Bond, three-centre

The need to speak of three-centre bonds in the context of MO theory may surprise the reader. The MO equivalent of a bond as understood in the language of Lewis or VB theory is a filled bonding MO whose antibonding counterpart is unoccupied. In a molecule AB (or in a 

After adding the requisite number of electrons to the MOs, we obtain a ground state in which we have three filled o bonding MOs, and one filled n 

Resonance is usually invoked in order to deal with delocalised Jt bonding and - if clearly understood - is a perfectly acceptable device which should cause no difficulty. 

Three-centre bonding is invoked in situations where the o framework cannot be described in terms of two-centre, electron-pair bonds, although it can often be accommodated by postulating resonance of a different type from that usually encountered. Two types of three-centre bond can be distinguished. The first is often postulated in hypervalent molecules/polyatomic ions AB where the central atom exceeds the octet in its Lewis formulation, as an alternative to the use of d orbitals which many chemists find objectionable. The second type occurs where there appear to be insufficient electrons - regardless of the supply of orbitals -to form the requisite number of bonds in a Lewis/VB description. In other words, the first type is postulated where we have an insufficiency of orbitals, and the second where there is a deficiency of electrons compounds containing the latter type are often described as electron-deficient . 

As an example of the first type, consider the linear XeF2 molecule. A Lewis structure with two-centre, electron-pair bonds offends the octet rule. This is not a problem if we allow the use of the Xe 5d orbitals. However, as discussed in Section 6.1, many authors prefer to avoid such use. If we restrict our basis set to the 5p(Xe) and 2p(F) orbitals, and if we consider only a overlap to be important, we need consider only three AOs 2p.(F,), 2p2(F2) and 5pz(Xe), where the molecular axis is labelled z. Thus we will obtain three MOs -vp, ij 2 and t )3 as shown below  

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A bridged carbocation with a two-electron, three-centre bond was proposed as early as 1939 (Nevell et al., 1939) for the 2-norbornyl cation [lO ] as a reactive intermediate in the solvolysis of 2-norbornyl system (see also Winstein and Trifan, 1949). It has now been isolated as the SbFe salt and the bridged structure is accounted for using solid-state nmr studies... 

The carbocations so far studied are called classical carbocations in which the positive charge is localized on one carbon atom or delocalized by resonance involving an unshared pair of electrons or a double or triple bond in the allylic positions (resonance in phenols or aniline). In a non-classical carbocation the positive charged is delocalized by double or triple bond that is not in the allylic position or by a single bond. These carbocations are cyclic, bridged ions and possess a three centre bond in which three atoms share two electrons. The examples are 7-norbomenyl cation, norbomyl cation and cyclopropylmethyl cation. 

About 300 (of the 1500 N—H- 0=C bonds considered) are three-centre bonds77. Three-centre bond (as shown in 15) is considered a better definition than bifurcated bond . The three-centre bond is a situation where the proton interacts with two hydrogen bond acceptor atoms both bonds are shorter than the sum of the van der Waals radii of the atoms involved. The two hydrogen bond acceptors may be different (Y Z in 15). 

Ahlrichs and Ehrhardt75 calculated shared electron numbers for 1. While bonding is normally reflected by two-centre contributions and negligible contributions from three and four-centre terms, a CCC shared electron number of 0.3 was calculated for 1, which is indicative of significant three-centre bonding. 

N.B. There are also a bond-pair bases which react with protons to form species containing three-centre bonds, e.g. CH4 + H+ - CHs+ however, by their very nature these compounds do not belong in this chapter on double-bonded groups.)... 

Chris Ramsden was born in Manchester, UK in 1946. He is a graduate of Sheffield University and received his PhD (W. D. Ollis) in 1970 and DSc in 1990. After post-doctoral work at the University of Texas (M. J. S. Dewar)(1971-3) and University of East Anglia (A. R. Katritzky)(1973-6), he worked in the pharmaceutical industry. He moved to Keele University as Professor of Organic Chemistry in 1992. His research interests are heterocycles, ortho-quinones and three-centre bonds, and applications of their chemistry to biological problems. 

These arguments have been debated for many years. Chemists who reject the use of nd orbitals in hybridisation schemes prefer three-centre bonds to describe hypervalent species. These are best portrayed in MO language (see Section 7.4) translated into VB terminology, they correspond to polar (or ionic) structures, e.g. ... 

The bonding in PH5 can be described in terms of sp3d hybridisation or alternatively in terms of polar structures H4P+H , i.e. three-centre bonds in MO language. PH5 has been the subject of much theoretical analysis... 

Good expositions of VB theory are given by Pauling (1960), Cartmell and Fowles (1977) (see Section A.7 of the Appendix) and Lagowski (1973) (see Section A.3). McWeeny s revisions of Coulson s classic book (1979 and 1982) (see Section A.7) emphasise the three-centre bond approach to hypervalent species. See also Dasent (1965) (Section A.8) for discussion of nonexistent compounds. 

The term three-centre bond in XeF2 is analogous to the term delocalised n bond which might be applied in describing the Jt bonding in COf- or N03". 

The fact that most hypervalent molecules are fluorides or oxofluorides can be easily explained in terms of the three-centre bond approach. Crucial to the viability of the linear X-E-X moiety is the stabilisation of the nonbonding MO j2. This is optimised if X is relatively small in size... 

This term is used to describe a three-centre bond - usually of the type E-H-E and non-linear, in contrast to the other variety - which we imagine to be formed by three orbitals (one on each atom) and two electrons (one furnished by the central H atom). Such bonding is invoked in electron-deficient compounds where there are insufficient electrons to form the requisite number of two-centre bonds in a Lewis/VB treatment. Electron-deficient compounds abound in boron chemistry the classic case of diborane B2H6 will be discussed in detail. 

The ketonic description of the C-O bond is supported by its length and stretching frequency but the M-C bonds should not be seen as simple a bonds. An MO description involving three-centre bonding is required, and it is noteworthy that a carbonyl bridge between two atoms always involves a direct M-M bond. One, two or three CO molecules may bridge two M atoms, as shown in the examples below ... 

LnClj + 6LiCH3—> Li3[Ln(CH3)6] + 3LiCl The structures suggest the formation of Li-H-C three-centre bonds. 

The NH hydrogen atoms tend to adopt an anti relationship to the carbonyl group and to form three-centre bonds to urea carbonyl groups, C(4)[R2(6)] (8.22). 

When co-crystals form, the NH protons form three-centre bonds to acceptor groups, R2 (6). 

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