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Valence Bond Theory in Heterocyclic Chemistry

  • Zahid Rashid
  • Ria Broer
  • Joop H. van Lenthe
  • Remco W. A. HavenithEmail author
Chapter
Part of the Topics in Heterocyclic Chemistry book series (TOPICS, volume 38)

Abstract

This chapter deals with the application of valence bond theory in heterocyclic chemistry. A short introduction to the different valence bond methods is given, followed by illustrative results obtained by valence bond calculations. The illustrations show the applicability of the valence bond theory to obtain detailed information on the electronic structure of molecules in terms of chemical concepts.

Keywords

Heterocyclic chemistry Valence bond theory Aromaticity 

Notes

Acknowledgement

RWAH and RB acknowledge the Zernike Institute for Advanced Materials for the financial support (“Dieptestrategie” programme).

References

  1. 1.
    Coulson CA (1961) Valence. Oxford University Press, LondonGoogle Scholar
  2. 2.
    Hall GG (1991) The Lennard-Jones paper of 1929 and the foundations of molecular orbital theory. In: Löwdin P-O, Sabin JR, Zerner MC (eds) Advances in quantum chemistry, vol 22. Academic Press, San Diego, pp 1–6Google Scholar
  3. 3.
    Hund F (1927) Zur Deutung der Molekelspektren. I. Z Physik 40:742–764CrossRefGoogle Scholar
  4. 4.
    Lennard-Jones JE (1929) The electronic structure of some diatomic molecules. Trans Faraday Soc 25:668–686CrossRefGoogle Scholar
  5. 5.
    Mulliken RS (1928) The assignment of quantum numbers for electrons in molecules. I. Phys Rev 32:186–222CrossRefGoogle Scholar
  6. 6.
    Boys SF (1960) Construction of some molecular orbitals to be approximately invariant for changes from one molecule to another. Rev Mod Phys 32:296–299CrossRefGoogle Scholar
  7. 7.
    Edmiston C, Ruedenberg K (1965) Localized atomic and molecular orbitals. II. J Chem Phys 43:S97–S116CrossRefGoogle Scholar
  8. 8.
    Pipek J, Mezey PG (1989) A fast intrinsic localization procedure applicable for ab initio and semiempirical linear combination of atomic orbital wave functions. J Chem Phys 90:4916–4926CrossRefGoogle Scholar
  9. 9.
    von Niessen W (1972) Density localization of atomic and molecular orbitals. I. J Chem Phys 56:4290–4297CrossRefGoogle Scholar
  10. 10.
    Hiberty PC, Shaik S (2007) A survey of recent developments in ab initio valence bond theory. J Comput Chem 28:137–151CrossRefGoogle Scholar
  11. 11.
    Shaik S, Hiberty PC (2004) Valence Bond, its history, fundamentals, and applications: a primer. In: Lipkowitz KB, Larter R, Cundary TR (eds) Reviews in computational chemistry. Wiley-VCH, New York, pp 1–100CrossRefGoogle Scholar
  12. 12.
    Lewis GN (1916) The atom and the molecule. J Am Chem Soc 38:762–785CrossRefGoogle Scholar
  13. 13.
    Heitler W, London F (1927) Wechselwirkung neutraler Atome und homöopolare Bindung nach der Quantenmechanik. Z Physik 44:455–472CrossRefGoogle Scholar
  14. 14.
    Heitler W, Rumer G (1931) Quantentheorie der chemischen Bindung für mehratomige Moleküle. Z Physik 68:12–41CrossRefGoogle Scholar
  15. 15.
    Slater JC (1931) Directed valence in polyatomic molecules. Phys Rev 37:481–489CrossRefGoogle Scholar
  16. 16.
    Pauling L (1931) The nature of the chemical bond. Application of results obtained from the quantum mechanics and from a theory of paramagnetic susceptibility to the structure of molecules. J Am Chem Soc 53:1367–1400CrossRefGoogle Scholar
  17. 17.
    Pauling L (1960) The nature of the chemical bond. Cornell University Press, IthacaGoogle Scholar
  18. 18.
    Gallup GA (2002) Valence bond methods: theory and applications. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  19. 19.
    Chirgwin BH, Coulson CA (1950) The electronic structure of conjugated systems. 6. Proc R Soc Lond Ser A 201:196–209CrossRefGoogle Scholar
  20. 20.
    Gallup GA, Norbeck JM (1973) Population analyses of valence-bond wavefunctions and BeH2. Chem Phys Lett 21:495–500CrossRefGoogle Scholar
  21. 21.
    Pauling L, Wheland GW (1933) The nature of the chemical bond. V. The quantum-mechanical calculation of the resonance energy of benzene and naphthalene and the hydrocarbon free radicals. J Chem Phys 1:362–374CrossRefGoogle Scholar
  22. 22.
    Broer R, Hozoi L, Nieuwpoort WC (2003) Non-orthogonal approaches to the study of magnetic interactions. Mol Phys 101:233–240CrossRefGoogle Scholar
  23. 23.
    Hozoi L, de Vries AH, Broer R, de Graaf C, Bagus PS (2006) Ni 3s-hole states in NiO by non-orthogonal configuration interaction. Chem Phys 331:178–185CrossRefGoogle Scholar
  24. 24.
    Coulson CA, Fischer I (1949) XXXIV. Notes on the molecular orbital treatment of the hydrogen molecule. Philos Mag 40:386–393Google Scholar
  25. 25.
    Goddard WA, Dunning TH, Hunt WJ, Hay PJ (1973) Generalized valence bond description of bonding in low-lying states of molecules. Acc Chem Res 6:368–376CrossRefGoogle Scholar
  26. 26.
    Hay PJ, Hunt WJ, Goddard WA (1972) Generalized valence bond description of simple alkanes, ethylene, and acetylene. J Am Chem Soc 94:8293–8301CrossRefGoogle Scholar
  27. 27.
    Hunt WJ, Hay PJ, Goddard WA (1972) Self-consistent procedures for generalized valence bond wavefunctions. Applications H3, BH, H2O, C2H6, and O2. J Chem Phys 57:738–748CrossRefGoogle Scholar
  28. 28.
    Moss BJ, Bobrowicz FW, Goddard WA (1975) The generalized valence bond description of O2. J Chem Phys 63:4632–4639CrossRefGoogle Scholar
  29. 29.
    Cooper DL, Gerratt J, Raimondi M, Wright SC (1987) The electronic structure of 1,3-dipoles: spin-coupled descriptions of nitrone and diazomethane. Chem Phys Lett 138:296–302CrossRefGoogle Scholar
  30. 30.
    Cooper DL, Gerratt J, Raimondi M (1984) Studies of molecular states using spin-coupled valence-bond theory, Faraday Symp. Chem Soc 19:149–163Google Scholar
  31. 31.
    Cooper DL, Gerratt J, Raimondi M (1987) Modern valence bond theory. In: Lawley KP (ed) Advances in chemical physics: Ab initio methods in quantum chemistry, vol 69. Wiley, London, pp 319–397CrossRefGoogle Scholar
  32. 32.
    Gerratt J (1971) General theory of spin-coupled wavefunctions for atoms and molecules. In: Bates D, Esterman I (eds) Advances in atomic and molecular physics, vol 7. Academic, New York, pp 141–221Google Scholar
  33. 33.
    Gerratt J, Raimondi M (1980) The spin-coupled valence bond theory of molecular electronic structure. I. Basic theory and application to the 2Σ+ states of BeH. Proc R Soc Lond A 371:525–552CrossRefGoogle Scholar
  34. 34.
    Small DW, Head-Gordon M (2011) Post-modern valence bond theory for strongly correlated electron pairs. Phys Chem Chem Phys 13:19285–19297CrossRefGoogle Scholar
  35. 35.
    Small DW, Head-Gordon M (2009) Tractable spin-pure methods for bondbreaking: local many-electron spin-vector sets and an approximate valence bond model. J Chem Phys 130:084103CrossRefGoogle Scholar
  36. 36.
    van Lenthe JH, Balint-Kurti GG (1980) The valence-bond SCF (VB SCF) method: synopsis of theory and test calculation of OH potential energy curve. Chem Phys Lett 76:138–142CrossRefGoogle Scholar
  37. 37.
    van Lenthe JH, Balint-Kurti GG (1983) The valence-bond self-consistent field method (VB-SCF): theory and test calculations. J Chem Phys 78:5699–5713CrossRefGoogle Scholar
  38. 38.
    van Lenthe JH, Dijkstra F, Havenith RWA (2002) TURTLE – a gradient VBSCF program. Theory and studies of aromaticity. In: Cooper DL (ed) Valence bond theory, vol 10, Theoretical and computational chemistry. Elsevier, Amsterdam, pp 79–112CrossRefGoogle Scholar
  39. 39.
    Dijkstra F, van Lenthe JH (1999) Gradients in valence bond theory. Chem Phys Lett 310:553–556CrossRefGoogle Scholar
  40. 40.
    Dijkstra F, van Lenthe JH (2000) Gradients in valence bond theory. J Chem Phys 113:2100–2108CrossRefGoogle Scholar
  41. 41.
    Havenith RWA (2005) Coupled valence bond theory. Chem Phys Lett 414:1–5CrossRefGoogle Scholar
  42. 42.
    Zielinski ML, van Lenthe JH (2010) Atoms in valence bond – AiVB. Synopsis and test results. Chem Phys Lett 500:155–160CrossRefGoogle Scholar
  43. 43.
    Rashid Z, van Lenthe JH, Havenith RWA (2012) Resonance and aromaticity: an ab initio valence bond approach. J Phys Chem A 116:4778–4788CrossRefGoogle Scholar
  44. 44.
    Hiberty PC (1997) Reconciling simplicity and accuracy: compact valence bond wave functions with breathing orbitals. J Mol Struct (Theochem) 398–399:35–43CrossRefGoogle Scholar
  45. 45.
    Hiberty PC, Flament JP, Noizet E (1992) Compact and accurate valence bond functions with different orbitals for different configurations: application to the two-configuration description of F2. Chem Phys Lett 189:259–265CrossRefGoogle Scholar
  46. 46.
    Hiberty PC, Humbel S, Byrman CP, van Lenthe JH (1994) Compact valence bond functions with breathing orbitals: application to the bond dissociation energies of F2 and FH. J Chem Phys 101:5969–5976CrossRefGoogle Scholar
  47. 47.
    Hiberty PC, Shaik S (2002) Breathing-orbital valence bond method – a modern valence bond method that includes dynamic correlation. Theor Chem Acc 108:255–272CrossRefGoogle Scholar
  48. 48.
    Mo Y (2009) The resonance energy of benzene: a revisit. J Phys Chem A 113:5163–5169CrossRefGoogle Scholar
  49. 49.
    Mo Y, Peyerimhoff SD (1998) Theoretical analysis of electronic delocalization. J Chem Phys 109:1687–1697CrossRefGoogle Scholar
  50. 50.
    Mo Y, von R. Schleyer P (2006) An energetic measure of aromaticity and antiaromaticity based on the Pauling-Wheland resonance energies. Chem Eur J 12:2009–2020CrossRefGoogle Scholar
  51. 51.
    Zielinski M, Havenith RWA, Jenneskens LW, van Lenthe JH (2010) A comparison of approaches to estimate the resonance energy. Theor Chem Acc 127:19–25CrossRefGoogle Scholar
  52. 52.
    Roos BO (1987) The complete active space self-consistent field method and its applications in electronic structure calculations. Adv Chem Phys 69:399–445Google Scholar
  53. 53.
    Angeli C, Cimiraglia R, Malrieu J-P (2008) On the relative merits of nonorthogonal and orthogonal valence bond methods illustrated on the hydrogen molecule. J Chem Educ 85:150–158CrossRefGoogle Scholar
  54. 54.
    Malrieu J-P, Guihéry N, Calzado CJ, Angeli C (2007) Bond electron pair: its relevance and analysis from the quantum chemistry point of view. J Comput Chem 28:35–50CrossRefGoogle Scholar
  55. 55.
    Löwdin P-O (1950) On the non-orthogonality problem connected with the use of atomic wave functions in the theory of molecules and crystals. J Chem Phys 18:365–375CrossRefGoogle Scholar
  56. 56.
    Löwdin P-O (1967) Group algebra, convolution algebra, and applications to quantum mechanics. Rev Mod Phys 39:259–287CrossRefGoogle Scholar
  57. 57.
    Benker D, Klapötke TM, Kuhn G, Li J, Miller C (2005) An ab initio valence bond (VB) calculation of the π delocalisation energy in borazine, B3N3H6. Heteroat Chem 16:311–315CrossRefGoogle Scholar
  58. 58.
    Engelberts JJ, Havenith RWA, van Lenthe JH, Jenneskens LW, Fowler PW (2005) The electronic structure of inorganic benzenes: valence bond and ringcurrent descriptions. Inorg Chem 44:5266–5272CrossRefGoogle Scholar
  59. 59.
    Soncini A, Domene C, Engelberts JJ, Fowler PW, Rassat A, van Lenthe JH, Havenith RWA, Jenneskens LW (2005) A unified orbital model of delocalised and localised currents in monocycles, from annulenes to azabora-heterocycles. Chem Eur J 11:1257–1266CrossRefGoogle Scholar
  60. 60.
    Cooper DL, Wright SC, Gerratt J, Hyams PA, Raimondi M (1989) The electronic structure of heteroaromatic molecules. Part 3. A comparison of benzene, borazine and boroxine. J Chem Soc Perkin Trans 2:719–724CrossRefGoogle Scholar
  61. 61.
    Cyrañski M, von R. Schleyer P, Krygowski TM, Jiao H, Hohlneicher G (2003) Facts and artifacts about aromatic stability estimation. Tetrahedron 59:1657–1665CrossRefGoogle Scholar
  62. 62.
    Steiner E, Fowler PW, Havenith RWA (2002) Current densities of localized and delocalized electrons in molecules. J Phys Chem A 106:7048–7056CrossRefGoogle Scholar
  63. 63.
    Karadakov PB, Ellis M, Gerratt J, Cooper DL, Raimondi M (1997) The electronic structure of borabenzene: combination of an aromatic π-sextet and a reactive σ-framework. Int J Quantum Chem 63:441–449CrossRefGoogle Scholar
  64. 64.
    Cooper DL, Wright SC, Gerratt J, Raimondi M (1989) The electronic structure of heteroaromatic molecules. Part 1. Six-membered rings. J Chem Soc Perkin Trans 2:255–261CrossRefGoogle Scholar
  65. 65.
    Cooper DL, Gerratt J, Raimondi M (1986) The electronic structure of the benzene molecule. Nature 323:699–701CrossRefGoogle Scholar
  66. 66.
    Wu JI, Wannere CS, Mo Y, von R. Schleyer P, Bunz UHF (2009) 4n π electrons but stable: N, N,-dihydrodiazapentacenes. J Org Chem 74:4343–4349CrossRefGoogle Scholar
  67. 67.
    Cooper DL, Wright SC, Gerratt J, Raimondi M (1989) The electronic structure of heteroaromatic molecules. Part 2. Five-membered rings. J Chem Soc Perkin Trans 2:263–267CrossRefGoogle Scholar
  68. 68.
    von R. Schleyer P, Maerker C, Dransfeld A, Jiao H, van Eikema Hommes NJR (1996) Nucleus-Independent chemical shifts: a simple and efficient aromaticity probe. J Am Chem Soc 118:6317–6318CrossRefGoogle Scholar
  69. 69.
    Karadakov PB, Gerratt J, Cooper DL, Raimondi M (1995) Modern valence bond description of bonding in strained three-membered rings: cyclopropane, aziridine, ethene oxide, phosphirane and thiirane. J Mol Struct (Theochem) 341:13–24CrossRefGoogle Scholar
  70. 70.
    Walsh AD (1949) The structures of ethylene oxide, cyclopropane, and related molecules. Trans Faraday Soc 45:179–190CrossRefGoogle Scholar
  71. 71.
    Cremer D, Gauss J (1986) Theoretical determination of molecular structure and conformation. 20. Reevaluation of the strain energies of cyclopropane and cyclobutane carbon-carbon and carbon-hydrogen bond energies, 1,3 interactions, and σ-aromaticity. J Am Chem Soc 108:7467–7477CrossRefGoogle Scholar
  72. 72.
    Coulson CA, Moffitt WE (1949) I. The properties of certain strained hydrocarbons. Philos Mag 40:1–35Google Scholar
  73. 73.
    Braïda B, Lo A, Hiberty PC (2012) Can aromaticity coexist with diradical character? An ab initio valence bond study of S2N2 and related 6π-electron four membered rings E2N2 and E4 2+ (E= S,Se,Te). Chem Phys Chem 13:811–819Google Scholar
  74. 74.
    Gerratt J, McNicholas SJ, Karadakov PB, Sironi M, Raimondi M, Cooper DL (1996) The extraordinary electronic structure of N2S2. J Am Chem Soc 118:6472–6476CrossRefGoogle Scholar
  75. 75.
    Thorsteinsson T, Cooper DL (1998) Nonorthogonal weights of modern VB wavefunctions. Implementation and applications within CASVB. J Math Chem 23:105–126CrossRefGoogle Scholar
  76. 76.
    Scheschkewitz D, Amii H, Gornitzka H, Schoeller WW, Bourissou D, Bertrand G (2002) Singlet diradicals: from transition states to crystalline compounds. Science 295:1880–1881CrossRefGoogle Scholar
  77. 77.
    Jung Y, Head-Gordon M (2003) How diradicaloid is a stable diradical? Chem Phys Chem 4:522–525Google Scholar
  78. 78.
    Jung Y, Head-Gordon M (2003) Controlling the extent of diradical character by utilizing neighboring group interactions. J Phys Chem A 107:7475–7481CrossRefGoogle Scholar
  79. 79.
    Seierstad M, Kinsinger CR, Cramer CJ (2002) Design of 1,3-diphospha-2,4-diboretane diradicals. Angew Chem Int Ed 41:3894–3896CrossRefGoogle Scholar
  80. 80.
    Havenith RWA, van Lenthe JH, van Walree CA, Jenneskens LW (2006) Orbital interactions expressed in resonance structures: an approach to compute stabilisation of cyclobutanediyl diradicals. J Mol Struct (Theochem) 763:43–50CrossRefGoogle Scholar
  81. 81.
    Angeli C, Calzado CJ, de Graaf C, Caballol R (2011) The electronic structure of Ullman's biradicals: an orthogonal valence bond interpretation. Phys Chem Chem Phys 13:14617–14628CrossRefGoogle Scholar
  82. 82.
    Mo Y (2010) Computational evidence that hyperconjugative interactions are not responsible for the anomeric effect. Nat Chem 2:666–671CrossRefGoogle Scholar
  83. 83.
    Wu W, Song L, Cao Z, Zhang Q, Shaik S (2002) Valence bond configuration interaction: a practical ab initio valence bond method that incorporates dynamic correlation. J Phys Chem A 106:2721–2726CrossRefGoogle Scholar
  84. 84.
    Chen Z, Song J, Shaik S, Hiberty PC, Wu W (2009) Valence bond perturbation theory. A valence bond method that incorporates perturbation theory. J Phys Chem A 113:11560–11569CrossRefGoogle Scholar
  85. 85.
    Song J, Wu W, Zhang Q, Shaik S (2004) A practical valence bond method: a configuration interaction method approach with perturbation theoretic facility. J Comput Chem 25:472–478CrossRefGoogle Scholar
  86. 86.
    Rashid Z, van Lenthe JH (2013) A quadratically convergent VBSCF method. J Chem Phys 138:54105CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Zahid Rashid
    • 1
  • Ria Broer
    • 2
  • Joop H. van Lenthe
    • 1
  • Remco W. A. Havenith
    • 3
    • 4
    Email author
  1. 1.Theoretical Chemistry Group, Department of Chemistry, Debye Institute For Nanomaterials ScienceUtrecht UniversityUtrechtThe Netherlands
  2. 2.Theoretical Chemistry, Zernike Institute for Advanced MaterialsUniversity of GroningenGroningenThe Netherlands
  3. 3.Stratingh Institute for ChemistryUniversity of GroningenGroningenThe Netherlands
  4. 4.Ghent Quantum Chemistry Group, Department of Inorganic and Physical ChemistryGhent UniversityGentBelgium

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