Fragment orbitals by the valence-bond method

The orbitals of methane, CH4, and those of the related fragments CH3, CH2, and CH can be described using the molecular orbital method, as we have done for all the systems studied so far in this book. But the valence-bond approach, introduced by L. Pauling, can also be used this is perhaps the simplest way to establish an initial relationship between the electronic structures of organic and inorganic fragments. 

In CH4, the carbon atom is at the centre of a tetrahedron defined by the four hydrogen atoms. The carbon atom s four valence orbitals (the 2s orbital and the three 2p orbitals) can be combined to give four equivalent hybrid orbitals (written sp ) that point towards the vertices of the tetrahedron. Since carbon has four valence electrons, one electron can be placed in each hybrid orbital. A Ish orbital, which is also singly occupied, can interact with the sp hybrid that points towards it, and in this way we can describe the four equivalent bonds in a tetrahedral arrangement. 

We now turn to an octahedral MLe complex with a electronic configuration, which we shall consider as the starting point for inorganic fragments. This complex obeys the 18-electron rule, just as methane obeys the octet rule. To be a Utde more concrete, though this choice is in no way unique, we shall consider a chromium complex [CrL ], with six neutral L-type ligands (PR3, CO, etc.), each of which supplies a pair of electrons to the metal, fn this complex, chromium is in the oxidation state zero, and the electronic configuration is indeed d.  

In the spirit of valence-bond theory, we must construct six hybrid orbitals that point towards the vertices of the octahedron. We must therefore combine just six of the nine valence orbitals of the metal it turns out that these are the s orbital, the three p orbitals, and two of the d orbitals (this hybridisation pattern will be written d sp, see Chapter 2, 2.1.2.3). Three d orbitals are therefore not involved in the hybridisation, and they stay unchanged (5-4). The link with MO theory is plain these are the three nonbonding orbitals of the octahedral tzg block. In a d complex, these three non-hybridized orbitals are doubly occupied. 

With the six metal electrons placed in this way, the hybrid orbitals are empty. Each of these interacts with the doubly occupied orbital of the ligand L towards which it points, thereby forming six bonds in an octahedral arrangement (5-5). 

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