Relativistic Effects on Properties

We can illustrate this principle with an analysis of the force constant. To do so, we write the relativistic energy as a function of position in terms of the nonrelativistic energy and a relativistic correction  

We expand the nonrelativistic energy in a Taylor series in the coordinates, 

We can similarly expand the relativistic correction to the energy, but this we do around the relativistic geometry  

we can decompose the relativistic correction to the quadratic force constant into a correction to the force constant at the relativistic geometry—the change in curvature 

This kind of analysis can be applied to other properties. For the correlation energy, the relativistic correction is simple  

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Achievements in the area of the theoretical chemistry of the heaviest elements are overviewed. The influence of relativistic effects on properties of the heaviest elements is elucidated. An emphasis is put on the predictive power of theoretical investigations with respect to the outcome of "one-atom-at-a-time" chemical experiments. 

The influence of relativistic effects on properties of MAu (M = Hg and Cn) was studied in [155]. Relativity is shown to increase De(HgAu) by 0.13 eV, but to decrease it by about the same amount (0.12 eV) in CnAu due to the contraction of the 7s(Cn) AO. This makes trends in the nonrelativistic vi. relativistic D. values opposite from HgAu to CnAu, so that D (CnAu) > D (HgAu), while rffXCnAu) < D (HgAu). Rf. is decreased by relativity in both systems and the trends are the same both for the non-relativistic and relativistic R. ... 

The colour of gold adds to the attractiveness of the metal, and the liquid state of mercury allows the metal to be used over a wide range of temperatures in thermometers and electrical contact switches. These unusual properties are explicable in terms of relativistic effects. The relativistic effects on the 6s orbital are at a maximum in gold and are considerable in mercury. 

Another notable difference in properties down groups is the inert psiir effect > as demonstrated by the chemical behaviour of Tl, Pb and Bi. The main oxidation states of these elements are + I, + 2 and + 3, respectively, which are lower by two units than those expected from the behaviour of the lighter members of each group. There is a smaller, but similar, effect in the chemistry of In, Sn and Sb. These effects are partially explained by the relativistic effects on the appropriate ionization energies, which make the achievement of the higher oxidation states (the participation of the pair of s-electrons in chemical bonding) relatively more difficult. 

In this section we discuss the various atomic properties that are the manifestation of the electronic configurations of the atoms discussed in the previous sections. These properties include ionization energy, electron affinity, electronegativity, etc. Other properties such as atomic and ionic radii will be discussed in subsequent chapters, as these properties are related to the interaction between atoms in a molecule. Toward the end of this section, we will also discuss the influence of relativistic effects on the properties of elements. 

In recent years, relativistic effects on the chemical properties of atoms have received considerable attention. In the theory of relativity, when an electron is traveling with high velocity v, its mass m is related to its rest mass m0 in the following way,... 

The influence of relativistic effects on the electronic structure and properties of the 6d transactinides was analyzed in detail on the example of MCE (M = V, Nb, Ta and Db) [117]. Opposite trends in the relativistic and non-relativistic energies of the valence orbitals from the 5d to the 6d elements were shown to result in opposite trends in molecular orbital (MO) energies, see Figure 12. Thus, the highest occupied MO (HOMO) of the 3p(Cl)... 

The special interest in the chemistry of elements 111 and 112 originates from the expectation of anomalous properties of their compounds as compared to homologues in groups 11 and 12 due to the predicted maximum of relativistic effects on the 7s electron shell see Section 3. The large relativistic destabilization and expansion of the 6d orbitals are also expected to influence their chemistry. 

Relativistic effects on the valence electrons are already evident by comparing the electropositive character of Fr and Ra with that of their preceding homologues. The ionization potentials of both elements are not lower than those of their homologues Cs and Ba, respectively, as expected by extrapolation, but the ionization potential of Fr is about the same as that of Cs and the ionization potential of Ra is somewhat higher than that of Ba. The influence of relativistic effects on the properties of the actinides is evident also from the tendency of the heavier actinides to form lower oxidation states. For example, Es already prefers the oxidation state Es2+. 

I, II, (>II ) noble metal, very volatile or gaseous oxides, chlorides and bromides unstable due to relativistic effect on 7s electrons, MF2 stable, stable complexes MX4 (X = 1, Br, Cl) in aqueous solutions, many complexes properties of M+ between those of Tl" and Ag" ", MCI... 

Relativistic effects on chemical properties have been reviewed by many authors For the present purpose, these may be briefly summarized on the basis of the review... 

Correlation and relativistic effects on Pb-Pb and Pb-O interactions in P-PbO have been examined using ab initio calculations and Pb NMR CSA tensor analysis. It has been shown that a covalent-like Pb -Pb interaction accounts for many facets of the NMR and the X-ray absorption near-edge structure, as well as other spectroscopic properties. 

Often one is especially interested in the relativistic effects on certain properties. These effects are directly obtained by means of perturbation theory, but in a less straightforward and less controlled way as differences between results of two independent calculations (i.e. relativistic and non-relativistic). E.g. which basis sets should be used for consistent results ... 

A detailed presentation of relativistic effects on magnetic properties is found in Ref. [60], especially for the H-atom in a homogeneous magnetic field in Ref. [61] Application of DPT to first-order magnetic properties were published by Hennum, et al. [62]. An earlier, more intuitive formulation, especially for NMR chemical shifts was given by Nomura et al. [63]. The fully relativistic theory has been studied by Pyykko [64] and Pyper [65]. 

Table 3 presents relativistic effects on several properties calculated as the difference (A) obtained in calculations which included the quasirelativistic correction, and corresponding calculations that excluded the correction, and used Hartree-Fock-Slater core orbitals rather than Dirac-Slater. The method finds significant relativistic Pt-C bond shortening, and little effect on the CO bond. The effect on adsorption energy is dramatic. Eads increases by about 50% when relativity is included. There is also an increase in the Pt-C force constant and frequency. The shortened Pt-C bond results in an increase in CO frequency through a wall effect, a Pauli repulsion effect. Ref. 34 ascribed the anomalously small shift in CO frequency from gas phase to adsorbed on Pt to the relativistic effect. 

Investigations of chemical properties of the heaviest elements belong to the most fundamental and important areas of chemical science. They seek to probe the uppermost reaches of the Periodic Table of the elements where the nuclei become extremely unstable and relativistic effects on electronic shells are very strong. This makes both theoretical and experimental research in this area extremely exciting and challenging. 

Relativistic effects on atomic properties of the heaviest elements... 

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. 

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