Skip to main content
SpringerLink
Log in

The multiconfiguration Spin-Coupled approach for the description of the three-center two-electron chemical bond of some carbenium and nonclassical ions

  • Regular Article
  • Published:
Theoretical Chemistry Accounts Aims and scope Submit manuscript

Abstract

The intrinsically elusive concepts of electronic “delocalization” and “chemical resonance” are briefly reviewed emphasizing their connection with Spin-Coupled (SC) descriptions of electronic structure. Multiconfiguration Spin-Coupled (MC-SC) calculations are performed to describe the three-center two-electron (3c-2e) bonding in some representative carbenium and nonclassical carbonium ions. Within the MC-SC approach, it is found that these cations present significant electronic energy stabilization when described by more than one valence SC spatial orbital configuration. It is shown that it is necessary to have a superposition of two chemical structures to completely span the orbital valence space of these cations. Two characteristic bonding themes are clearly distinguished. One specific to allyl-type carbenium ions and another specific to the nonclassical carbonium ions. In both situations, the 3c-2e bond is described by two chemical structures. The 3c-2e bond present in these carbocations is described clearly within this conceptual framework. The results point out for the robustness of the Spin-Coupled description in yielding a general picture of bonding, even when considering valence-bond type multiconfiguration effects.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

References

  1. Longuet-Higgins HC, Bell RP (1943) J Chem Soc (Resumed). https://doi.org/10.1039/jr9430000250

    Google Scholar 

  2. Eberhardt WH, Crawford B, Lipscomb WN (1954) J Chem Phys 22:989

    Article  CAS  Google Scholar 

  3. Kleier DA, Halgren TA, Hall JH, Lipscomb WN (1974) J Chem Phys 61:3905. https://doi.org/10.1063/1.1681683

    Article  CAS  Google Scholar 

  4. Hirst DM, Linnett JW (1962) J Chem Soc. https://doi.org/10.1039/jr9620001035

    Google Scholar 

  5. Clark DT, Armstron DR (1969) Theoret Chim Acta 13:365. https://doi.org/10.1007/bf00527014

    Article  CAS  Google Scholar 

  6. Winstein S, Trifan DS (1949) J Am Chem Soc 71:2953. https://doi.org/10.1021/ja01176a536

    Article  CAS  Google Scholar 

  7. Brown HC (1977) The nonclassical ion problem. Springer, Berlin

    Book  Google Scholar 

  8. Brown HC (1983) Acc Chem Res 16:432. https://doi.org/10.1021/ar00096a002

    Article  CAS  Google Scholar 

  9. Olah GA, Prakash GKS, Saunders M (1983) Acc Chem Res 16:440. https://doi.org/10.1021/ar00096a003

    Article  CAS  Google Scholar 

  10. Scholz F, Himmel D, Heinemann FW, Schleyer PV, Meyer K, Krossing I (2013) Science 341:62. https://doi.org/10.1126/science.1238849

    Article  CAS  Google Scholar 

  11. Winstein S, Shatavsky M, Norton C, Woodward RB (1955) J Am Chem Soc 77:4183. https://doi.org/10.1021/ja01620a078

    Article  CAS  Google Scholar 

  12. Winstein S, Ordronneau C (1960) J Am Chem Soc 82:2084. https://doi.org/10.1021/ja01493a068

    Article  CAS  Google Scholar 

  13. Fleming FP, Barbosa AGH, Esteves PM (2006) J Phys Chem A 110:11903. https://doi.org/10.1021/jp0654260

    Article  CAS  Google Scholar 

  14. Hinkle CE, McCoy AB, Huang X, Bowman JM (2007) J Phys Chem A 111:2033. https://doi.org/10.1021/jp067486b

    Article  CAS  Google Scholar 

  15. Fleming FP, Barbosa AGH, Esteves PM (2007) J Phys Chem A 111:2971. https://doi.org/10.1021/jp0685131

    Article  CAS  Google Scholar 

  16. Esteves PM, Fleming FP, Barbosa AGH (2007) Theoretical studies on structure and dynamics od carbonium ions. In: Recent developments in carbocation and onium ion chemistry—ACS symposium series 965:297

  17. Ivanov SD, Witt A, Marx D (2013) Phys Chem Chem Phys 15:10270. https://doi.org/10.1039/c3cp44523b

    Article  CAS  Google Scholar 

  18. Lewis GN (1916) J Am Chem Soc 38:762. https://doi.org/10.1021/ja02261a002

    Article  CAS  Google Scholar 

  19. Langmuir I (1919) J Am Chem Soc 41:868. https://doi.org/10.1021/ja02227a002

    Article  CAS  Google Scholar 

  20. Lewis GN (1933) J Chem Phys 1:17. https://doi.org/10.1063/1.1749214

    Article  CAS  Google Scholar 

  21. Wigner EP (1959) Group theory and its application to the quantum mechanics of atomic spectra. Academic Press Inc., New York

    Google Scholar 

  22. Lowdin PO (1955) Phys Rev 97:1474. https://doi.org/10.1103/PhysRev.97.1474

    Article  Google Scholar 

  23. Szabo A, Ostlund NS (1989) Modern quantum chemistry: introduction to advanced electronic structure theory. Dover

  24. Truhlar DG (2012) J Chem Educ 89:573. https://doi.org/10.1021/ed200565h

    Article  CAS  Google Scholar 

  25. Ingold CK (1934) Chem Rev 15:225. https://doi.org/10.1021/cr60051a003

    Article  CAS  Google Scholar 

  26. Slater JC (1931) Phys Rev 38:1109

    Article  CAS  Google Scholar 

  27. Slater JC (1931) Phys Rev 37:481

    Article  CAS  Google Scholar 

  28. Pauling L (1933) J Chem Phys 1:280. https://doi.org/10.1063/1.1749284

    Article  CAS  Google Scholar 

  29. Cooper DL (ed) (2002) Theoretical and computational chemistry. Elsevier, Amsterdam, p ii

    Google Scholar 

  30. Pauling L, Wheland GW (1933) J Chem Phys 1:362. https://doi.org/10.1063/1.1749304

    Article  CAS  Google Scholar 

  31. Zielinski M, van Lenthe JH (2008) J Phys Chem A 112:13197. https://doi.org/10.1021/jp801780u

    Article  CAS  Google Scholar 

  32. Lefkovits HC, Fain J, Matsen FA (1955) J Chem Phys 23:1690. https://doi.org/10.1063/1.1742412

    Article  CAS  Google Scholar 

  33. Simonetta M, Heilbronner E (1964) Theoret Chim Acta 2:228. https://doi.org/10.1007/bf00528282

    Article  CAS  Google Scholar 

  34. Linares M, Braida B, Humbel S (2006) J Phys Chem A 110:2505. https://doi.org/10.1021/jp056090h

    Article  CAS  Google Scholar 

  35. Linares M, Humbel S, Braida B (2008) J Phys Chem A 112:13249. https://doi.org/10.1021/jp8038169

    Article  CAS  Google Scholar 

  36. Levin G, Goddard WA, Huestis DL (1974) Chem Phys 4:409. https://doi.org/10.1016/0301-0104(74)85007-x

    Article  CAS  Google Scholar 

  37. Truhlar DG (2007) J Chem Educ 84:781

    Article  CAS  Google Scholar 

  38. Zielinski M, Havenith RWA, Jenneskens LW, van Lenthe JH (2010) Theor Chem Acc 127:19. https://doi.org/10.1007/s00214-010-0793-8

    Article  CAS  Google Scholar 

  39. Lowdin PO (1955) Phys Rev 97:1490. https://doi.org/10.1103/PhysRev.97.1490

    Article  Google Scholar 

  40. Edmiston C, Ruedenberg K (1963) Rev Mod Phys 35:457. https://doi.org/10.1103/RevModPhys.35.457

    Article  CAS  Google Scholar 

  41. Lykos P, Pratt GW (1963) Rev Mod Phys 35(3): 496–501. https://doi.org/10.1103/revmodphys.35.496

    Article  Google Scholar 

  42. Gallup GA (1968) J Chem Phys 48:1752. https://doi.org/10.1063/1.1668907

    Article  CAS  Google Scholar 

  43. Mayer I (1980) Adv Quantum Chem 12:189. https://doi.org/10.1016/S0065-3276(08)60317-2

    Article  CAS  Google Scholar 

  44. Gerratt J (1971) Adv At Mol Phys 7:141. https://doi.org/10.1016/S0065-2199(08)60360-7

    Article  Google Scholar 

  45. Gerratt J, Cooper DL, Karadakov PB, Raimondi M (1997) Chem Soc Rev 26:87. https://doi.org/10.1039/cs9972600087

    Article  CAS  Google Scholar 

  46. Goddard WA (1967) Phys Rev 157:73

    Article  CAS  Google Scholar 

  47. Goddard WA (1967) Phys Rev 157:81

    Article  CAS  Google Scholar 

  48. Ladner RC, Goddard WA (1969) J Chem Phys 51:1073. https://doi.org/10.1063/1.1672106

    Article  CAS  Google Scholar 

  49. Chambaud G, Levy B, Millie P (1978) Theoret Chim Acta 48:103. https://doi.org/10.1007/bf02399021

    Article  CAS  Google Scholar 

  50. Dehareng D, Dive G (2000) J Comput Chem 21:483. https://doi.org/10.1002/(SICI)1096-987X(20000430)21:6<483::AID-JCC7>3.0.CO;2-O

    Article  CAS  Google Scholar 

  51. Bader RFW (1991) Chem Rev 91:893. https://doi.org/10.1021/cr00005a013

    Article  CAS  Google Scholar 

  52. Silvi B (2017) Theor Chem Acc. https://doi.org/10.1007/s00214-017-2146-3

    Google Scholar 

  53. Wilson CW, Goddard WA (1972) Theoret Chim Acta 26:195. https://doi.org/10.1007/bf00529306

    Article  CAS  Google Scholar 

  54. Goddard WA, Wilson CW (1972) Theoret Chim Acta 26:211. https://doi.org/10.1007/bf00529307

    Article  CAS  Google Scholar 

  55. Streitwieser A (1961) Molecular orbital theory for organic chemists. Wiley

  56. Pauncz R (1979) Spin eigenfunctions. Plenum

  57. Cooper DL, Gerratt J, Raimondi M (1987) Adv Chem Phys 69:319. https://doi.org/10.1002/9780470142943.ch6

    CAS  Google Scholar 

  58. Raos G, Gerratt J, Cooper DL, Raimondi M (1993) Mol Phys 79:197. https://doi.org/10.1080/00268979300101151

    Article  CAS  Google Scholar 

  59. Matsen FA (1970) J Am Chem Soc 92:3525. https://doi.org/10.1021/ja00715a001

    Article  CAS  Google Scholar 

  60. Cooper DL, Gerratt J, Raimondi M (1986) Nature 323:699

    Article  CAS  Google Scholar 

  61. Barbosa AGH (2002) Many particle quantum mechanics and the theory of the chemical bond. Universidade Federal do Rio de Janeiro, Rio de Janeiro

    Google Scholar 

  62. Davidson ER, Borden WT (1983) J Phys Chem 87:4783. https://doi.org/10.1021/j150642a005

    Article  CAS  Google Scholar 

  63. Hyams PA (1989) Ab initio calculations of structures and properties using the spin-coupled wave function, University of Bristol, Bristol

    Google Scholar 

  64. Barbosa AGH, Nascimento MAC (2004) Int J Quantum Chem 99:317. https://doi.org/10.1002/qua.10866

    Article  CAS  Google Scholar 

  65. Eisfeld W, Morokuma K (2000) J Chem Phys 113:5587. https://doi.org/10.1063/1.1290607

    Article  CAS  Google Scholar 

  66. Liu Y, Zou WL, Bersuker IB, Boggs JE (2009) J Chem Phys. https://doi.org/10.1063/1.3129822

    Google Scholar 

  67. Voter AF, Goddard WA (1986) J Am Chem Soc 108:2830. https://doi.org/10.1021/ja00271a008

    Article  CAS  Google Scholar 

  68. Penotti FE (2000) Int J Quantum Chem 78:378. https://doi.org/10.1002/(SICI)1097-461X(2000)78:5<378::AID-QUA7>3.0.CO;2-Y

    Article  CAS  Google Scholar 

  69. Barbosa AGH, Monteiro JGS (2012) Theoret Chem Acc 131:1297. https://doi.org/10.1007/s00214-012-1297-5

    Article  Google Scholar 

  70. Pyper NC, Gerratt J (1977) Proc R Soc Lond Ser A Math Phys Eng Sci 355:407. https://doi.org/10.1098/rspa.1977.0104

    Article  CAS  Google Scholar 

  71. Voter AF, Goddard WA (1981) Chem Phys 57:253. https://doi.org/10.1016/0301-0104(81)80206-6

    Article  CAS  Google Scholar 

  72. Vanlenthe JH, Balintkurti GG (1983) J Chem Phys 78:5699. https://doi.org/10.1063/1.445451

    Article  CAS  Google Scholar 

  73. Hollauer E, Nascimento MAC (1993) J Chem Phys 99:1207. https://doi.org/10.1063/1.465364

    Article  CAS  Google Scholar 

  74. Floriano WB, Blaszkowski SR, Nascimento MAC (1995) J Mol Struct Theochem 335:51. https://doi.org/10.1016/0166-1280(94)03982-q

    Article  CAS  Google Scholar 

  75. Shavitt I (1977) In: Schaefer HF (ed) Methods of electronic structure theory. Springer, Boston, p 189

    Chapter  Google Scholar 

  76. Saunders VR, Vanlenthe JH (1983) Mol Phys 48:923. https://doi.org/10.1080/00268978300100661

    Article  CAS  Google Scholar 

  77. Knowles PJ, Handy NC (1984) Chem Phys Lett 111:315. https://doi.org/10.1016/0009-2614(84)85513-x

    Article  CAS  Google Scholar 

  78. Sherrill CD, Schaefer HF (1999) In: Lowdin PO, Sabin JR, Zerners MC, Brandas E (eds) Advances in quantum chemistry, Vol 34 p 143

  79. Gallup GA, Vance RL, Collins JR, Norbeck JM (1982) Adv Quantum Chem 16:229. https://doi.org/10.1016/s0065-3276(08)60354-8

    Article  CAS  Google Scholar 

  80. Verbeek J, Vanlenthe JH (1991) Theochem-J Mol Struct 75:115

    Article  CAS  Google Scholar 

  81. Chen ZH, Chen X, Wu W (2013) J Chem Phys. https://doi.org/10.1063/1.4801631

    Google Scholar 

  82. Olsen J (2015) J Chem Phys. https://doi.org/10.1063/1.4929724

    Google Scholar 

  83. Karadakov PB, Cooper DL, Duke BJ, Li J (2012) J Phys Chem A 116:7238. https://doi.org/10.1021/jp303998h

    Article  CAS  Google Scholar 

  84. Barbosa AGH, Barcelos AM (2008) Theoret Chem Acc 122:51. https://doi.org/10.1007/s00214-008-0484-x

    Article  Google Scholar 

  85. Henriques AM, Barbosa AGH (2011) J Phys Chem A 115:12259. https://doi.org/10.1021/jp202762p

    Article  CAS  Google Scholar 

  86. Penotti FE (1996) Int J Quantum Chem 59:349. https://doi.org/10.1002/(SICI)1097-461X(1996)59:5<349::AID-QUA1>3.3.CO;2-3

    Article  CAS  Google Scholar 

  87. Penotti FE (2002) In: David LC (ed) Theoretical and computational chemistry. Elsevier, Amsterdam, p 279

    Google Scholar 

  88. Duke BJ, Havenith RWA (2016) Theoret Chem Acc 135:82. https://doi.org/10.1007/s00214-016-1831-y

    Article  Google Scholar 

  89. Bitzer RS, Barbosa AGH, da Silva CO, Nascimento MAC (2005) Carbohyd Res 340:2171. https://doi.org/10.1016/j.carres.2005.07.001

    Article  CAS  Google Scholar 

  90. Henriques AM, Monteiro JGS, Barbosa AGH (2016) Theoret Chem Acc 136:4. https://doi.org/10.1007/s00214-016-2027-1

    Article  Google Scholar 

  91. Schmidt MW, Baldridge KK, Boatz JA, Elbert ST, Gordon MS, Jensen JH, Koseki S, Matsunaga N, Nguyen KA, Su SJ, Windus TL, Dupuis M, Montgomery JA (1993) J Comput Chem 14:1347. https://doi.org/10.1002/jcc.540141112

    Article  CAS  Google Scholar 

  92. Li JB, McWeeny R (2002) Int J Quantum Chem 89:208. https://doi.org/10.1002/qua.10293

    Article  CAS  Google Scholar 

  93. Thorsteinsson T, Cooper DL (1998) J Math Chem 23:105. https://doi.org/10.1023/a:1019100703879

    Article  CAS  Google Scholar 

  94. Raghavachari K, Haddon RC, Schleyer PV, Schaefer HF (1983) J Am Chem Soc 105:5915. https://doi.org/10.1021/ja00356a034

    Article  CAS  Google Scholar 

  95. Sousa DWOD, Nascimento MAC (2017) Acc Chem Res 50:2264. https://doi.org/10.1021/acs.accounts.7b00260

    Article  CAS  Google Scholar 

Download references

Acknowledgements

The authors acknowledge Brazilian funding agencies (CNPq and FAPERJ) for financial support. This work is dedicated to Prof. Marco Antonio Chaer Nascimento, on the occasion of his 70th anniversary.

Author information

Authors and Affiliations

  1. Instituto de Química, Universidade Federal Fluminense, Niterói, RJ, Brazil

    André G. H. Barbosa, André M. Henriques & João G. S. Monteiro

  2. Centro de Pesquisas da Petrobrás, Rio de Janeiro, RJ, Brazil

    Felipe P. Fleming

  3. Instituto de Química, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, Brazil

    Felipe P. Fleming & Pierre M. Esteves

Authors
  1. André G. H. Barbosa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. André M. Henriques
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. João G. S. Monteiro
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Felipe P. Fleming
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Pierre M. Esteves
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to André G. H. Barbosa.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (PDF 1978 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Barbosa, A.G.H., Henriques, A.M., Monteiro, J.G.S. et al. The multiconfiguration Spin-Coupled approach for the description of the three-center two-electron chemical bond of some carbenium and nonclassical ions. Theor Chem Acc 137, 21 (2018). https://doi.org/10.1007/s00214-017-2193-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00214-017-2193-9

Keywords

Search

Navigation