Hydrogen, ligand, vibrational model

The localized-electron model or the ligand-field approach is essentially the same as the Heitler-London theory for the hydrogen molecule. The model assumes that a crystal is composed of an assembly of independent ions fixed at their lattice sites and that overlap of atomic orbitals is small. When interatomic interactions are weak, intraatomic exchange (Hund s rule splitting) and electron-phonon interactions favour the localized behaviour of electrons. This increases the relaxation time of a charge carrier from about 10 s in an ordinary metal to 10 s, which is the order of time required for a lattice vibration in a polar crystal. 

It is possible to test the validity of the vibrational model by calculating the INS spectrum with DFT. Fig. 6.16a shows the results for [W(CO)3(H2) P(isopropyl)3 2]. The complexity of the spectrum is readily apparent hence the need for the difference technique outlined above. Fig. 6.16b shows the same spectrum (with a xlO ordinate expansion) but with the cross sections of all the atoms except for the two hydrogen atoms in the dihydrogen ligand set to zero. It can be seen that there are many modes that involve significant dihydrogen motion. 

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