Effects in Atoms with Consequences for Chemical Bonding

Effects in Atoms with Consequences for Chemical Bonding 

The importance of relativity to chemistry was first noticed on the basis of atomic calculations [1008,1009], because effects on bonding may be qualitatively anticipated in terms of the LCAO model. Moreover, atoms and their ions can be studied with the utmost accuracy (in the case of one-electron ions even exactly), and we are therefore advised to start with a comparison of Schrodinger and Dirac atoms. Such comparisons have been made several times throughout this book on a formal basis. Now, we recall some typical effects on one-electron states and orbital energies. 

Since especially diatomics built from atoms with large nuclear charge number Z and an open p shell are significantly affected by scalar and spin-orbit effects, molecules containing thallium became perfect test cases for relativistic electronic structure methods. Some representative results for TIH are collected in a later section. 

After what has been derived in chapter 13, it is clear how this equation works. All difficulties with the elimination of the small component in chapter 13 stem from the fact that the relation between large and small component contains the potential energy operator V and also the energy. In the L6vy-Leblond equation this is avoided because the lower part of the matrix equation does not depend on either of them. This is most easily seen in split notation. 

We have already discussed in chapters 12 and 13 that low-order scalar-relativistic operators such as DKH2 or ZORA provide very efficient variational schemes, which comprise all effects for which the (non-variational) Pauli Hamiltonian could account for (as is clear from the derivations in chapters 11 and 13). It is for this reason that historically important scalar relativistic corrections which can only be considered perturbatively (such as the mass-velocity and Darwin terms in the Pauli approximation in section 13.1), are no longer needed and their significance fades away. There is also no further need to develop new pseudo-relativistic one- and two-electron operators. This is very beneficial in view of the desired comparability of computational studies. In other words, if there were very many pseudo-relativistic Hamiltonians available, computational studies with different operators of this sort on similar molecular systems would hardly be comparable. 

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