Molecular geometries relativistic effects

Relativistic effects on calculated NMR shieldings and chemical shifts have sometimes been divided into "direct" and "indirect" effects. According to this point of view, indirect effects are those that result from relativistic changes of the molecular geometry (the well-known relativistic bond contraction (55) in particular) whereas direct effects refer to a fixed geometry. 

Most of the molecular relativistic calculations were performed for compounds studied experimentally various halides, oxyhalides and oxides of elements 104 through 108 and of their homologs in the chemical groups. The aim of those works was to predict stability, molecular geometry, type of bonding (ionic/covalence effects) and the influence of relativistic effects on those properties. On their basis, predictions of experimental behavior were made (see Section 3). A number of hydrides and fluorides of elements 111 and 112, as well as of simple compounds of the 7p elements up to Z=118 were also considered with the aim to study scalar relativistic and spin-orbit effects for various properties. 

These observations are consistent with a model in which the Pb s and p orbitals hybridize under normal energetic conditions to yield a stereochemically active lone pair and hemidirected structures. [The symmetries of either the nonrelativistic or the relativistic sets of orbitals are consistent with this hybridization (77, 78).] In the holodirected case, on the other hand, no hybridization takes place. The 6s electrons remain in the spherically symmetric s orbital and do not affect the molecular geometry. Holodirected complexes only appear with very large or bulky ligands, in which steric effects outweigh... 

The transformed Hamiltonians that we have derived allow us to calculate intrinsic molecular properties, such as geometries and harmonic frequencies. We would like to be able to calculate response properties as well, with wave functions derived from the transformed Hamiltonian. If we used a method such as the Douglas-Kroll-Hess method, it would be tempting to simply evaluate the property using the nonrelativistic property operators and the transformed wave function. As we saw in section 15.3, the property operators can have a relativistic correction, and for properties sensitive to the environment close to the nuclei where the relativistic effects are strong, these corrections are likely to be significant. To ensure that we do not omit important effects, we must derive a transformed property operator, starting from the Dirac form of the property operator. 

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