Sigma-pi and equivalent-orbital models
The σ-π model and equivalent-orbital model refer to two possible representations of molecules in valence bond theory. The σ-π model differentiates bonds and lone pairs of σ symmetry from those of π symmetry, while the equivalent-orbital model hybridizes them. The σ-π treatment takes into account molecular symmetry and is better suited to interpretation of aromatic molecules (Hückel's rule) and photoelectron spectra, although computational calculations of certain molecules tend to optimize better under the equivalent-orbital treatment. The total wave functions of the two representations are mathematically equivalent and different localization procedures yield either of the two. In a 1996 review, Kenneth B. Wiberg concluded that "although a conclusive statement cannot be made on the basis of the currently available information, it seems likely that we can continue to consider the σ/π and bent-bond descriptions of ethylene to be equivalent. Ian Fleming goes further in a 2010 textbook, noting that "the overall distribution of electrons [...] is exactly the same" in the two models.
Two different explanations for the nature of double and triple covalent bonds in organic molecules were proposed in the 1930s. Linus Pauling proposed that the double bond results from two equivalent tetrahedral orbitals from each atom, which later came to be called banana bonds or tau bonds. Erich Hückel proposed a representation of the double bond as a combination of a sigma bond plus a pi bond. The Hückel representation is the better-known one, and it is the one found in most textbooks since the late-20th century.
Multiple lone pairs
Initially, Linus Pauling's scheme of water as presented in his hallmark paper on valence bond theory consists of two inequivalent lone pairs of σ and π symmetry. As a result of later developments resulting partially from the introduction of VSEPR, an alternative view arose which considers the two lone pairs to be equivalent, colloquially called rabbit ears. Due to the prevalence of the sigma-pi model for multiple bonds, there has been a call for lone pairs to be represented analogously.
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- Peter B. Karadakov; Joseph Gerratt; David L. Cooper; Mario Raimondi (1993), "Bent versus .sigma.-.pi. bonds in ethene and ethyne: the spin-coupled point of view", J. Am. Chem. Soc., 115 (15): 6863–6869, doi:10.1021/ja00068a050.
- Wiberg, Kenneth B. (1996), "Bent Bonds in Organic Compounds", Acc. Chem. Res., 29 (5): 229–34, doi:10.1021/ar950207a.
- Fleming, Ian (2010), Molecular Orbitals and Organic Chemical Reactions (reference ed.), London: Wiley, p. 61, ISBN 0-470-74658-0.
- Pauling, Linus (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 (4): 1367–1400, doi:10.1021/ja01355a027.
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- Hückel, E. (1930), "Zur Quantentheorie der Doppelbindung", Z. Phys., 60 (7–8): 423, Bibcode:1930ZPhy...60..423H, doi:10.1007/BF01341254
- Penney, W. G. (1934), "The Theory of the Structure of Ethylene and a Note on the Structure of Ethane", Proceedings of the Royal Society, A144: 166, Bibcode:1934RSPSA.144..166P, doi:10.1098/rspa.1934.0041
- Penney, W. G. (1934), "The Theory of the Stability of the Benzene Ring and Related Compounds", Proceedings of the Royal Society, A146: 223, Bibcode:1934RSPSA.146..223P, doi:10.1098/rspa.1934.0151.
- Allen D. Clauss, Stephen F. Nelsen, Mohamed Ayoub, John W. Moore, Clark R. Landis and Frank Weinhold (2014). "Rabbit-ears hybrids, VSEPR sterics, and other orbital anachronisms". Chemistry Education Research and Practice. 15 (4): 417–434. doi:10.1039/C4RP00057A.