Three-centred orbitals

One very important difference between VSEPR theory and MO theory should be noted. The MOs of the water molecule which participate in the bonding are three-centre orbitals. They are associated with all three atoms of the molecule. There are no localized electron pair bonds between pairs of atoms as used in the application of VSEPR theory. The existence of three-centre orbitals (and multi-centre orbitals in more complicated molecules) is not only more consistent with symmetry theory, it... 

Figure 5.17 The three-centre orbitals of the XeF2 molecule...

Uc et al determined the CPs on the PES describing the addition of OH- to toluene at post-HF level. The position of the two BCPs points between the hydrogen atom of the OH radical and the Cip o and Cp , which are detected in the prereactive complex, could indicate that a three-centre orbital is formed, similar to those in diborane. 

A common interpretation of the interaction of chalcogens with nucleophiles considers donation of electron density from a lone pair on the donor atom into the o- (E-X) orbital (Figure 15.1). As the degree of covalency increases, a hypervalent three-centre four-electron bond is formed. Real systems fall somewhere between secondary interactions and hypervalent (three centre - four electron) bonds. The two extremes can be distinguished by the correlation of X-E and E D distances.In the hypervalent case both bond distances decrease simultaneously, whereas in the secondary bond the distances are anticorrelated. This concept has been applied in a study of selenoquinones 15.17 (R = Ph, Me) with short Se 0 contacts,for... 

Figure 1.10 The three-centre molecular orbitals in [Os2OCl 0]4. ...

Corresponding to this valence bond view is a molecular orbital picture. The three cr-orbitals of a CH3 group are regarded as a basis from which three group orbitals may be constructed. One of the possible combinations of the tr-orbitals has the same local symmetry as the vacant p-orbital on the cationic centre, and hence may overlap with it. Therefore, a withdrawal of electrons from the methyl group can take place. The orbital from which electron density... 

The energy difference is expected to be reduced and perhaps eliminated when the calculations are repeated utilizing the 4-3IG basis set because of Pople s experience with the C3H7 ion. The non-classical form should be preferentially stabilized by the improved representation of the atomic orbitals, which should enable calculations to give a better account of the long bonds and three-centre ring. 

Some comment is necessary here to emphasize the three-centre nature of the bonding in CO particularly with respect to the n orbitals. The three p orbitals in the xz plane and the three in the yz plane (remember that the molecular axis is conventionally taken to coincide with the z axis) form the three-centre set of three tc MOs, 1jtm (bonding), 17 (non-bonding) and 27tm (anti-bonding), the first two orbitals being fully... 

Q (i) Take the 2p orbitals of three fluorine atoms pointing towards the centre of an equilateral triangle and classify their combinations in terms of the Dih point group, (ii) Classify the three 2p orbitals which are perpendicular to the trigonal plane. 

FIGURE 7. Molecular orbitals for a three-centre, four electron bond (a) antibonding (n) non-bonding (b) bonding... 

In addition to the VSEPR theory8 mentioned above, other theoretical or semiempirical approaches have addressed the problem of the positions occupied by various ligands as a function of their nature, for comparison with the numerous experimental results now available molecular orbital calculations, (four-electron, three-centre model with neglect of the P d orbitals)18,19 semiempirical calculations20,21 non-empirical calculations22,23 and hybrid orbitals24,25. 

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. ... 

Hydrogen, having one valence orbital and one electron, may be expected to form just one a bond. In fact, the covalent bonding in many hydrides is much more complicated than this, with H atoms often being bonded to two other atoms, forming a three-centre two-electron bond. Such electron-deficient species are discussed more fully in Section 7.4. 

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 . 

In translating this MO description into VB language, we speak of a three-centre, four-electron bond, often abbreviated as (3c,4e) three orbitals rather than four are used to hold the three atoms together. An equivalent description in VB language involves resonance structures ... 

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. 

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