Role of relativistic effects

Calculations using the methods of non-relativistic quantum mechanics have now advanced to the point at which they can provide quantitative predictions of the structure and properties of atoms, their ions, molecules, and solids containing atoms from the first two rows of the Periodical Table. However, there is much evidence that relativistic effects grow in importance with the increase of atomic number, and the competition between relativistic and correlation effects dominates over the properties of materials from the first transition row onwards. This makes it obligatory to use methods based on relativistic quantum mechanics if one wishes to obtain even qualitatively realistic descriptions of the properties of systems containing heavy elements. Many of these dominate in materials being considered as new high-temperature superconductors. 

It is apparent that progress in our understanding of the properties of neutral heavy elements and their ions, including very highly ionized ones, as well as their role as constituents of molecules and solids, will depend on the development of theoretical methods and computational techniques, which are based on relativistic quantum mechanics. Fairly efficient methods of this kind have already been elaborated and many versions of relativistic codes for work with isolated atoms and ions are already available and in daily use by internationally known theoretical and experimental physicists and chemists [18, 54-57], 

It is very important to evaluate the accuracy and the regions of applicability of the methods developed for the effective study of the structure and properties of many-body systems, to demonstrate their utility on selected problems of genuine physical and chemical interest, to improve understanding of the fundamentals on which these methods are based, and to perform mutual checking and validation of results obtained by various 

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The Electronic Structure and Properties of Gas-Phase Compounds. Role of Relativistic Effects... 

In this chapter, results of recent theoretical investigations in the chemistry of the heaviest elements are reviewed. Chemical properties, trends and an analysis of the role of relativistic effects are discussed. The results obtained by various calculational methods are critically compared. Special attention is paid to the predictions of properties of superheavy elements studied by experiment. 

Results of the liquid extraction experiments caimot provide the information on the complex formation and role of relativistic effects in a straightforward way. For that piupose assistance of theory is indispensable, and relativistic effects can be detected only by comparing experimental behaviour with that predicted on the basis of relativistic versus nonrelativistic calculations. 

Today, the role relativistic effects play for NMR and EPR parameters has been appreciated to very different extents for different properties and by different communities of experimentalists and theoreticians. For example, it has been known early on in the EPR community that the electronic g-tensors of EPR spectroscopy are basically dominated by spin-orbit coupling and are thus intrinsically relativistic [2]. On the other hand, in spite of much early work on relativistic theories of NMR chemical shifts, and much associated recent cori5)utational developments and applications [3,4,5,6,7], most users of NMR spectroscopy still seem largely unaware of the important role of relativistic effects. This holds in particular for the role of spin-orbit effects, in what is often simply called heavy-atom effects on NMR chemical shifts. This can be seen easily when inspecting most NMR textbooks and much of the research literature. 

Semi-quantitative arguments on the role of relativistic effects in the chemical applications can be already presented within the very simply model. One of the principle axiom of the theory of relativity is the assumption that the speed of light is the finite and constant number (c 137.036 au) in all inertial frames. The quantity which characterizes the limit of validity of classical mechanics is the ratio of velocity of particle to the velocity of light ... 

The nature is always relativistic. Non-relativistic objects do not exists. The only way to see the role of relativistic effects in chemistry is through the comparison between relativistic and nonrelativistic theory and results. The values of the relativistic effects for a given quantity X are then usually calculated as a difference between the relativistic and nonrelativistic values of this quantity, i.e. AX = X rel) — X nrel) calculated at the same level of theory. Therefore, from both fundamental and practical points of view there is a necessity for relativistic quantum chemistry theory and applications. While the Hamiltonian of a molecule is exactly known in nonrelativistic quantum mechanics, this is no longer the case for the relativistic formulation. Many relativistic Hamiltonians have been derived over the past decades. It goes beyond the goal of this chapter to review all of the... 

The numerical examples of the role of relativistic effects in the calculations of dipole moments of Cm//, AgH and AuH diatomic species and dipole polarizabilities of GeO, SnO and PbO molecules are shown in Tables 4.3 and4.4. 

The core ionization potentials, more frequently called core electron binding energies (CEBEs) when molecular systems are studied, have been also recently calculated for the tautomeric structures of thio- and seleno-cytosine [35]. The role of relativistic effects in ly ionization have been studied for selenocytosine by the comparison of the nonrelativistic and relativistic SCE and MP2 results of the calculations. 

Abstract Theoretical chemical research in the area of the heaviest elements is extremely important. It deals with predictions of properties of exotic species and their behavior in sophisticated and expensive experiments with single atoms and permits the interpretation of experimental results. Spectacular developments in the relativistic quantum theory and computational algorithms have allowed for accurate calculations of electronic structures of the heaviest elements and their compounds. Due to the experimental restrictions in this area, the theoretical studies are often the only source of useful chemical information. The works on relativistic calculations and predictions of chemical properties of elements with Z > 104 are overviewed. Preference is given to those related to the experimental research. The increasingly important role of relativistic effects in this part of the Periodic Table is demonstrated. 

Theoretical chemical research on the heaviest elements is not less challenging than the experimental one. It should be based on the most accurate relativistic electronic structure calculations in order to reliably predict properties and experimental behavior of the new elements and their compounds. It also needs development of special approaches that bridge calculations with quantities that cannot be so easily predicted from calculations. Due to recent spectacular developments in the relativistic quantum theory, computational algorithms and techniques, very accurate calculations of properties of the transactinide elements and their compounds are now possible, which allow for reliable predictions of their experimental behavior. These theoretical works are overviewed here. Special attention is paid to the predictive power of the theoretical studies for the chemical experiments. The role of relativistic effects is discussed in detail. 

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