); P. C. Hiberty and G. Ohanessian, Int. J. Quant. Chem., 27, 259 (1978); P. C. Hiberty, Int. J. Quant. Chem., 19, 259 (1981); S. S. Shaik, J. Am. Chem. Soc., 103, 3692 (1981); P. C. Hiberty and G. Ohanessian, J. Am. Chem. Soc,. 104, 66 (1982); P. C. Hiberty, G. Ohanessian, and F. Delbecq, J. Am. Chem. Soc., 107, 3095 (1985); R. M. Parrondo, P. Karafiloglou, and E. Sánchez Marcos, Int. J. Quantum Chem., 52, 1127 (1994). (b) S. S. Shaik, H. B. Schlegel, and S. T. Wolfe, Theoretical Aspects of Physical Organic Chemistry, Wiley, New York, 1992; A. Pross, Theoretical and Physical Principles of Organic Reactivity, Wiley, New York, 1995; N. D. Epiotis, Lecture Notes in Chemistry, Vol. 34, American Chemical Society, New York, 1983; F. Bernardi and M. A. Robb, J. Am. Chem. Soc., 106, 54 (1984); Y. Apeloig and D. Arad, J. Am. Chem. Soc., 108, 3241 (1986); P. W. Anderson, Science, 235, 1196 (1987); F. Bernardi, A. Bottoni, M. Olivucci, A. Venturini, and M. A. Robb, J. Chem. Soc. Faraday Trans., 90, 1617 (1994). (c) G. A. Gallup, R. L. Vance, J. R. Collins, and J. M. Norbeck, Adv. Quantum Chem., 16, 229 (1982); D. L. Cooper, J. Gerratt, and M. Raimondi, Nature, 323, 699 (1986), Adv. Chem. Phys., 69, 319 (1987); F. W. Bobrowitz and W. A. Goddard, in H. F. Schaefer (ed.), Methods of Electronic Structure Theory, Vol. 3, Plenum, New York, 1977, p. 72; A. F. Voter and W. A. Goddard, J. Am. Chem. Soc., 108, 2830 (1986); J. H. Van Lanthe, J. Verbeek, and P. Pulay, Mol. Phys., 73, 1159 (1991). (d) S. J. Cyvin and I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons, Springer, Berlin, 1988.
39. A useful historical overview of VB/resonance concepts and applications is given by D. J. Klein and N. Trinajstic, J. Chem. Ed., 67, 633 (1990). For representative works pertaining to (a) projecting VB-type structures from MO or MO-CI wave functions or density matrices, (b) VB-mixing descriptions of reactivity and properties, (c) classical or self-consistent VB computational methods, or (d) graph-theoretic methods, see: (a) M. Craig and R. S. Berry, J. Am. Chem. Soc., 89, 2801 (1967); P. C. Hiberty and C. Leforestier, J. Am. Chem. Soc., 100, 2012 (1978); P. C. Hiberty and G. Ohanessian, Int. J. Quant. Chem., 27, 259 (1978); P. C. Hiberty, Int. J. Quant. Chem., 19, 259 (1981); S. S. Shaik, J. Am. Chem. Soc., 103, 3692 (1981); P. C. Hiberty and G. Ohanessian, J. Am. Chem. Soc,. 104, 66 (1982); P. C. Hiberty, G. Ohanessian, and F. Delbecq, J. Am. Chem. Soc., 107, 3095 (1985); R. M. Parrondo, P. Karafiloglou, and E. Sánchez Marcos, Int. J. Quantum Chem., 52, 1127 (1994). (b) S. S. Shaik, H. B. Schlegel, and S. T. Wolfe, Theoretical Aspects of Physical Organic Chemistry, Wiley, New York, 1992; A. Pross, Theoretical and Physical Principles of Organic Reactivity, Wiley, New York, 1995; N. D. Epiotis, Lecture Notes in Chemistry, Vol. 34, American Chemical Society, New York, 1983; F. Bernardi and M. A. Robb, J. Am. Chem. Soc., 106, 54 (1984); Y. Apeloig and D. Arad, J. Am. Chem. Soc., 108, 3241 (1986); P. W. Anderson, Science, 235, 1196 (1987); F. Bernardi, A. Bottoni, M. Olivucci, A. Venturini, and M. A. Robb, J. Chem. Soc. Faraday Trans., 90, 1617 (1994). (c) G. A. Gallup, R. L. Vance, J. R. Collins, and J. M. Norbeck, Adv. Quantum Chem., 16, 229 (1982); D. L. Cooper, J. Gerratt, and M. Raimondi, Nature, 323, 699 (1986), Adv. Chem. Phys., 69, 319 (1987); F. W. Bobrowitz and W. A. Goddard, in H. F. Schaefer (ed.), Methods of Electronic Structure Theory, Vol. 3, Plenum, New York, 1977, p. 72; A. F. Voter and W. A. Goddard, J. Am. Chem. Soc., 108, 2830 (1986); J. H. Van Lanthe, J. Verbeek, and P. Pulay, Mol. Phys., 73, 1159 (1991). (d) S. J. Cyvin and I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons, Springer, Berlin, 1988.
40. A useful historical overview of VB/resonance concepts and applications is given by D. J. Klein and N. Trinajstic, J. Chem. Ed., 67, 633 (1990). For representative works pertaining to (a) projecting VB-type structures from MO or MO-CI wave functions or density matrices, (b) VB-mixing descriptions of reactivity and properties, (c) classical or self-consistent VB computational methods, or (d) graph-theoretic methods, see: (a) M. Craig and R. S. Berry, J. Am. Chem. Soc., 89, 2801 (1967); P. C. Hiberty and C. Leforestier, J. Am. Chem. Soc., 100, 2012 (1978); P. C. Hiberty and G. Ohanessian, Int. J. Quant. Chem., 27, 259 (1978); P. C. Hiberty, Int. J. Quant. Chem., 19, 259 (1981); S. S. Shaik, J. Am. Chem. Soc., 103, 3692 (1981); P. C. Hiberty and G. Ohanessian, J. Am. Chem. Soc,. 104, 66 (1982); P. C. Hiberty, G. Ohanessian, and F. Delbecq, J. Am. Chem. Soc., 107, 3095 (1985); R. M. Parrondo, P. Karafiloglou, and E. Sánchez Marcos, Int. J. Quantum Chem., 52, 1127 (1994). (b) S. S. Shaik, H. B. Schlegel, and S. T. Wolfe, Theoretical Aspects of Physical Organic Chemistry, Wiley, New York, 1992; A. Pross, Theoretical and Physical Principles of Organic Reactivity, Wiley, New York, 1995; N. D. Epiotis, Lecture Notes in Chemistry, Vol. 34, American Chemical Society, New York, 1983; F. Bernardi and M. A. Robb, J. Am. Chem. Soc., 106, 54 (1984); Y. Apeloig and D. Arad, J. Am. Chem. Soc., 108, 3241 (1986); P. W. Anderson, Science, 235, 1196 (1987); F. Bernardi, A. Bottoni, M. Olivucci, A. Venturini, and M. A. Robb, J. Chem. Soc. Faraday Trans., 90, 1617 (1994). (c) G. A. Gallup, R. L. Vance, J. R. Collins, and J. M. Norbeck, Adv. Quantum Chem., 16, 229 (1982); D. L. Cooper, J. Gerratt, and M. Raimondi, Nature, 323, 699 (1986), Adv. Chem. Phys., 69, 319 (1987); F. W. Bobrowitz and W. A. Goddard, in H. F. Schaefer (ed.), Methods of Electronic Structure Theory, Vol. 3, Plenum, New York, 1977, p. 72; A. F. Voter and W. A. Goddard, J. Am. Chem. Soc., 108, 2830 (1986); J. H. Van Lanthe, J. Verbeek, and P. Pulay, Mol. Phys., 73, 1159 (1991). (d) S. J. Cyvin and I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons, Springer, Berlin, 1988.
41. A useful historical overview of VB/resonance concepts and applications is given by D. J. Klein and N. Trinajstic, J. Chem. Ed., 67, 633 (1990). For representative works pertaining to (a) projecting VB-type structures from MO or MO-CI wave functions or density matrices, (b) VB-mixing descriptions of reactivity and properties, (c) classical or self-consistent VB computational methods, or (d) graph-theoretic methods, see: (a) M. Craig and R. S. Berry, J. Am. Chem. Soc., 89, 2801 (1967); P. C. Hiberty and C. Leforestier, J. Am. Chem. Soc., 100, 2012 (1978); P. C. Hiberty and G. Ohanessian, Int. J. Quant. Chem., 27, 259 (1978); P. C. Hiberty, Int. J. Quant. Chem., 19, 259 (1981); S. S. Shaik, J. Am. Chem. Soc., 103, 3692 (1981); P. C. Hiberty and G. Ohanessian, J. Am. Chem. Soc,. 104, 66 (1982); P. C. Hiberty, G. Ohanessian, and F. Delbecq, J. Am. Chem. Soc., 107, 3095 (1985); R. M. Parrondo, P. Karafiloglou, and E. Sánchez Marcos, Int. J. Quantum Chem., 52, 1127 (1994). (b) S. S. Shaik, H. B. Schlegel, and S. T. Wolfe, Theoretical Aspects of Physical Organic Chemistry, Wiley, New York, 1992; A. Pross, Theoretical and Physical Principles of Organic Reactivity, Wiley, New York, 1995; N. D. Epiotis, Lecture Notes in Chemistry, Vol. 34, American Chemical Society, New York, 1983; F. Bernardi and M. A. Robb, J. Am. Chem. Soc., 106, 54 (1984); Y. Apeloig and D. Arad, J. Am. Chem. Soc., 108, 3241 (1986); P. W. Anderson, Science, 235, 1196 (1987); F. Bernardi, A. Bottoni, M. Olivucci, A. Venturini, and M. A. Robb, J. Chem. Soc. Faraday Trans., 90, 1617 (1994). (c) G. A. Gallup, R. L. Vance, J. R. Collins, and J. M. Norbeck, Adv. Quantum Chem., 16, 229 (1982); D. L. Cooper, J. Gerratt, and M. Raimondi, Nature, 323, 699 (1986), Adv. Chem. Phys., 69, 319 (1987); F. W. Bobrowitz and W. A. Goddard, in H. F. Schaefer (ed.), Methods of Electronic Structure Theory, Vol. 3, Plenum, New York, 1977, p. 72; A. F. Voter and W. A. Goddard, J. Am. Chem. Soc., 108, 2830 (1986); J. H. Van Lanthe, J. Verbeek, and P. Pulay, Mol. Phys., 73, 1159 (1991). (d) S. J. Cyvin and I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons, Springer, Berlin, 1988.
42. A useful historical overview of VB/resonance concepts and applications is given by D. J. Klein and N. Trinajstic, J. Chem. Ed., 67, 633 (1990). For representative works pertaining to (a) projecting VB-type structures from MO or MO-CI wave functions or density matrices, (b) VB-mixing descriptions of reactivity and properties, (c) classical or self-consistent VB computational methods, or (d) graph-theoretic methods, see: (a) M. Craig and R. S. Berry, J. Am. Chem. Soc., 89, 2801 (1967); P. C. Hiberty and C. Leforestier, J. Am. Chem. Soc., 100, 2012 (1978); P. C. Hiberty and G. Ohanessian, Int. J. Quant. Chem., 27, 259 (1978); P. C. Hiberty, Int. J. Quant. Chem., 19, 259 (1981); S. S. Shaik, J. Am. Chem. Soc., 103, 3692 (1981); P. C. Hiberty and G. Ohanessian, J. Am. Chem. Soc,. 104, 66 (1982); P. C. Hiberty, G. Ohanessian, and F. Delbecq, J. Am. Chem. Soc., 107, 3095 (1985); R. M. Parrondo, P. Karafiloglou, and E. Sánchez Marcos, Int. J. Quantum Chem., 52, 1127 (1994). (b) S. S. Shaik, H. B. Schlegel, and S. T. Wolfe, Theoretical Aspects of Physical Organic Chemistry, Wiley, New York, 1992; A. Pross, Theoretical and Physical Principles of Organic Reactivity, Wiley, New York, 1995; N. D. Epiotis, Lecture Notes in Chemistry, Vol. 34, American Chemical Society, New York, 1983; F. Bernardi and M. A. Robb, J. Am. Chem. Soc., 106, 54 (1984); Y. Apeloig and D. Arad, J. Am. Chem. Soc., 108, 3241 (1986); P. W. Anderson, Science, 235, 1196 (1987); F. Bernardi, A. Bottoni, M. Olivucci, A. Venturini, and M. A. Robb, J. Chem. Soc. Faraday Trans., 90, 1617 (1994). (c) G. A. Gallup, R. L. Vance, J. R. Collins, and J. M. Norbeck, Adv. Quantum Chem., 16, 229 (1982); D. L. Cooper, J. Gerratt, and M. Raimondi, Nature, 323, 699 (1986), Adv. Chem. Phys., 69, 319 (1987); F. W. Bobrowitz and W. A. Goddard, in H. F. Schaefer (ed.), Methods of Electronic Structure Theory, Vol. 3, Plenum, New York, 1977, p. 72; A. F. Voter and W. A. Goddard, J. Am. Chem. Soc., 108, 2830 (1986); J. H. Van Lanthe, J. Verbeek, and P. Pulay, Mol. Phys., 73, 1159 (1991). (d) S. J. Cyvin and I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons, Springer, Berlin, 1988.
43. A useful historical overview of VB/resonance concepts and applications is given by D. J. Klein and N. Trinajstic, J. Chem. Ed., 67, 633 (1990). For representative works pertaining to (a) projecting VB-type structures from MO or MO-CI wave functions or density matrices, (b) VB-mixing descriptions of reactivity and properties, (c) classical or self-consistent VB computational methods, or (d) graph-theoretic methods, see: (a) M. Craig and R. S. Berry, J. Am. Chem. Soc., 89, 2801 (1967); P. C. Hiberty and C. Leforestier, J. Am. Chem. Soc., 100, 2012 (1978); P. C. Hiberty and G. Ohanessian, Int. J. Quant. Chem., 27, 259 (1978); P. C. Hiberty, Int. J. Quant. Chem., 19, 259 (1981); S. S. Shaik, J. Am. Chem. Soc., 103, 3692 (1981); P. C. Hiberty and G. Ohanessian, J. Am. Chem. Soc,. 104, 66 (1982); P. C. Hiberty, G. Ohanessian, and F. Delbecq, J. Am. Chem. Soc., 107, 3095 (1985); R. M. Parrondo, P. Karafiloglou, and E. Sánchez Marcos, Int. J. Quantum Chem., 52, 1127 (1994). (b) S. S. Shaik, H. B. Schlegel, and S. T. Wolfe, Theoretical Aspects of Physical Organic Chemistry, Wiley, New York, 1992; A. Pross, Theoretical and Physical Principles of Organic Reactivity, Wiley, New York, 1995; N. D. Epiotis, Lecture Notes in Chemistry, Vol. 34, American Chemical Society, New York, 1983; F. Bernardi and M. A. Robb, J. Am. Chem. Soc., 106, 54 (1984); Y. Apeloig and D. Arad, J. Am. Chem. Soc., 108, 3241 (1986); P. W. Anderson, Science, 235, 1196 (1987); F. Bernardi, A. Bottoni, M. Olivucci, A. Venturini, and M. A. Robb, J. Chem. Soc. Faraday Trans., 90, 1617 (1994). (c) G. A. Gallup, R. L. Vance, J. R. Collins, and J. M. Norbeck, Adv. Quantum Chem., 16, 229 (1982); D. L. Cooper, J. Gerratt, and M. Raimondi, Nature, 323, 699 (1986), Adv. Chem. Phys., 69, 319 (1987); F. W. Bobrowitz and W. A. Goddard, in H. F. Schaefer (ed.), Methods of Electronic Structure Theory, Vol. 3, Plenum, New York, 1977, p. 72; A. F. Voter and W. A. Goddard, J. Am. Chem. Soc., 108, 2830 (1986); J. H. Van Lanthe, J. Verbeek, and P. Pulay, Mol. Phys., 73, 1159 (1991). (d) S. J. Cyvin and I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons, Springer, Berlin, 1988.
44. A useful historical overview of VB/resonance concepts and applications is given by D. J. Klein and N. Trinajstic, J. Chem. Ed., 67, 633 (1990). For representative works pertaining to (a) projecting VB-type structures from MO or MO-CI wave functions or density matrices, (b) VB-mixing descriptions of reactivity and properties, (c) classical or self-consistent VB computational methods, or (d) graph-theoretic methods, see: (a) M. Craig and R. S. Berry, J. Am. Chem. Soc., 89, 2801 (1967); P. C. Hiberty and C. Leforestier, J. Am. Chem. Soc., 100, 2012 (1978); P. C. Hiberty and G. Ohanessian, Int. J. Quant. Chem., 27, 259 (1978); P. C. Hiberty, Int. J. Quant. Chem., 19, 259 (1981); S. S. Shaik, J. Am. Chem. Soc., 103, 3692 (1981); P. C. Hiberty and G. Ohanessian, J. Am. Chem. Soc,. 104, 66 (1982); P. C. Hiberty, G. Ohanessian, and F. Delbecq, J. Am. Chem. Soc., 107, 3095 (1985); R. M. Parrondo, P. Karafiloglou, and E. Sánchez Marcos, Int. J. Quantum Chem., 52, 1127 (1994). (b) S. S. Shaik, H. B. Schlegel, and S. T. Wolfe, Theoretical Aspects of Physical Organic Chemistry, Wiley, New York, 1992; A. Pross, Theoretical and Physical Principles of Organic Reactivity, Wiley, New York, 1995; N. D. Epiotis, Lecture Notes in Chemistry, Vol. 34, American Chemical Society, New York, 1983; F. Bernardi and M. A. Robb, J. Am. Chem. Soc., 106, 54 (1984); Y. Apeloig and D. Arad, J. Am. Chem. Soc., 108, 3241 (1986); P. W. Anderson, Science, 235, 1196 (1987); F. Bernardi, A. Bottoni, M. Olivucci, A. Venturini, and M. A. Robb, J. Chem. Soc. Faraday Trans., 90, 1617 (1994). (c) G. A. Gallup, R. L. Vance, J. R. Collins, and J. M. Norbeck, Adv. Quantum Chem., 16, 229 (1982); D. L. Cooper, J. Gerratt, and M. Raimondi, Nature, 323, 699 (1986), Adv. Chem. Phys., 69, 319 (1987); F. W. Bobrowitz and W. A. Goddard, in H. F. Schaefer (ed.), Methods of Electronic Structure Theory, Vol. 3, Plenum, New York, 1977, p. 72; A. F. Voter and W. A. Goddard, J. Am. Chem. Soc., 108, 2830 (1986); J. H. Van Lanthe, J. Verbeek, and P. Pulay, Mol. Phys., 73, 1159 (1991). (d) S. J. Cyvin and I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons, Springer, Berlin, 1988.
45. A useful historical overview of VB/resonance concepts and applications is given by D. J. Klein and N. Trinajstic, J. Chem. Ed., 67, 633 (1990). For representative works pertaining to (a) projecting VB-type structures from MO or MO-CI wave functions or density matrices, (b) VB-mixing descriptions of reactivity and properties, (c) classical or self-consistent VB computational methods, or (d) graph-theoretic methods, see: (a) M. Craig and R. S. Berry, J. Am. Chem. Soc., 89, 2801 (1967); P. C. Hiberty and C. Leforestier, J. Am. Chem. Soc., 100, 2012 (1978); P. C. Hiberty and G. Ohanessian, Int. J. Quant. Chem., 27, 259 (1978); P. C. Hiberty, Int. J. Quant. Chem., 19, 259 (1981); S. S. Shaik, J. Am. Chem. Soc., 103, 3692 (1981); P. C. Hiberty and G. Ohanessian, J. Am. Chem. Soc,. 104, 66 (1982); P. C. Hiberty, G. Ohanessian, and F. Delbecq, J. Am. Chem. Soc., 107, 3095 (1985); R. M. Parrondo, P. Karafiloglou, and E. Sánchez Marcos, Int. J. Quantum Chem., 52, 1127 (1994). (b) S. S. Shaik, H. B. Schlegel, and S. T. Wolfe, Theoretical Aspects of Physical Organic Chemistry, Wiley, New York, 1992; A. Pross, Theoretical and Physical Principles of Organic Reactivity, Wiley, New York, 1995; N. D. Epiotis, Lecture Notes in Chemistry, Vol. 34, American Chemical Society, New York, 1983; F. Bernardi and M. A. Robb, J. Am. Chem. Soc., 106, 54 (1984); Y. Apeloig and D. Arad, J. Am. Chem. Soc., 108, 3241 (1986); P. W. Anderson, Science, 235, 1196 (1987); F. Bernardi, A. Bottoni, M. Olivucci, A. Venturini, and M. A. Robb, J. Chem. Soc. Faraday Trans., 90, 1617 (1994). (c) G. A. Gallup, R. L. Vance, J. R. Collins, and J. M. Norbeck, Adv. Quantum Chem., 16, 229 (1982); D. L. Cooper, J. Gerratt, and M. Raimondi, Nature, 323, 699 (1986), Adv. Chem. Phys., 69, 319 (1987); F. W. Bobrowitz and W. A. Goddard, in H. F. Schaefer (ed.), Methods of Electronic Structure Theory, Vol. 3, Plenum, New York, 1977, p. 72; A. F. Voter and W. A. Goddard, J. Am. Chem. Soc., 108, 2830 (1986); J. H. Van Lanthe, J. Verbeek, and P. Pulay, Mol. Phys., 73, 1159 (1991). (d) S. J. Cyvin and I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons, Springer, Berlin, 1988.
46. P.-O. Löwdin, Phys. Rev., 97, 1474 (1955); E. R. Davidson, Reduced Density Matrices in Quantum, Chemistry, Academic, New York, 1976.
47. P.-O. Löwdin, Phys. Rev., 97, 1474 (1955); E. R. Davidson, Reduced Density Matrices in Quantum, Chemistry, Academic, New York, 1976.
48. J. P. Foster and F. Weinhold, J. Am. Chem. Soc., 102, 7211 (1980); A. E. Reed and F. Weinhold, J. Chem. Phys., 78, 4066 (1983); F. Weinhold and J. Carpenter, in R. Naaman and Z. Vager (eds.), The Structure of Small Molecules and Ions, Plenum, New York, 1988; A. E. Reed, L. A. Curtiss, and F. Weinhold, Chem. Rev., 88, 899 (1988).
49. J. P. Foster and F. Weinhold, J. Am. Chem. Soc., 102, 7211 (1980); A. E. Reed and F. Weinhold, J. Chem. Phys., 78, 4066 (1983); F. Weinhold and J. Carpenter, in R. Naaman and Z. Vager (eds.), The Structure of Small Molecules and Ions, Plenum, New York, 1988; A. E. Reed, L. A. Curtiss, and F. Weinhold, Chem. Rev., 88, 899 (1988).
50. J. P. Foster and F. Weinhold, J. Am. Chem. Soc., 102, 7211 (1980); A. E. Reed and F. Weinhold, J. Chem. Phys., 78, 4066 (1983); F. Weinhold and J. Carpenter, in R. Naaman and Z. Vager (eds.), The Structure of Small Molecules and Ions, Plenum, New York, 1988; A. E. Reed, L. A. Curtiss, and F. Weinhold, Chem. Rev., 88, 899 (1988).
51. J. P. Foster and F. Weinhold, J. Am. Chem. Soc., 102, 7211 (1980); A. E. Reed and F. Weinhold, J. Chem. Phys., 78, 4066 (1983); F. Weinhold and J. Carpenter, in R. Naaman and Z. Vager (eds.), The Structure of Small Molecules and Ions, Plenum, New York, 1988; A. E. Reed, L. A. Curtiss, and F. Weinhold, Chem. Rev., 88, 899 (1988).
52. J. M. Norbeck and G. A. Gallup, J. Am. Chem. Soc., 96, 3386 (1974); P. A. Mills, and F. Weinhold, University of Wisconsin Theoretical Chemistry Institute Report WIS-TCI-674, University of Wisconsin, Madison, 1982; for an earlier critique of valance bond theory with orthogonal atomic orbitals, see R. McWeeny, Proc. R. Soc. London, A223, 63, 306 (1954).
53. J. M. Norbeck and G. A. Gallup, J. Am. Chem. Soc., 96, 3386 (1974); P. A. Mills, and F. Weinhold, University of Wisconsin Theoretical Chemistry Institute Report WIS-TCI-674, University of Wisconsin, Madison, 1982; for an earlier critique of valance bond theory with orthogonal atomic orbitals, see R. McWeeny, Proc. R. Soc. London, A223, 63, 306 (1954).
54. J. M. Norbeck and G. A. Gallup, J. Am. Chem. Soc., 96, 3386 (1974); P. A. Mills, and F. Weinhold, University of Wisconsin Theoretical Chemistry Institute Report WIS-TCI-674, University of Wisconsin, Madison, 1982; for an earlier critique of valance bond theory with orthogonal atomic orbitals, see R. McWeeny, Proc. R. Soc. London, A223, 63, 306 (1954).
55. J. Braunstein and W. T. Simpson, J. Chem. Phys., 23, 176 (1955).
56. Pauling (reference 3, pp. 64-68) acknowledges the continuous nature of the change in bond type from covalent to ionic, but states that "the bond might be described as resonating between the covalent extreme and the ionic extreme" [p. 66; Pauling's italics] and that "whenever a question arises as to the properties expected for a covalent bond with partial ionic character, it is to be answered by consideration of the corresponding resonating structures" (p. 67).
57. R. S. Mulliken, J. Chem. Phys., 3, 573 (1935); for discussion of advantages of a general polar covalent description over that based on extreme covalent and ionic bond types, see R. T. Sanderson, Polar Covalence, Academic, New York, 1983.
58. R. S. Mulliken, J. Chem. Phys., 3, 573 (1935); for discussion of advantages of a general polar covalent description over that based on extreme covalent and ionic bond types, see R. T. Sanderson, Polar Covalence, Academic, New York, 1983.
59. A. Streitwiesser, Molecular Orbital Theory for Organic Chemists, Wiley, New York, 1961, p. 26.
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61. w criterion to describe the accuracy of the NRT expansion.
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64. The generalization to treat open-shell species is based on the concept of "different Lewis structures for different spins"; J. E. Carpenter and F. Weinhold, J. Mol. Struct. Theochem., 169, 41 (1988); see following paper.
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