Relativistic bond energy changes

Figure 4.10 Calculated relativistic bond contractions ARte in A (circles and solid line, axis on the left-hand side) and relativistic change in the dissociation energy contractions (triangles and dashed line, axis on the right-hand side) for various diatomic compounds as a function ofthe electronegativity of the ligand.

The corrections due to a relativistic treatment of the Hartree potential are considerably smaller than spin-orbit effects, as can be seen by comparing DKnuc and DKee2 results (Table 3.3) [19]. Bond length, vibrational frequency, and binding energy change by about -0.5 pm, 2 cm and 10 kJ/mol, respectively. 

Relativistic bond length (A) and energy (eV) changes for selected lanthanide molecules... 

Fully relativistic calculations even for atoms are quite complicated. The relativistic ECP parameters are, therefore, usually derived from atomic calculations that include only the most important relativistic terms of the Dirac-Fock Hamiltonian, namely, the mass-velocity correction, the spin-orbit coupling, and the so-called Darwin term.6 This is why the reference atomic calculations and the derived ECP parameters are sometimes termed quasi-relativistic. The basic assumption of relativistic ECPs is that the relativistic effects can be incorporated into the atom via the derived ECP parameters as a constant, which does not change during formation of the molecule. Experience shows that this assumption is justified for calculating geometries and bond energies of molecules. 

In the third transition series, the 5d orbital expands and the 6s orbital contracts due to relativistic effects, as we have seen above, and many of the elements of this series display higher oxidation states than those in the second series. The greater participation of the 5d orbital in the late part of the series can change the qualitative bonding picture. An example comes from the activation of methane by Pf ". In nonrelativistic calculations, the PtCHj product has only a single bond between the Pf " d ion and the methylene, and the unpaired electron is located on the methylene carbon. When scalar relativistic effects are introduced, the d s state of Pf " is stabilized, and both electrons of the methylene can bond to the platinum ion, resulting in a double bond. The unpaired electron is now located on the platinum. The Pt-C bond energy more than doubles with scalar relativistic effects, from 200 to 450 kJ/mol (Heinemann et al. 1996). 

For solids with heavy atoms, relativistic shifts may affect the bonding properties, and also optical properties may be influenced. The relativistic shifts of the 5d bands relative to the s-p bands in gold change the main inter band edge more than 1 eV. Already Pyykko and Desclaux mentioned [1] that the fact that gold is yellow is a result of relativistic effects. These are indirect [2] (see also the introduction. Sect. 1), and the picture was confirmed by relativistic band structure calculations [3,4]. Also the optical properties of semiconductors are influenced by relativistic shifts which affect the gap between occupied and empty states, see for example Ref. [5]. Two additional examples may be mentioned where relativistic shifts in the energy band structure drastically influence the physical properties. First,... 

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