Natural resonance theory: II. Natural bond order and valency

Journal of Computational Chemistry

Volumn 19, Issue 6, 1998, Pages 610-627

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

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b INDIANA STATE UNIVERSITY   (United States)

Author keywords

Bond order; Natural resonance theory; Resonance theory; Valency

Indexed keywords

EID: 0742313022     PISSN: 01928651     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1096-987X(19980430)19:6<610::AID-JCC4>3.0.CO;2-U     Document Type: Article

References (77)

1. (a) 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), G. W. Wheland, The Theory of Resonance and Its Application to Organic Chemistry, John Wiley, New York, 1955.
2. (a) 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), G. W. Wheland, The Theory of Resonance and Its Application to Organic Chemistry, John Wiley, New York, 1955.
3. (a) 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), G. W. Wheland, The Theory of Resonance and Its Application to Organic Chemistry, John Wiley, New York, 1955.
4. (b) L. Pauling, Nature of the Chemical Bond, 3rd ed., Cornell University Press, Ithaca, NY, 1960.
5. P.-O Löwdin, Phys. Rev., 97, 1474, (1955); E. R. Davidson, Density Matrices in Quantum Chemistry, Academic, New York, 1976.
6. P.-O Löwdin, Phys. Rev., 97, 1474, (1955); E. R. Davidson, Density Matrices in Quantum Chemistry, Academic, New York, 1976.
7. 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); A. E. Reed, R. B. Weinstock, and F. Weinhold, J. Chem. Phys., 83, 735 (1985); A. E. Reed and F. Weinhold, J. Chem. Phys., 83, 1736 (1985).
8. 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); A. E. Reed, R. B. Weinstock, and F. Weinhold, J. Chem. Phys., 83, 735 (1985); A. E. Reed and F. Weinhold, J. Chem. Phys., 83, 1736 (1985).
9. 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); A. E. Reed, R. B. Weinstock, and F. Weinhold, J. Chem. Phys., 83, 735 (1985); A. E. Reed and F. Weinhold, J. Chem. Phys., 83, 1736 (1985).
10. 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); A. E. Reed, R. B. Weinstock, and F. Weinhold, J. Chem. Phys., 83, 735 (1985); A. E. Reed and F. Weinhold, J. Chem. Phys., 83, 1736 (1985).
11. NBO Program: E. D. Glendening, A. E. Reed, J. E. Carpenter, and F. Weinhold, QCPE Bull., 10, 58 (1990); A. E. Reed and F. Weinhold QCPE Bull., 5, 141 (1985). Reviews of NBO Method and Applications: A. E. Reed, L. A. Curtiss, and F. Weinhold, Chem. Rev., 88, 899 (1988); F. Weinhold and J. E. Carpenter, in R. Naaman and Z. Vager (eds.), The Structure of Small Molecules and Ions, Plenum, New York, 1988.
12. NBO Program: E. D. Glendening, A. E. Reed, J. E. Carpenter, and F. Weinhold, QCPE Bull., 10, 58 (1990); A. E. Reed and F. Weinhold QCPE Bull., 5, 141 (1985). Reviews of NBO Method and Applications: A. E. Reed, L. A. Curtiss, and F. Weinhold, Chem. Rev., 88, 899 (1988); F. Weinhold and J. E. Carpenter, in R. Naaman and Z. Vager (eds.), The Structure of Small Molecules and Ions, Plenum, New York, 1988.
13. NBO Program: E. D. Glendening, A. E. Reed, J. E. Carpenter, and F. Weinhold, QCPE Bull., 10, 58 (1990); A. E. Reed and F. Weinhold QCPE Bull., 5, 141 (1985). Reviews of NBO Method and Applications: A. E. Reed, L. A. Curtiss, and F. Weinhold, Chem. Rev., 88, 899 (1988); F. Weinhold and J. E. Carpenter, in R. Naaman and Z. Vager (eds.), The Structure of Small Molecules and Ions, Plenum, New York, 1988.
14. NBO Program: E. D. Glendening, A. E. Reed, J. E. Carpenter, and F. Weinhold, QCPE Bull., 10, 58 (1990); A. E. Reed and F. Weinhold QCPE Bull., 5, 141 (1985). Reviews of NBO Method and Applications: A. E. Reed, L. A. Curtiss, and F. Weinhold, Chem. Rev., 88, 899 (1988); F. Weinhold and J. E. Carpenter, in R. Naaman and Z. Vager (eds.), The Structure of Small Molecules and Ions, Plenum, New York, 1988.
15. (a) Bond length: L. Pauling, J. Am. Chem. Soc., 69, 542 (1947); Reference 1(b), p. 255; C. A. Coulson, Proc. R. Soc. London, A207, 91 (1951); C. A. Coulson and A. Golebiewski, Proc. Phys. Soc., 78, 1310 (1961); G. Grampp, M. Cebe, and E. Cebe, Z. Phys. Chem., 166, 93 (1990).
16. (a) Bond length: L. Pauling, J. Am. Chem. Soc., 69, 542 (1947); Reference 1(b), p. 255; C. A. Coulson, Proc. R. Soc. London, A207, 91 (1951); C. A. Coulson and A. Golebiewski, Proc. Phys. Soc., 78, 1310 (1961); G. Grampp, M. Cebe, and E. Cebe, Z. Phys. Chem., 166, 93 (1990).
17. (a) Bond length: L. Pauling, J. Am. Chem. Soc., 69, 542 (1947); Reference 1(b), p. 255; C. A. Coulson, Proc. R. Soc. London, A207, 91 (1951); C. A. Coulson and A. Golebiewski, Proc. Phys. Soc., 78, 1310 (1961); G. Grampp, M. Cebe, and E. Cebe, Z. Phys. Chem., 166, 93 (1990).
18. (a) Bond length: L. Pauling, J. Am. Chem. Soc., 69, 542 (1947); Reference 1(b), p. 255; C. A. Coulson, Proc. R. Soc. London, A207, 91 (1951); C. A. Coulson and A. Golebiewski, Proc. Phys. Soc., 78, 1310 (1961); G. Grampp, M. Cebe, and E. Cebe, Z. Phys. Chem., 166, 93 (1990).
19. (b) Bond energy: H. S. Johnson, Adv. Chem. Phys., 3, 131 (1960); H. S. Johnston and A. C. Parr, J. Am. Chem. Soc., 85, 2544 (1963); N. Agmon and R. D. Levine, J. Chem. Phys., 71, 3034 (1979); P. Politzer and S. Ranganathan, Chem. Phys. Lett., 124, 527 (1986).
20. (b) Bond energy: H. S. Johnson, Adv. Chem. Phys., 3, 131 (1960); H. S. Johnston and A. C. Parr, J. Am. Chem. Soc., 85, 2544 (1963); N. Agmon and R. D. Levine, J. Chem. Phys., 71, 3034 (1979); P. Politzer and S. Ranganathan, Chem. Phys. Lett., 124, 527 (1986).
21. (b) Bond energy: H. S. Johnson, Adv. Chem. Phys., 3, 131 (1960); H. S. Johnston and A. C. Parr, J. Am. Chem. Soc., 85, 2544 (1963); N. Agmon and R. D. Levine, J. Chem. Phys., 71, 3034 (1979); P. Politzer and S. Ranganathan, Chem. Phys. Lett., 124, 527 (1986).
22. (b) Bond energy: H. S. Johnson, Adv. Chem. Phys., 3, 131 (1960); H. S. Johnston and A. C. Parr, J. Am. Chem. Soc., 85, 2544 (1963); N. Agmon and R. D. Levine, J. Chem. Phys., 71, 3034 (1979); P. Politzer and S. Ranganathan, Chem. Phys. Lett., 124, 527 (1986).
23. (c) Other: W. Gordy, J. Chem. Phys., 14, 305 (1946); L. Peter, J. Chem. Ed., 63, 123 (1986); M. Barfield, M. J. Collins, J. E. Gready, S. Sternhell, and C. W. Tansey, J. Am. Chem. Soc., 111, 4285 (1989); D. K. Maity and S. P. Bhattacharyya, J. Am. Chem. Soc., 112, 3223 (1990).
24. (c) Other: W. Gordy, J. Chem. Phys., 14, 305 (1946); L. Peter, J. Chem. Ed., 63, 123 (1986); M. Barfield, M. J. Collins, J. E. Gready, S. Sternhell, and C. W. Tansey, J. Am. Chem. Soc., 111, 4285 (1989); D. K. Maity and S. P. Bhattacharyya, J. Am. Chem. Soc., 112, 3223 (1990).
25. (c) Other: W. Gordy, J. Chem. Phys., 14, 305 (1946); L. Peter, J. Chem. Ed., 63, 123 (1986); M. Barfield, M. J. Collins, J. E. Gready, S. Sternhell, and C. W. Tansey, J. Am. Chem. Soc., 111, 4285 (1989); D. K. Maity and S. P. Bhattacharyya, J. Am. Chem. Soc., 112, 3223 (1990).
26. (c) Other: W. Gordy, J. Chem. Phys., 14, 305 (1946); L. Peter, J. Chem. Ed., 63, 123 (1986); M. Barfield, M. J. Collins, J. E. Gready, S. Sternhell, and C. W. Tansey, J. Am. Chem. Soc., 111, 4285 (1989); D. K. Maity and S. P. Bhattacharyya, J. Am. Chem. Soc., 112, 3223 (1990).
27. L. Pauling, L. O. Brockway, and J. Y. Beach, J. Am. Chem. Soc., 57, 2705 (1935).
28. Reference 1(b), p. 282.
29. Reference 1(b), p. 499; Pauling, L. Proc. Roy. Soc. London, A356, 433 (1977).
30. Useful discussion of the nature of valency, electrovalency, and covalency from a historical perspective are given by N. V. Sidgwick, The Electronic Theory of Valency, Oxford University Press, Longon, 1929, particularly Chapter VI; C. A. Russell, History of Valency, University Press, Leicester, 1971.
31. Useful discussion of the nature of valency, electrovalency, and covalency from a historical perspective are given by N. V. Sidgwick, The Electronic Theory of Valency, Oxford University Press, Longon, 1929, particularly Chapter VI; C. A. Russell, History of Valency, University Press, Leicester, 1971.
32. In principle, one might have (e.g., for an excited state) higher occupancy of an antibond than of the corresponding bond, which would lead to a net negative contribution to formal bond order. However, this situation is not provided for in the present version of the NRT program.
33. See, e.g., Reference 1(b) pp. 88-95, for discussion of the relationship of bond energies to electronegativity differences.
34. C. A. Coulson, Proc. R. Soc. London, A169, 413 (1939), A207, 91 (1951); C. A. Coulson, Valence, 2nd ed., Oxford University Press, London, 1961, pp. 266-270.
35. C. A. Coulson, Proc. R. Soc. London, A169, 413 (1939), A207, 91 (1951); C. A. Coulson, Valence, 2nd ed., Oxford University Press, London, 1961, pp. 266-270.
36. C. A. Coulson, Proc. R. Soc. London, A169, 413 (1939), A207, 91 (1951); C. A. Coulson, Valence, 2nd ed., Oxford University Press, London, 1961, pp. 266-270.
37. K. B. Wiberg, Tetrahedron, 24, 1083 (1968).
38. D. R. Armstrong, P. G. Perkins, and J. J. P. Stewart, J. Chem Soc., Dalton Trans., 1973, 838 (1973); N. P. Boresova and S. G. Semenov, Vestn. Leningrad Univ., 16, 119 (1973); M. S. Gopinathan and K. Jug, Theor. Chim. Acta, 63, 497, 511 (1983); I. Mayer and M. Revesz, Inorg. Chim. Acta, 77, L205 (1983); I. Mayer, Chem. Phys. Lett., 97, 270 (1983); I. Mayer, Int. J. Quantum Chem., 26, 151 (1984); M. S. de Giambiagi, M. Giambiagi, and F. E. Jorge, Z. Naturforsch., A39, 1259 (1984); M. A. Natiello and J. A. Medrano, Chem. Phys. Lett., 105, 180 (1984); K. Jug, J. Comput. Chem., 5, 555 (1984); I. Mayer, Int. J. Quantum Chem., 29, 477 (1986); I. Mayer, J. Mol. Struct. Theochem., 149, 81 (1957); K. Jug, E. Fasold, and M. S. Gopinathan, J. Comput. Chem., 10, 965 (1989); G. Lendvay, J. Phys. Chem., 93, 4422 (1989).
39. D. R. Armstrong, P. G. Perkins, and J. J. P. Stewart, J. Chem Soc., Dalton Trans., 1973, 838 (1973); N. P. Boresova and S. G. Semenov, Vestn. Leningrad Univ., 16, 119 (1973); M. S. Gopinathan and K. Jug, Theor. Chim. Acta, 63, 497, 511 (1983); I. Mayer and M. Revesz, Inorg. Chim. Acta, 77, L205 (1983); I. Mayer, Chem. Phys. Lett., 97, 270 (1983); I. Mayer, Int. J. Quantum Chem., 26, 151 (1984); M. S. de Giambiagi, M. Giambiagi, and F. E. Jorge, Z. Naturforsch., A39, 1259 (1984); M. A. Natiello and J. A. Medrano, Chem. Phys. Lett., 105, 180 (1984); K. Jug, J. Comput. Chem., 5, 555 (1984); I. Mayer, Int. J. Quantum Chem., 29, 477 (1986); I. Mayer, J. Mol. Struct. Theochem., 149, 81 (1957); K. Jug, E. Fasold, and M. S. Gopinathan, J. Comput. Chem., 10, 965 (1989); G. Lendvay, J. Phys. Chem., 93, 4422 (1989).
40. D. R. Armstrong, P. G. Perkins, and J. J. P. Stewart, J. Chem Soc., Dalton Trans., 1973, 838 (1973); N. P. Boresova and S. G. Semenov, Vestn. Leningrad Univ., 16, 119 (1973); M. S. Gopinathan and K. Jug, Theor. Chim. Acta, 63, 497, 511 (1983); I. Mayer and M. Revesz, Inorg. Chim. Acta, 77, L205 (1983); I. Mayer, Chem. Phys. Lett., 97, 270 (1983); I. Mayer, Int. J. Quantum Chem., 26, 151 (1984); M. S. de Giambiagi, M. Giambiagi, and F. E. Jorge, Z. Naturforsch., A39, 1259 (1984); M. A. Natiello and J. A. Medrano, Chem. Phys. Lett., 105, 180 (1984); K. Jug, J. Comput. Chem., 5, 555 (1984); I. Mayer, Int. J. Quantum Chem., 29, 477 (1986); I. Mayer, J. Mol. Struct. Theochem., 149, 81 (1957); K. Jug, E. Fasold, and M. S. Gopinathan, J. Comput. Chem., 10, 965 (1989); G. Lendvay, J. Phys. Chem., 93, 4422 (1989).
41. D. R. Armstrong, P. G. Perkins, and J. J. P. Stewart, J. Chem Soc., Dalton Trans., 1973, 838 (1973); N. P. Boresova and S. G. Semenov, Vestn. Leningrad Univ., 16, 119 (1973); M. S. Gopinathan and K. Jug, Theor. Chim. Acta, 63, 497, 511 (1983); I. Mayer and M. Revesz, Inorg. Chim. Acta, 77, L205 (1983); I. Mayer, Chem. Phys. Lett., 97, 270 (1983); I. Mayer, Int. J. Quantum Chem., 26, 151 (1984); M. S. de Giambiagi, M. Giambiagi, and F. E. Jorge, Z. Naturforsch., A39, 1259 (1984); M. A. Natiello and J. A. Medrano, Chem. Phys. Lett., 105, 180 (1984); K. Jug, J. Comput. Chem., 5, 555 (1984); I. Mayer, Int. J. Quantum Chem., 29, 477 (1986); I. Mayer, J. Mol. Struct. Theochem., 149, 81 (1957); K. Jug, E. Fasold, and M. S. Gopinathan, J. Comput. Chem., 10, 965 (1989); G. Lendvay, J. Phys. Chem., 93, 4422 (1989).
42. D. R. Armstrong, P. G. Perkins, and J. J. P. Stewart, J. Chem Soc., Dalton Trans., 1973, 838 (1973); N. P. Boresova and S. G. Semenov, Vestn. Leningrad Univ., 16, 119 (1973); M. S. Gopinathan and K. Jug, Theor. Chim. Acta, 63, 497, 511 (1983); I. Mayer and M. Revesz, Inorg. Chim. Acta, 77, L205 (1983); I. Mayer, Chem. Phys. Lett., 97, 270 (1983); I. Mayer, Int. J. Quantum Chem., 26, 151 (1984); M. S. de Giambiagi, M. Giambiagi, and F. E. Jorge, Z. Naturforsch., A39, 1259 (1984); M. A. Natiello and J. A. Medrano, Chem. Phys. Lett., 105, 180 (1984); K. Jug, J. Comput. Chem., 5, 555 (1984); I. Mayer, Int. J. Quantum Chem., 29, 477 (1986); I. Mayer, J. Mol. Struct. Theochem., 149, 81 (1957); K. Jug, E. Fasold, and M. S. Gopinathan, J. Comput. Chem., 10, 965 (1989); G. Lendvay, J. Phys. Chem., 93, 4422 (1989).
43. D. R. Armstrong, P. G. Perkins, and J. J. P. Stewart, J. Chem Soc., Dalton Trans., 1973, 838 (1973); N. P. Boresova and S. G. Semenov, Vestn. Leningrad Univ., 16, 119 (1973); M. S. Gopinathan and K. Jug, Theor. Chim. Acta, 63, 497, 511 (1983); I. Mayer and M. Revesz, Inorg. Chim. Acta, 77, L205 (1983); I. Mayer, Chem. Phys. Lett., 97, 270 (1983); I. Mayer, Int. J. Quantum Chem., 26, 151 (1984); M. S. de Giambiagi, M. Giambiagi, and F. E. Jorge, Z. Naturforsch., A39, 1259 (1984); M. A. Natiello and J. A. Medrano, Chem. Phys. Lett., 105, 180 (1984); K. Jug, J. Comput. Chem., 5, 555 (1984); I. Mayer, Int. J. Quantum Chem., 29, 477 (1986); I. Mayer, J. Mol. Struct. Theochem., 149, 81 (1957); K. Jug, E. Fasold, and M. S. Gopinathan, J. Comput. Chem., 10, 965 (1989); G. Lendvay, J. Phys. Chem., 93, 4422 (1989).
44. D. R. Armstrong, P. G. Perkins, and J. J. P. Stewart, J. Chem Soc., Dalton Trans., 1973, 838 (1973); N. P. Boresova and S. G. Semenov, Vestn. Leningrad Univ., 16, 119 (1973); M. S. Gopinathan and K. Jug, Theor. Chim. Acta, 63, 497, 511 (1983); I. Mayer and M. Revesz, Inorg. Chim. Acta, 77, L205 (1983); I. Mayer, Chem. Phys. Lett., 97, 270 (1983); I. Mayer, Int. J. Quantum Chem., 26, 151 (1984); M. S. de Giambiagi, M. Giambiagi, and F. E. Jorge, Z. Naturforsch., A39, 1259 (1984); M. A. Natiello and J. A. Medrano, Chem. Phys. Lett., 105, 180 (1984); K. Jug, J. Comput. Chem., 5, 555 (1984); I. Mayer, Int. J. Quantum Chem., 29, 477 (1986); I. Mayer, J. Mol. Struct. Theochem., 149, 81 (1957); K. Jug, E. Fasold, and M. S. Gopinathan, J. Comput. Chem., 10, 965 (1989); G. Lendvay, J. Phys. Chem., 93, 4422 (1989).
45. D. R. Armstrong, P. G. Perkins, and J. J. P. Stewart, J. Chem Soc., Dalton Trans., 1973, 838 (1973); N. P. Boresova and S. G. Semenov, Vestn. Leningrad Univ., 16, 119 (1973); M. S. Gopinathan and K. Jug, Theor. Chim. Acta, 63, 497, 511 (1983); I. Mayer and M. Revesz, Inorg. Chim. Acta, 77, L205 (1983); I. Mayer, Chem. Phys. Lett., 97, 270 (1983); I. Mayer, Int. J. Quantum Chem., 26, 151 (1984); M. S. de Giambiagi, M. Giambiagi, and F. E. Jorge, Z. Naturforsch., A39, 1259 (1984); M. A. Natiello and J. A. Medrano, Chem. Phys. Lett., 105, 180 (1984); K. Jug, J. Comput. Chem., 5, 555 (1984); I. Mayer, Int. J. Quantum Chem., 29, 477 (1986); I. Mayer, J. Mol. Struct. Theochem., 149, 81 (1957); K. Jug, E. Fasold, and M. S. Gopinathan, J. Comput. Chem., 10, 965 (1989); G. Lendvay, J. Phys. Chem., 93, 4422 (1989).
46. D. R. Armstrong, P. G. Perkins, and J. J. P. Stewart, J. Chem Soc., Dalton Trans., 1973, 838 (1973); N. P. Boresova and S. G. Semenov, Vestn. Leningrad Univ., 16, 119 (1973); M. S. Gopinathan and K. Jug, Theor. Chim. Acta, 63, 497, 511 (1983); I. Mayer and M. Revesz, Inorg. Chim. Acta, 77, L205 (1983); I. Mayer, Chem. Phys. Lett., 97, 270 (1983); I. Mayer, Int. J. Quantum Chem., 26, 151 (1984); M. S. de Giambiagi, M. Giambiagi, and F. E. Jorge, Z. Naturforsch., A39, 1259 (1984); M. A. Natiello and J. A. Medrano, Chem. Phys. Lett., 105, 180 (1984); K. Jug, J. Comput. Chem., 5, 555 (1984); I. Mayer, Int. J. Quantum Chem., 29, 477 (1986); I. Mayer, J. Mol. Struct. Theochem., 149, 81 (1957); K. Jug, E. Fasold, and M. S. Gopinathan, J. Comput. Chem., 10, 965 (1989); G. Lendvay, J. Phys. Chem., 93, 4422 (1989).
47. D. R. Armstrong, P. G. Perkins, and J. J. P. Stewart, J. Chem Soc., Dalton Trans., 1973, 838 (1973); N. P. Boresova and S. G. Semenov, Vestn. Leningrad Univ., 16, 119 (1973); M. S. Gopinathan and K. Jug, Theor. Chim. Acta, 63, 497, 511 (1983); I. Mayer and M. Revesz, Inorg. Chim. Acta, 77, L205 (1983); I. Mayer, Chem. Phys. Lett., 97, 270 (1983); I. Mayer, Int. J. Quantum Chem., 26, 151 (1984); M. S. de Giambiagi, M. Giambiagi, and F. E. Jorge, Z. Naturforsch., A39, 1259 (1984); M. A. Natiello and J. A. Medrano, Chem. Phys. Lett., 105, 180 (1984); K. Jug, J. Comput. Chem., 5, 555 (1984); I. Mayer, Int. J. Quantum Chem., 29, 477 (1986); I. Mayer, J. Mol. Struct. Theochem., 149, 81 (1957); K. Jug, E. Fasold, and M. S. Gopinathan, J. Comput. Chem., 10, 965 (1989); G. Lendvay, J. Phys. Chem., 93, 4422 (1989).
48. D. R. Armstrong, P. G. Perkins, and J. J. P. Stewart, J. Chem Soc., Dalton Trans., 1973, 838 (1973); N. P. Boresova and S. G. Semenov, Vestn. Leningrad Univ., 16, 119 (1973); M. S. Gopinathan and K. Jug, Theor. Chim. Acta, 63, 497, 511 (1983); I. Mayer and M. Revesz, Inorg. Chim. Acta, 77, L205 (1983); I. Mayer, Chem. Phys. Lett., 97, 270 (1983); I. Mayer, Int. J. Quantum Chem., 26, 151 (1984); M. S. de Giambiagi, M. Giambiagi, and F. E. Jorge, Z. Naturforsch., A39, 1259 (1984); M. A. Natiello and J. A. Medrano, Chem. Phys. Lett., 105, 180 (1984); K. Jug, J. Comput. Chem., 5, 555 (1984); I. Mayer, Int. J. Quantum Chem., 29, 477 (1986); I. Mayer, J. Mol. Struct. Theochem., 149, 81 (1957); K. Jug, E. Fasold, and M. S. Gopinathan, J. Comput. Chem., 10, 965 (1989); G. Lendvay, J. Phys. Chem., 93, 4422 (1989).
49. D. R. Armstrong, P. G. Perkins, and J. J. P. Stewart, J. Chem Soc., Dalton Trans., 1973, 838 (1973); N. P. Boresova and S. G. Semenov, Vestn. Leningrad Univ., 16, 119 (1973); M. S. Gopinathan and K. Jug, Theor. Chim. Acta, 63, 497, 511 (1983); I. Mayer and M. Revesz, Inorg. Chim. Acta, 77, L205 (1983); I. Mayer, Chem. Phys. Lett., 97, 270 (1983); I. Mayer, Int. J. Quantum Chem., 26, 151 (1984); M. S. de Giambiagi, M. Giambiagi, and F. E. Jorge, Z. Naturforsch., A39, 1259 (1984); M. A. Natiello and J. A. Medrano, Chem. Phys. Lett., 105, 180 (1984); K. Jug, J. Comput. Chem., 5, 555 (1984); I. Mayer, Int. J. Quantum Chem., 29, 477 (1986); I. Mayer, J. Mol. Struct. Theochem., 149, 81 (1957); K. Jug, E. Fasold, and M. S. Gopinathan, J. Comput. Chem., 10, 965 (1989); G. Lendvay, J. Phys. Chem., 93, 4422 (1989).
50. D. R. Armstrong, P. G. Perkins, and J. J. P. Stewart, J. Chem Soc., Dalton Trans., 1973, 838 (1973); N. P. Boresova and S. G. Semenov, Vestn. Leningrad Univ., 16, 119 (1973); M. S. Gopinathan and K. Jug, Theor. Chim. Acta, 63, 497, 511 (1983); I. Mayer and M. Revesz, Inorg. Chim. Acta, 77, L205 (1983); I. Mayer, Chem. Phys. Lett., 97, 270 (1983); I. Mayer, Int. J. Quantum Chem., 26, 151 (1984); M. S. de Giambiagi, M. Giambiagi, and F. E. Jorge, Z. Naturforsch., A39, 1259 (1984); M. A. Natiello and J. A. Medrano, Chem. Phys. Lett., 105, 180 (1984); K. Jug, J. Comput. Chem., 5, 555 (1984); I. Mayer, Int. J. Quantum Chem., 29, 477 (1986); I. Mayer, J. Mol. Struct. Theochem., 149, 81 (1957); K. Jug, E. Fasold, and M. S. Gopinathan, J. Comput. Chem., 10, 965 (1989); G. Lendvay, J. Phys. Chem., 93, 4422 (1989).
51. 14 see I. Mayer, Theor. Chim. Acta, 67, 315 (1985); note that the orbitals called "natural hybrid orbitals" and "natural bond orbitals" by Jug and coworkers in 1983 are unrelated to the corresponding quantities defined previously in references 3 and 4.
52. 14 are closely associated with Mulliken population analysis and its well-known pathologies in larger basis sets. For example, Baker [J. Baker, Theor. Chim. Acta, 68, 221 (1985)] cites an example in which the calculated Mayer valency of carbon changes from +3.39 to -(!)4.86 when diffuse functions are added.
53. Jug and coworkers (see citations in reference 14) have variously suggested Wiberg's formula with no overlap, with Löwdin orthogonalization, and with a modified scheme of occupancy-weighted symmetric orthogonalization.
54. F. Weinhold and J. E. Carpenter, J. Mol. Struct. Theochem., 165, 189 (1980).
55. A. E. Reed and P. v. R. Schleyer, Inorg Chem., 27, 3969 (1988); J. Am. Chem. Soc., 112, 1434 (1990).
56. A. E. Reed and P. v. R. Schleyer, Inorg Chem., 27, 3969 (1988); J. Am. Chem. Soc., 112, 1434 (1990).
57. J. Cioslowski and S. T. Mixon, J. Am. Chem. Soc., 113, 4142 (1991).
58. R. F. W. Bader and T. T. Nguyen-Dang, Adv. Quantum Chem., 14, 63 (1981).
59. K. B. Wiberg and P. R. Rablen, J. Am. Chem. Soc., 115, 614 (1943).
60. I. D. Brown and R. D. Shannon, Acta Crystall., A29, 266 (1973); I. D. Brown and D. Altermatt, Acta Crystall., B41, 244 (1985). For applications, see I. D. Brown, J. Solid State Chem., 82, 122 (1989); M.-H. Whangbo and C. C. Torardi, Science, 249, 1143 (1990).
61. I. D. Brown and R. D. Shannon, Acta Crystall., A29, 266 (1973); I. D. Brown and D. Altermatt, Acta Crystall., B41, 244 (1985). For applications, see I. D. Brown, J. Solid State Chem., 82, 122 (1989); M.-H. Whangbo and C. C. Torardi, Science, 249, 1143 (1990).
62. I. D. Brown and R. D. Shannon, Acta Crystall., A29, 266 (1973); I. D. Brown and D. Altermatt, Acta Crystall., B41, 244 (1985). For applications, see I. D. Brown, J. Solid State Chem., 82, 122 (1989); M.-H. Whangbo and C. C. Torardi, Science, 249, 1143 (1990).
63. I. D. Brown and R. D. Shannon, Acta Crystall., A29, 266 (1973); I. D. Brown and D. Altermatt, Acta Crystall., B41, 244 (1985). For applications, see I. D. Brown, J. Solid State Chem., 82, 122 (1989); M.-H. Whangbo and C. C. Torardi, Science, 249, 1143 (1990).
64. W. G. Penny, Proc. R. Soc. London, A158, 306 (1937); W. C. Herndon, J. Am. Chem. Soc., 95, 2404 (1973); I. Gutman and N. Trinajstic, Top. Curr. Chem., 42, 49 (1973); I. Gutman and H. Sachs, Z. Phys. Chem., 268, 257 (1987), and references therein.
65. W. G. Penny, Proc. R. Soc. London, A158, 306 (1937); W. C. Herndon, J. Am. Chem. Soc., 95, 2404 (1973); I. Gutman and N. Trinajstic, Top. Curr. Chem., 42, 49 (1973); I. Gutman and H. Sachs, Z. Phys. Chem., 268, 257 (1987), and references therein.
66. W. G. Penny, Proc. R. Soc. London, A158, 306 (1937); W. C. Herndon, J. Am. Chem. Soc., 95, 2404 (1973); I. Gutman and N. Trinajstic, Top. Curr. Chem., 42, 49 (1973); I. Gutman and H. Sachs, Z. Phys. Chem., 268, 257 (1987), and references therein.
67. W. G. Penny, Proc. R. Soc. London, A158, 306 (1937); W. C. Herndon, J. Am. Chem. Soc., 95, 2404 (1973); I. Gutman and N. Trinajstic, Top. Curr. Chem., 42, 49 (1973); I. Gutman and H. Sachs, Z. Phys. Chem., 268, 257 (1987), and references therein.
68. J. A. Pople and M. Gordon, J. Am. Chem. Soc., 87, 4253 (1967).
69. For a comprehensive description of computational methods and basis set designations used herein, see W. J. Hehre, L. Radom, P. v. R. Schleyer, and J. A Pople, Ab Initio Molecular Orbital Theory, John Wiley, New York, 1986. All wave function calculations were performed with the Gaussian 92 program system: M. J. Frisch, G. W. Trucks, M. Head-Gordon, P. M. W. Gill, M. W. Wong, J. B. Foresman, B. G. Johnson, H. B. Schlegel, M. A. Robb, E. S. Repogle, R. Gomperts, J. L. Andres, K. Raghavachari, J. S. Binkley, C. Gonzalez, R. L. Martin, D. J. Fox, D. J. Defrees, J. Baker, J. J. P. Stewart, and J. A. Pople, Gaussian 92, Revision A, Gaussian, Inc., Pittsburgh, 1992.
70. For a comprehensive description of computational methods and basis set designations used herein, see W. J. Hehre, L. Radom, P. v. R. Schleyer, and J. A Pople, Ab Initio Molecular Orbital Theory, John Wiley, New York, 1986. All wave function calculations were performed with the Gaussian 92 program system: M. J. Frisch, G. W. Trucks, M. Head-Gordon, P. M. W. Gill, M. W. Wong, J. B. Foresman, B. G. Johnson, H. B. Schlegel, M. A. Robb, E. S. Repogle, R. Gomperts, J. L. Andres, K. Raghavachari, J. S. Binkley, C. Gonzalez, R. L. Martin, D. J. Fox, D. J. Defrees, J. Baker, J. J. P. Stewart, and J. A. Pople, Gaussian 92, Revision A, Gaussian, Inc., Pittsburgh, 1992.
71. AB.
72. max) ensures that only the most strongly delocalized systems will have more than a single reference structure.
73. The default NRT expansions for these wave functions include about 20 additional structures (not shown) with smaller weightings ≥ 0.01%.
74. The superficially high weight of "long bond" structures in earlier RT treatments can be attributed to the "overcorrelation" artifact of Heitler-London valence-bond wave functions; see R. McWeeny, Proc. R. Soc. London, A223, 63, 306 (1954).
75. CF reported in references 20 (0.572, RHF/6-31+ + G** level) and 22 (0.616 RHF/6-311 + + G** level) is therefore puzzling.
76. C is rather close to the NRT covalency (2.427) in this case, but the corresponding valencies for fluorine differ by almost a factor of two.
77. J. E. Carpeter and F. Weinhold, J. Mol. Struct. Theochem., 169, 41 (1988).