On obtaining localized bonding schemes from delocalized molecular-orbital wave functions

Theoretical Chemistry Accounts

Volumn 96, Issue 4, 1997, Pages 223-242

  Bachler, Vinzenz ^a  

^a MAX PLANCK INSTITUTE FOR CHEMICAL ENERGY CONVERSION   (Germany)

Author keywords

Bonding schemes; Localization

Indexed keywords

EID: 0031285743     PISSN: 1432881X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002140050225     Document Type: Article

References (154)

1. For a comprehensive compilation of ab initio results see Hehre WJ, Radom L, PvR Schleyer, Pople JA (1986) Ab initio molecular orbital theory. Wiley, New York
2. Bartlett RJ, Stanton JF (1994) Rev Comp Chem, vol V, Chap 2; Hirst DM (1982) Adv Chem Phys 50:517; Bruna PJ, Peyerimhoff SD (1987) Adv Chem Phys 67:1
3. Bartlett RJ, Stanton JF (1994) Rev Comp Chem, vol V, Chap 2; Hirst DM (1982) Adv Chem Phys 50:517; Bruna PJ, Peyerimhoff SD (1987) Adv Chem Phys 67:1
4. Bartlett RJ, Stanton JF (1994) Rev Comp Chem, vol V, Chap 2; Hirst DM (1982) Adv Chem Phys 50:517; Bruna PJ, Peyerimhoff SD (1987) Adv Chem Phys 67:1
5. For a comprehensive review see Fukui K (1975) Theory of orientation and stereoselection. Springer, Berlin Heidelberg New York
6. Pearson RG (1976) Symmetry rules for chemical reactions. Wiley, New York; Woodward RB, Hoffmann R (1970) Die Erhaltung der Orbitalsymmetrie. Verlag Chemie, Weinheim; Halevi EA (1992) Orbital symmetry and reaction mechanisms. The OCAMS view. Springer, Berlin Heidelberg New York
7. Pearson RG (1976) Symmetry rules for chemical reactions. Wiley, New York; Woodward RB, Hoffmann R (1970) Die Erhaltung der Orbitalsymmetrie. Verlag Chemie, Weinheim; Halevi EA (1992) Orbital symmetry and reaction mechanisms. The OCAMS view. Springer, Berlin Heidelberg New York
8. Pearson RG (1976) Symmetry rules for chemical reactions. Wiley, New York; Woodward RB, Hoffmann R (1970) Die Erhaltung der Orbitalsymmetrie. Verlag Chemie, Weinheim; Halevi EA (1992) Orbital symmetry and reaction mechanisms. The OCAMS view. Springer, Berlin Heidelberg New York
9. Roothaan CCJ (1951) Rev Mod Phys 23. 69, in particular Sect. V
10. Edmiston C, Ruedenberg K (1965) J Chem Phys 43:S97; Foster JM, Boys SF (1960) Rev Mod Phys 32:300; Magnasco V, Perico A (1967) J Chem Phys 47:971; Magnasco V, Perico A (1968) J Chem Phys 48:800
11. Edmiston C, Ruedenberg K (1965) J Chem Phys 43:S97; Foster JM, Boys SF (1960) Rev Mod Phys 32:300; Magnasco V, Perico A (1967) J Chem Phys 47:971; Magnasco V, Perico A (1968) J Chem Phys 48:800
12. Edmiston C, Ruedenberg K (1965) J Chem Phys 43:S97; Foster JM, Boys SF (1960) Rev Mod Phys 32:300; Magnasco V, Perico A (1967) J Chem Phys 47:971; Magnasco V, Perico A (1968) J Chem Phys 48:800
13. Edmiston C, Ruedenberg K (1965) J Chem Phys 43:S97; Foster JM, Boys SF (1960) Rev Mod Phys 32:300; Magnasco V, Perico A (1967) J Chem Phys 47:971; Magnasco V, Perico A (1968) J Chem Phys 48:800
14. See for e.g. England W, Salmon LS, Ruedenberg K (1971) Top Curr Chem 23:31
15. (a) Heitler W, London F (1927) Z Physik 44:455;
16. (b) For an elementary introduction to the Slater-Pauling VB method for conjugated molecules, see Pilar FL (1968) Elementary quantum chemistry. McGraw Hill, New York pp 655-667;
17. (c) A comprehensive treatment is given in Wheland GW (1955) Resonance in organic chemistry. Chap. 9. Wiley, New York, p 544
18. Wheland GW (1955) Resonance in organic chemistry, Chap. 1. Wiley, New York
19. For a discussion on the mathematical foundations of resonance see Ref. [9] Chap. 1.5, p 24
20. For a summary of VB calculations and their dependence on the number of applied structures, see the review by Gerrat J (1974) Valence bond theory. In: Theoretical chemistry. A specialist periodical report, vol I, p 60, in particular Table 1
21. See for e.g. Pauncz R (1979) Spin eigenfunctions. Plenum, New York in particular Chap. 5 for Spin paired spin eigenfunctions, p 77
22. For a comparison of non-orthogonal and orthogonal VB approaches see Campion WJ, Karplus M (1973) Mol Phys 25:921
23. For a review see Pross A, Shaik SS (1983) Acc Chem Res 16:363; Shaik SS, Hiberty PC (1991) In: Maksic ZB (ed) Theoretical models of chemical bonding, part 4. Springer, Berlin Heidelberg New York
24. For a review see Pross A, Shaik SS (1983) Acc Chem Res 16:363; Shaik SS, Hiberty PC (1991) In: Maksic ZB (ed) Theoretical models of chemical bonding, part 4. Springer, Berlin Heidelberg New York
25. Shaik SS (1985) Prog Phys Org Chem 15:197
26. Harcourt RD (1992) New J Chem 16:667
27. Harcourt RD, Little RD (1984) J Am Chem Soc 106:41
28. Harcourt RD (1982) Qualitative valence bond descriptions of electron rich molecules. (Lecture notes in chemistry. Chap. 21) Springer, Berlin Heidelberg New York
29. Epiotis ND (1982) Unified valence bond theory of electronic structure. (Lecture notes in chemistry) Springer, Berlin Heidelberg New York; Epiotis ND (1983) Unified valence bond theory of electronic structure applications. Springer, Berlin Heidelberg New York
30. Epiotis ND (1982) Unified valence bond theory of electronic structure. (Lecture notes in chemistry) Springer, Berlin Heidelberg New York; Epiotis ND (1983) Unified valence bond theory of electronic structure applications. Springer, Berlin Heidelberg New York
31. Malrieu JP, Maynau D, Daudey JP (1984) Phys Rev B30:1817; Said M, Maynau D, Malrieu JP, Garcia Bach MA (1984) J Am Chem Soc 106:571; Said M, Maynau D, Malrieu JP (1984) J Am Chem Soc 106:580; Maynau D, Malrieu JP (1982) J Am Chem Soc 104:3029; Sanchez-Martin J, Malrieu JP (1985) J Am Chem Soc 107:1985; Malrieu JP, (1986) Nouv J Chim 10:61; Durand P, Malrieu JP (1987) Adv Chem Phys 67:321
32. Malrieu JP, Maynau D, Daudey JP (1984) Phys Rev B30:1817; Said M, Maynau D, Malrieu JP, Garcia Bach MA (1984) J Am Chem Soc 106:571; Said M, Maynau D, Malrieu JP (1984) J Am Chem Soc 106:580; Maynau D, Malrieu JP (1982) J Am Chem Soc 104:3029; Sanchez-Martin J, Malrieu JP (1985) J Am Chem Soc 107:1985; Malrieu JP, (1986) Nouv J Chim 10:61; Durand P, Malrieu JP (1987) Adv Chem Phys 67:321
33. Malrieu JP, Maynau D, Daudey JP (1984) Phys Rev B30:1817; Said M, Maynau D, Malrieu JP, Garcia Bach MA (1984) J Am Chem Soc 106:571; Said M, Maynau D, Malrieu JP (1984) J Am Chem Soc 106:580; Maynau D, Malrieu JP (1982) J Am Chem Soc 104:3029; Sanchez-Martin J, Malrieu JP (1985) J Am Chem Soc 107:1985; Malrieu JP, (1986) Nouv J Chim 10:61; Durand P, Malrieu JP (1987) Adv Chem Phys 67:321
34. Malrieu JP, Maynau D, Daudey JP (1984) Phys Rev B30:1817; Said M, Maynau D, Malrieu JP, Garcia Bach MA (1984) J Am Chem Soc 106:571; Said M, Maynau D, Malrieu JP (1984) J Am Chem Soc 106:580; Maynau D, Malrieu JP (1982) J Am Chem Soc 104:3029; Sanchez-Martin J, Malrieu JP (1985) J Am Chem Soc 107:1985; Malrieu JP, (1986) Nouv J Chim 10:61; Durand P, Malrieu JP (1987) Adv Chem Phys 67:321
35. Malrieu JP, Maynau D, Daudey JP (1984) Phys Rev B30:1817; Said M, Maynau D, Malrieu JP, Garcia Bach MA (1984) J Am Chem Soc 106:571; Said M, Maynau D, Malrieu JP (1984) J Am Chem Soc 106:580; Maynau D, Malrieu JP (1982) J Am Chem Soc 104:3029; Sanchez-Martin J, Malrieu JP (1985) J Am Chem Soc 107:1985; Malrieu JP, (1986) Nouv J Chim 10:61; Durand P, Malrieu JP (1987) Adv Chem Phys 67:321
36. Malrieu JP, Maynau D, Daudey JP (1984) Phys Rev B30:1817; Said M, Maynau D, Malrieu JP, Garcia Bach MA (1984) J Am Chem Soc 106:571; Said M, Maynau D, Malrieu JP (1984) J Am Chem Soc 106:580; Maynau D, Malrieu JP (1982) J Am Chem Soc 104:3029; Sanchez-Martin J, Malrieu JP (1985) J Am Chem Soc 107:1985; Malrieu JP, (1986) Nouv J Chim 10:61; Durand P, Malrieu JP (1987) Adv Chem Phys 67:321
37. Malrieu JP, Maynau D, Daudey JP (1984) Phys Rev B30:1817; Said M, Maynau D, Malrieu JP, Garcia Bach MA (1984) J Am Chem Soc 106:571; Said M, Maynau D, Malrieu JP (1984) J Am Chem Soc 106:580; Maynau D, Malrieu JP (1982) J Am Chem Soc 104:3029; Sanchez-Martin J, Malrieu JP (1985) J Am Chem Soc 107:1985; Malrieu JP, (1986) Nouv J Chim 10:61; Durand P, Malrieu JP (1987) Adv Chem Phys 67:321
38. Roth WR, Staemmler V, Neumann M, Schmuck C (1995) Liebigs Ann 1061
39. Treboux G, Maynau D, Malrieu JP (1995) J Phys Chem 99:6417
40. Bernardi F, Olivucci M, Robb MA (1992) J Am Chem Soc 114:1606
41. Bernardi F, Olivucci M, Ragazos IN, Robb MA (1992) J Am Chem Soc 114:8211
42. Hiberty PC, Flament JP, Noizet E (1992) Chem Phys Lett 189:259; Maitre P, Lefour JM, Ohanessian G, Hiberty PC (1990) J Phys Chem 94:4082; Harcourt RD, Roso W (1978) Can J Chem 56:1093
43. Hiberty PC, Flament JP, Noizet E (1992) Chem Phys Lett 189:259; Maitre P, Lefour JM, Ohanessian G, Hiberty PC (1990) J Phys Chem 94:4082; Harcourt RD, Roso W (1978) Can J Chem 56:1093
44. Hiberty PC, Flament JP, Noizet E (1992) Chem Phys Lett 189:259; Maitre P, Lefour JM, Ohanessian G, Hiberty PC (1990) J Phys Chem 94:4082; Harcourt RD, Roso W (1978) Can J Chem 56:1093
45. Cooper DL, Gerratt J, Raimondi M (1987) Adv Chem Phys 69:319
46. See Ref. [26] in particular Eq. (21)
47. For a review see Cooper DL, Gerratt J, Raimondi M (1991) Chem Rev 91:929
48. See e.g. Häser M, Ahlrichs R, Baron HP, Weiss P, Horn H (1992) Theor Chim Acta 83:455; Schneider U, Richard S, Kappers MM, Ahlrichs R (1993) Chem Phys Lett 210:165
49. See e.g. Häser M, Ahlrichs R, Baron HP, Weiss P, Horn H (1992) Theor Chim Acta 83:455; Schneider U, Richard S, Kappers MM, Ahlrichs R (1993) Chem Phys Lett 210:165
50. See e.g. Hurley AC (1960) Rev Mod Phys 32:400; Berry RS (1959) J Chem Phys 30:936; Harcourt RD, Harcourt A (1974) J Chem Soc Faraday Trans II 70:743; Harcourt RD (1964) Theor Chim Acta 2:437; Harcourt RD (1966) 6:131; Harcourt RD (1970) Int J Quantum Chem 4:173; Harcourt RD, Sillitoe JF (1974) Aust J Chem 27:691
51. See e.g. Hurley AC (1960) Rev Mod Phys 32:400; Berry RS (1959) J Chem Phys 30:936; Harcourt RD, Harcourt A (1974) J Chem Soc Faraday Trans II 70:743; Harcourt RD (1964) Theor Chim Acta 2:437; Harcourt RD (1966) 6:131; Harcourt RD (1970) Int J Quantum Chem 4:173; Harcourt RD, Sillitoe JF (1974) Aust J Chem 27:691
52. See e.g. Hurley AC (1960) Rev Mod Phys 32:400; Berry RS (1959) J Chem Phys 30:936; Harcourt RD, Harcourt A (1974) J Chem Soc Faraday Trans II 70:743; Harcourt RD (1964) Theor Chim Acta 2:437; Harcourt RD (1966) 6:131; Harcourt RD (1970) Int J Quantum Chem 4:173; Harcourt RD, Sillitoe JF (1974) Aust J Chem 27:691
53. See e.g. Hurley AC (1960) Rev Mod Phys 32:400; Berry RS (1959) J Chem Phys 30:936; Harcourt RD, Harcourt A (1974) J Chem Soc Faraday Trans II 70:743; Harcourt RD (1964) Theor Chim Acta 2:437; Harcourt RD (1966) 6:131; Harcourt RD (1970) Int J Quantum Chem 4:173; Harcourt RD, Sillitoe JF (1974) Aust J Chem 27:691
54. See e.g. Hurley AC (1960) Rev Mod Phys 32:400; Berry RS (1959) J Chem Phys 30:936; Harcourt RD, Harcourt A (1974) J Chem Soc Faraday Trans II 70:743; Harcourt RD (1964) Theor Chim Acta 2:437; Harcourt RD (1966) 6:131; Harcourt RD (1970) Int J Quantum Chem 4:173; Harcourt RD, Sillitoe JF (1974) Aust J Chem 27:691
55. See e.g. Hurley AC (1960) Rev Mod Phys 32:400; Berry RS (1959) J Chem Phys 30:936; Harcourt RD, Harcourt A (1974) J Chem Soc Faraday Trans II 70:743; Harcourt RD (1964) Theor Chim Acta 2:437; Harcourt RD (1966) 6:131; Harcourt RD (1970) Int J Quantum Chem 4:173; Harcourt RD, Sillitoe JF (1974) Aust J Chem 27:691
56. See e.g. Hurley AC (1960) Rev Mod Phys 32:400; Berry RS (1959) J Chem Phys 30:936; Harcourt RD, Harcourt A (1974) J Chem Soc Faraday Trans II 70:743; Harcourt RD (1964) Theor Chim Acta 2:437; Harcourt RD (1966) 6:131; Harcourt RD (1970) Int J Quantum Chem 4:173; Harcourt RD, Sillitoe JF (1974) Aust J Chem 27:691
57. Hiberty PC, Leforestier C (1978) J Am Chem Soc 100:2012
58. See Ref. [31], Eq. (13)
59. Rumer G (1932) Göttinger Nachr 377 for a comprehensive outline see Ref. [12]
60. Hiberty PC (1990) Klein DJ, Trinjastic N (eds) In: Valence bond theory and chemical structure. Elsevier, Amsterdam p 221
61. Karafiloglou P, Malrieu JP (1986) Chem Phys 104:383
62. See Ref. [35] the two formulas in Sect. 2.4
63. Karafiloglou P, Ohanessian G (1991) J Chem Ed 68:583
64. Moffit W (1953) Proc R Soc Lond A 218:486
65. Mestres J, Lledos A, Duran M, Betran J (1992) J Mol Struct (Theochem) 92:259 for the weight variations along the reaction coordinate see Figs. 2 and 3
66. Sola M, Lledos A, Duran M, Bertran J (1991) Int J Quantum Chem 40:511
67. Maki I, Kitaura K, Nishimoto K (1994) Theor Chim Acta 89:89
68. Pople JA, Nesbet RK (1954) J Chem Phys 22:571
69. See for e.g. Pauncz R (1967) Alternant molecular orbital method. Saunders, Philadelphia. pp 9, 38-40. The three electron case is treated in Ref. [8b], p 291
70. For a thorough discussion of this theorem see Gantmacher FR (1986) Matrizentheorie. Springer, Berlin Heidelberg New York p 27, Eq. (16)
71. Baba H, Suzuki S, Takemura T (1969) J Chem Phys 50:2078
72. Hohlneicher G, Börsch-Pulm B (1987) Ber Bunsenges Phys Chem 91:929
73. Platt JR (1949) J Chem Phys 17:484
74. Balint-Kurti GG, Karplus M (1969) J Chem Phys 50:478 in particular Appendix A Eq. (A3)
75. See Ref. [46] the sentence below A2
76. Lievin J, Breulet J, Clerq P, Metz JY (1982) Theor Chim Acta 61:513
77. For the π-electron system of naphtaline a set of 63504 AO determinants is obtained. This number is also given in Ref. [31]
78. Karafiloglou P, Akrivos P (1988) Chem Phys 127:41
79. For a comparison of weights when orthogonal or non-orthogonal VB functions are applied see Ohanessian G, Hiberty PC (1987) Chem Phys Lett 137:437
80. See for e.g. Ref [31] and Ref. [35]
81. Hiberty PC, Ohanessian G (1985) Int J Quantum Chem 27:245 Eq. (3)
82. This weight formula was applied by M. Simonetta. His results for benzene and butadiene are outlined in Levine IN (1970) Quantum chemistry, vol. I, Sect. 15.10. Allyn and Bacon, Boston pp 550-551
83. Gaussian 92/DFT, Revision g.4. Frisch MJ, Trucks GW, Schlegel HB, Gill PMW, Johnson BG, Wong MW, Foresman JB, Robb MA, Head-Gordon M, Repogle ES, Gomperts R, Andres JL, Raghavachari K, Binkley JS, Gonzales C, Martin RL, Fox DJ, Defrees DJ, Baker J, Stewart JJP, Pople JA (1993) Gaussian Inc., Pittsburg, Pa
84. Hehre WJ, Stewart RF, Pople JA (1969) J Chem Phys 51:2657
85. The Chemical Society (1965) Tables of interatomic distances and configurations in molecules and ions. Supplement, M78s. London
86. For a comparison of covalent and ionic weights at the SCF level see Ref. [55] but Sects. 4 and 5, see also Ref. [34]
87. 2 and CO this finding is illustrated in Ref. [35] Figs. 1 and 2, respectively
88. Hiberty PC, Ohanessian G (1985) Int J Quantum Chem 27:259
89. Lepetit MB, Oujia B, Malrieu JP, Maynau D (1989) Phys Rev A 39:3274
90. Oujia B, Lepetit MB, Maynau D, Malrieu JP (1989) Phys Rev A 39:3289
91. Oujia B, Malrieu JP (1991) Phys Rev B 44:1480
92. Fulde P (1995) Electron correlations in molecules and solids. 3rd edn. Springer, Berlin Heidelberg New York; Fulde P (1990) Calculation of electron correlation by using local operators. In: Maksic ZB (ed) Theoretical models of chemical bonding, Part 2. Springer, Berlin Heidelberg New York, p 377; Stollhoff G, Fulde P (1977) Z Phys B26:251; Stollhoff G, Fulde P (1978) 29:231; Stollhoff G, Fulde P (1980) J Chem Phys 73:4548 Local operators have been applied early to transition metals, see Gutzwiller MC (1963) Phys Rev Lett 10:159
93. Fulde P (1995) Electron correlations in molecules and solids. 3rd edn. Springer, Berlin Heidelberg New York; Fulde P (1990) Calculation of electron correlation by using local operators. In: Maksic ZB (ed) Theoretical models of chemical bonding, Part 2. Springer, Berlin Heidelberg New York, p 377; Stollhoff G, Fulde P (1977) Z Phys B26:251; Stollhoff G, Fulde P (1978) 29:231; Stollhoff G, Fulde P (1980) J Chem Phys 73:4548 Local operators have been applied early to transition metals, see Gutzwiller MC (1963) Phys Rev Lett 10:159
94. Fulde P (1995) Electron correlations in molecules and solids. 3rd edn. Springer, Berlin Heidelberg New York; Fulde P (1990) Calculation of electron correlation by using local operators. In: Maksic ZB (ed) Theoretical models of chemical bonding, Part 2. Springer, Berlin Heidelberg New York, p 377; Stollhoff G, Fulde P (1977) Z Phys B26:251; Stollhoff G, Fulde P (1978) 29:231; Stollhoff G, Fulde P (1980) J Chem Phys 73:4548 Local operators have been applied early to transition metals, see Gutzwiller MC (1963) Phys Rev Lett 10:159
95. Fulde P (1995) Electron correlations in molecules and solids. 3rd edn. Springer, Berlin Heidelberg New York; Fulde P (1990) Calculation of electron correlation by using local operators. In: Maksic ZB (ed) Theoretical models of chemical bonding, Part 2. Springer, Berlin Heidelberg New York, p 377; Stollhoff G, Fulde P (1977) Z Phys B26:251; Stollhoff G, Fulde P (1978) 29:231; Stollhoff G, Fulde P (1980) J Chem Phys 73:4548 Local operators have been applied early to transition metals, see Gutzwiller MC (1963) Phys Rev Lett 10:159
96. Fulde P (1995) Electron correlations in molecules and solids. 3rd edn. Springer, Berlin Heidelberg New York; Fulde P (1990) Calculation of electron correlation by using local operators. In: Maksic ZB (ed) Theoretical models of chemical bonding, Part 2. Springer, Berlin Heidelberg New York, p 377; Stollhoff G, Fulde P (1977) Z Phys B26:251; Stollhoff G, Fulde P (1978) 29:231; Stollhoff G, Fulde P (1980) J Chem Phys 73:4548 Local operators have been applied early to transition metals, see Gutzwiller MC (1963) Phys Rev Lett 10:159
97. Fulde P (1995) Electron correlations in molecules and solids. 3rd edn. Springer, Berlin Heidelberg New York; Fulde P (1990) Calculation of electron correlation by using local operators. In: Maksic ZB (ed) Theoretical models of chemical bonding, Part 2. Springer, Berlin Heidelberg New York, p 377; Stollhoff G, Fulde P (1977) Z Phys B26:251; Stollhoff G, Fulde P (1978) 29:231; Stollhoff G, Fulde P (1980) J Chem Phys 73:4548 Local operators have been applied early to transition metals, see Gutzwiller MC (1963) Phys Rev Lett 10:159
98. Overhauser AW (1960) Phys Rev Lett 4:462; Overhauser AW (1962) Phys Rev 128:1437
99. Overhauser AW (1960) Phys Rev Lett 4:462; Overhauser AW (1962) Phys Rev 128:1437
100. Misurkin LA, Ovchinnikov AA (1967) Zh Exp Theor Fiz 3:431
101. (a) Koutecky J (1967) J Chem Phys 46:2443; Harris RA, Falicov LM (1969) J Chem Phys 51:5034; Paldus J, Cizek J (1970) J Chem Phys 52:2919; Paldus J, Cizek J (1971) J Chem Phys 54:2293; Laidlaw WG (1973) Int J Quantum Chem 7:87; Chambaud G, Levy B, Millie P (1978) Theor Chim Acta 48:103; Dewar MJS, McKee ML (1980) Pure Appl Chem 52:1431; Paldus J, Chin E, Grey MG (1983) Int J Quantum Chem 24:395
102. (a) Koutecky J (1967) J Chem Phys 46:2443; Harris RA, Falicov LM (1969) J Chem Phys 51:5034; Paldus J, Cizek J (1970) J Chem Phys 52:2919; Paldus J, Cizek J (1971) J Chem Phys 54:2293; Laidlaw WG (1973) Int J Quantum Chem 7:87; Chambaud G, Levy B, Millie P (1978) Theor Chim Acta 48:103; Dewar MJS, McKee ML (1980) Pure Appl Chem 52:1431; Paldus J, Chin E, Grey MG (1983) Int J Quantum Chem 24:395
103. (a) Koutecky J (1967) J Chem Phys 46:2443; Harris RA, Falicov LM (1969) J Chem Phys 51:5034; Paldus J, Cizek J (1970) J Chem Phys 52:2919; Paldus J, Cizek J (1971) J Chem Phys 54:2293; Laidlaw WG (1973) Int J Quantum Chem 7:87; Chambaud G, Levy B, Millie P (1978) Theor Chim Acta 48:103; Dewar MJS, McKee ML (1980) Pure Appl Chem 52:1431; Paldus J, Chin E, Grey MG (1983) Int J Quantum Chem 24:395
104. (a) Koutecky J (1967) J Chem Phys 46:2443; Harris RA, Falicov LM (1969) J Chem Phys 51:5034; Paldus J, Cizek J (1970) J Chem Phys 52:2919; Paldus J, Cizek J (1971) J Chem Phys 54:2293; Laidlaw WG (1973) Int J Quantum Chem 7:87; Chambaud G, Levy B, Millie P (1978) Theor Chim Acta 48:103; Dewar MJS, McKee ML (1980) Pure Appl Chem 52:1431; Paldus J, Chin E, Grey MG (1983) Int J Quantum Chem 24:395
105. (a) Koutecky J (1967) J Chem Phys 46:2443; Harris RA, Falicov LM (1969) J Chem Phys 51:5034; Paldus J, Cizek J (1970) J Chem Phys 52:2919; Paldus J, Cizek J (1971) J Chem Phys 54:2293; Laidlaw WG (1973) Int J Quantum Chem 7:87; Chambaud G, Levy B, Millie P (1978) Theor Chim Acta 48:103; Dewar MJS, McKee ML (1980) Pure Appl Chem 52:1431; Paldus J, Chin E, Grey MG (1983) Int J Quantum Chem 24:395
106. (a) Koutecky J (1967) J Chem Phys 46:2443; Harris RA, Falicov LM (1969) J Chem Phys 51:5034; Paldus J, Cizek J (1970) J Chem Phys 52:2919; Paldus J, Cizek J (1971) J Chem Phys 54:2293; Laidlaw WG (1973) Int J Quantum Chem 7:87; Chambaud G, Levy B, Millie P (1978) Theor Chim Acta 48:103; Dewar MJS, McKee ML (1980) Pure Appl Chem 52:1431; Paldus J, Chin E, Grey MG (1983) Int J Quantum Chem 24:395
107. (a) Koutecky J (1967) J Chem Phys 46:2443; Harris RA, Falicov LM (1969) J Chem Phys 51:5034; Paldus J, Cizek J (1970) J Chem Phys 52:2919; Paldus J, Cizek J (1971) J Chem Phys 54:2293; Laidlaw WG (1973) Int J Quantum Chem 7:87; Chambaud G, Levy B, Millie P (1978) Theor Chim Acta 48:103; Dewar MJS, McKee ML (1980) Pure Appl Chem 52:1431; Paldus J, Chin E, Grey MG (1983) Int J Quantum Chem 24:395
108. (a) Koutecky J (1967) J Chem Phys 46:2443; Harris RA, Falicov LM (1969) J Chem Phys 51:5034; Paldus J, Cizek J (1970) J Chem Phys 52:2919; Paldus J, Cizek J (1971) J Chem Phys 54:2293; Laidlaw WG (1973) Int J Quantum Chem 7:87; Chambaud G, Levy B, Millie P (1978) Theor Chim Acta 48:103; Dewar MJS, McKee ML (1980) Pure Appl Chem 52:1431; Paldus J, Chin E, Grey MG (1983) Int J Quantum Chem 24:395
109. (b) Cizek J, Paldus J (1970) J Chem Phys 53: 821
110. Löwdin PO (1963) Rev Mod Phys 35:496; Löwdin PO (1960) Adv Chem Phys 14:283 in particular pp 325-328
111. Löwdin PO (1963) Rev Mod Phys 35:496; Löwdin PO (1960) Adv Chem Phys 14:283 in particular pp 325-328
112. Cizek J, Paldus J (1967) J Chem Phys 47:3976, see Ref. [69b]; Löwdin PO, Calais JL, Calazans JM (1981) Int J Quantum Chem 20:1201; Seeger R, Pople JA (1977) J Chem Phys 66:3045
113. Cizek J, Paldus J (1967) J Chem Phys 47:3976, see Ref. [69b]; Löwdin PO, Calais JL, Calazans JM (1981) Int J Quantum Chem 20:1201; Seeger R, Pople JA (1977) J Chem Phys 66:3045
114. Cizek J, Paldus J (1967) J Chem Phys 47:3976, see Ref. [69b]; Löwdin PO, Calais JL, Calazans JM (1981) Int J Quantum Chem 20:1201; Seeger R, Pople JA (1977) J Chem Phys 66:3045
115. Fukutome H (1981) Int J Quantum Chem 20:955
116. See for e.g. McWeeny R, Sutcliffe BT (1969) Methods of molecular quantum mechanics. Academic Press, London, Chap. 5.2, in particular p 121
117. Ditchfield R, Hehre WJ, Pople JA (1971) J Chem Phys 54: 724
118. Krishnan K, Binkley JS, Seeger R, Pople JA (1980) J Chem Phys 72: 650
119. The UHF dissociation problem for diatomic molecules is treated in Ref. [78], Chap. 3.8.7, p 221
120. McKelvey JM, Berthier G (1976) Chem Phys Lett 41:476
121. Szabo A, Ostlund NS (1989) Modern quantum chemistry. McGraw-Hill, New York in particular pp 205-229
122. See Ref. [59] but 62s
123. See Ref. [59] but M 109s
124. Mulliken RS (1955) J Chem Phys 23:1833, 1841, 2338, 2343; Mulliken RS (1962) 36:3428
125. Mulliken RS (1955) J Chem Phys 23:1833, 1841, 2338, 2343; Mulliken RS (1962) 36:3428
126. See for e.g. McWeeny R, Sutcliffe BT (1969) Methods of molecular quantum mechanics. Chap. 6 Academic Press, London
127. See Ref. [12] Chap. 5
128. Maynau D, Said M, Malrieu JP (1983) J Am Chem Soc 105: 5244 in particular Eq. (18)
129. See Ref. [84] but Eq. (14)
130. von E Doering W, Roth WR, Bauer F, Boenke M, Breuckman R. Ruhkamp J, Wortmann O (1991) Chem Ber 124: 1461 in particular Table 3
131. Squillacote ME, Sheridan RS, Chapman OL, Anet FAL (1979) J Am Chem Soc 101:3657
132. For the importance of these resonance structures, see for e.g. Roberts JD, Stewart R, Caserio MC (1971) Organic chemistry. Benjamin, Menlo Park pp 135-138
133. See for e.g. Salem L (1966) The molecular orbital theory of conjugated systems. Benjamin, New York p 86
134. (a) England W, Ruedenberg K (1971) Theor Chim Acta 22:196
135. (b) See Ref. [7]
136. (c) England W, Ruedenberg K (1973) J Am Chem Soc 95:8769
137. See Ref. [90a], Eq. (29); see Ref. [90c], Eq. (1)
138. See Ref. [90a], Table 4
139. See Ref. [90a], p 212
140. See Ref. [9a], Eq. (8) and references therein
141. See Ref. [90a], p 212; see Ref. [90c], p 8774; see Ref. [90b], p 65
142. See also Ref. [90c], Fig. 5
143. Hiberty PC, Ohanessian G (1985) Int J Quantum Chem 27: 245
144. See Ref. [62] in particular Table III
145. Hiberty PC, Ohanessian G (1982) J Am Chem Soc 104: 66
146. Chambaud G, Gerard-Ain M, Kassab E, Levy B, Pernot P (1984) Chem Phys 90:271
147. See for e.g. Reed AE, Curtiss LA, Weinhold F (1988) Chem Rev 88:899 and references therein
148. Heinzmann R, Ahlrichs R (1976) Theor Chim Acta 42:33
149. For a description of conjugated hydrocarbons in terms of magnetic properties see Malrieu JP (1990) The magnetic description of conjugated hydrocarbons. In: Maksic ZB (ed) Theoretical models of chemical bonding, part 2. Springer, Berlin Heidelberg New York, p 107
150. Schäfer H, Steckhan E (1969) Angew Chem 81: 532; Schäfer H (1970) Chem Ing Techn 42:164
151. Schäfer H, Steckhan E (1969) Angew Chem 81: 532; Schäfer H (1970) Chem Ing Techn 42:164
152. See for e.g. Beck F (1974) Elektroorganische Chemie. Verlag Chemie, Weinheim p 239, in particular scheme (386)
153. For a detailed discussion see for e.g. Fry AJ (1972) Synthetic organic chemistry. Sect. 7.1.2 Harper and Row, New York p 248; see Ref. [105] but Sect. 4.6.2 in particular scheme (337)
154. See Ref. [105] p 212 below scheme (337)