Indirect Relativistic Effects

Although the increased electron affinity associated with the heavier elements usually manifests itself only indirectly (via electronegativity, etc.), it is directly responsible for the fact that cesium auride, Cs Au, is an ionic salt rather than an alloy. Both the increased ionization energy and increased electron affinity in these elements result from 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. 

In contrast, the valence d and f orbitals in heavy atoms are expanded and destabilized by the relativistic effects. This is because the contraction of the s orbitals increases the shielding effect, which gives rise to a smaller effective nuclear charge for the d and f electrons. This is known as the indirect relativistic orbital expansion and destabilization. In addition, if a filled d or f subshell lies just inside a valence orbital, that orbital will experience a larger effective nuclear charge which will lead to orbital contraction and stabilization. This is because the d and f orbitals have been expanded and their shielding effect accordingly lowered. 

Relativistic effects are implemented in many ECPs and these are denoted RECPs. RECPs can be generated by several techniques34,86,93, e.g. ab initio ECPs can be derived from the relativistic all-electron Dirac-Fock solution of the atom. Thus, the RECPs implicitly include the indirect relativistic effects of the core electrons on the radial distribution of the valence electrons94. The use of RECPs therefore enables one to carry out... 

The contraction of the inner s- and pia shells provides various indirect relativistic effects. Thus, 5f in the gaseous uranium atom149 is destabilized by 6 eV compared to a non-relativistic wave-function. It is interesting to note that the average radius of the 5 f shell149 is close to 1.5 bohr (0.8 A) and slightly smaller than 1.8 bohr of the 6p shell. 

The second (indirect) relativistic effect is the expansion of outer d and f orbitals The relativistic contraction of the s and pi/2 shells results in a more efficient screening of the nuclear charge, so that the outer orbitals which never come to the core become more expanded and energetically destabilized. While the direct relativistic effect originates in the immediate vicinity of the nucleus, the indirect relativistic effect is influenced by the outer core orbitals. It should be realized that though contracted s and pi/2 core (innermore) orbitals cause indirect destabilization of the outer orbitals, relativistically expanded d and f orbitals cause the indirect stabilization of the valence s and p-orbitals. That partially explains the very large relativistic stabilization of the 6s and 7s orbitals in Au and element 112, respectively Since d shells (it is also valid for the f shells) become fully populated at the end of the nd series, there will occur a maximum of the indirect stabilization of the valence s and p orbitals [34],... 

One century after the beginning of most dramatic changes in physics and chemistry, after the advent of quantum theory and in the year of the 100th anniversary of Paul A.M. Dirac, modern relativistic atomic and molecular calculations clearly show the very strong influence of direct and indirect relativistic effects not only on electronic configurations but also on chemical properties of the heaviest elements. The actual state of the theoretical chemistry of the heaviest elements is comprehensively covered in Chapter 2. It does not only discuss most recent theoretical developments and results, where especially up to date molecular calculations dramatically increased our insights over the last decade, but it also relates these results to experimental observations. 

The second but often dominant effect is the so-called indirect relativistic effect. This occurs as a change in the radial distribution of the wavefunctions because in a many-electron atom the inner electrons contract and thus shield the outer ones more effectively. As a result, this effect often compensates the direct relativistic effect for the d-wavefunctions for the 5f-wavefimctions, however, this leads to an increased radius and the 4f-wavefunctions are hardly affected at all. As a consequence, the 5f-wavefunctions are chemically much more active in the Actinides than the 4f-wavefunctions in the Lanthanides. 

Effective core potentials address the aforementioned problems that arise when using theoretical methods to study heavy-element systems. First, ECPs decrease the number of electrons involved in the calculation, reducing the computational effort, while also facilitating the use of larger basis sets for an improved description of the valence electrons. In addition, ECPs indirectly address electron correlation because ECPs may be used within DFT, or because fewer valence electrons may allow implementation of post-HF, electron correlation methods. Finally, ECPs account for relativistic effects by first replacing the electrons that are most affected by relativity, with ECPs derived from atomic calculations that explicitly include relativistic effects via Dirac-Fock calculations. Because ECPs incorporate relativistic effects, they may also be termed relativistic effective core potentials (RECPs). 

The NpPolMe basis sets were developed recently (10) for the investigation of relativistic effects using the DK transformed hamiltonian (13, 18-20). This is the spin-averaged no-pair approximation which reduces the 4-component relativistic one-electron hamiltonian to a 1-component form without introducing strongly singular operators. NpPolMe basis sets indirectly incorporate some relativistic effects on the wave function. Let us note that both PolMe and NpPolMe contracted sets share the same exponents of primitive Gaussians. Contraction coefficients are, however,... 

This destabilization may lead, in turn, to an indirect stabilization of the next higher s and p shells with spatial extent similar to the d shell in question. This situation occurs in the case of the late transition metals and leads to the gold maximum of relativistic effects and the unusually large relativistic effects in the elements of groups 10-12. If the d shell is only weakly occupied, as is the case in the early transition metals, the direct effect on the s and p shells is partly balanced by the indirect effect on those shells, and the relativistic effects are generally much smaller. 

However, relativistic effects have a much more profound influence on a material s properties. Thus, the existence of a spin quantum number allows for the existence of magnetism. Moreover, as shown in most standard textbooks on physical chemistry, the phenomenon of phosphorescence can only be explained through the existence of relativistic effects. Phosphorescence involves transitions between, for example, singlet and triplet states which are only possible if some spin-operating effects exist, e.g. spin-orbit couplings. Furthermore, several experimental techniques are indirectly based on exploiting relativistic effects. These include, for example, electron-spin and NMR spectroscopies. 

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