Heavy atom, relativistic effect

Heavy-atom relativistic effects influence these shifts. 

Lo et a/,102 have calculated spin-orbit coupling constants for first- and second-row atoms and for the first transition series, results agreeing with the work of Blume and Watson. Karayanis103 has extended the calculation to triply ionized rare earths. However, with very heavy atoms relativistic effects on the part of the wavefunction near the nucleus become severe, leading to a breakdown of the conditions under which simple perturbation theory ought to be applied. Lewis and co-workers104 have used relativistic self-consistent Dirac-Slater and Dirac-Fock wavefunctions to evaluate spin orbit coupling... 

HAHA Heavy atom heavy atom relativistic effect... 

Configuration Interaction Density Functional Theory (DFT), Hartree-Fock (HF), and the Self-consistent Field Density Functional Theory Applications to Transition Metal Problems Metal Complexes Relativistic Effective Core Potential Techniques for Molecules Containing Very Heavy Atoms Relativistic Effects of the Superheavy Elements Relativistic Theory and Applications Transition Metal Chemistry Transition Metals Applications. 

For solids with heavy atoms, relativistic shifts may affect the bonding properties, and also optical properties may be influenced. The relativistic shifts of the 5d bands relative to the s-p bands in gold change the main inter band edge more than 1 eV. Already Pyykko and Desclaux mentioned [1] that the fact that gold is yellow is a result of relativistic effects. These are indirect [2] (see also the introduction. Sect. 1), and the picture was confirmed by relativistic band structure calculations [3,4]. Also the optical properties of semiconductors are influenced by relativistic shifts which affect the gap between occupied and empty states, see for example Ref. [5]. Two additional examples may be mentioned where relativistic shifts in the energy band structure drastically influence the physical properties. First,... 

It should be clear from the examples provided in this article, that relativistic effects cannot be ignored when one wants to understand NMR chemical shifts throughout the periodic table. While the local heavy-atom effects on the heavy atoms ( HAHA effects) can be very large for absolute shield ings, they tend to cancel to a large extent in relative shifts and are thus probably less important for the interpretation of the observed shifts for different compounds. HAHA effects are nevertheless of interest, not only for the development of reliable relativistic computational methods but also, for example, when deriving absolute shielding scales for heavy nuclei (section 5). 

Although electron correlation is still the main bottleneck toward a rigorous quantum chemistry, one should not forget that for molecules containing heavy elements relativistic effects are not less important [17], while for molecules with lighter atoms adiabatic and even non-adiabatic effects need to be considered [18]. The theory of both types of effects is, fortunately on a good way. 

The relativistic effects are important for both light and heavy elements. For very precise calculations, while searching the limit of accuracy of quantum mechanics or quantum electrodynamics the relativistic energy contributions are already needed for H or He atoms. For heavy elements, relativistic effects are important in atomic and in chemical calculations when one search for a chemical accuracy of about 0.1 eV. 

Pitzer, K.S., 1983, Electron structure of molecules with very heavy atoms using effective core potentials, in Relativistic Effects in Atoms, Molecules and Solids, NATO ASI Series, Series B Physics, Vol. 87, ed. G.L. Malli (Plenum, New York) p. 403. 

Since for a heavy atom, the effective exponent of the atomic orbitals decreases when moving from the low-energy compact I5 orbital to higher-energy outer orbitals, this means that the most important relativistic orbital contraction occurs for the inner shells. The chemical properties of an atom depend on what happens to its outer shells (valence shell). Therefore, we may conclude that the relativistic corrections are expected to play a secondary role in chemistry. ... 

Basis Sets Correlation Consistent Sets Benchmark Studies on Small Molecules Complete Active Space Self-consistent Field (CASSCF) Second-order Perturbation Theory (CASPT2) Configuration Interaction Configuration Interaction PCI-X and Applications Core-Valence Correlation Effects Coupled-cbister Theory Density Functional Applications Density Functional Theory (DFT), Har-tree-Fock (HF), and the Self-consistent Field Density Functional Theory Applications to Transition Metal Problems Electronic Structure of Meted and Mixed Nonstoi-chiometric Clusters G2 Theory Gradient Theory Heats of Formation Hybrid Methods Metal Complexes Relativistic Effective Core Potential Techniques for Molecules Containing Very Heavy Atoms Relativistic Theory and Applications Semiempiriced Methetds Transition Metals Surface Chemi-ced Bond Transition Meted Chemistry. 

Finally, the synthesis of superheavy elements over the past 60 years or so, and in particular the synthesis of elements with atomic numbers beyond 103 has raised some new philosophical questions regarding the status of the periodic law. In these heavy elements relativistic effects contribute significantly to the extent that the periodic law may cease to hold. For example, chemical experiments on minute quantities of rutherfordium (104) and dubnium (105) indicate considerable differences in properties from those expected on the basis of the groups of the periodic table in which they occur. However, similar chemical experiments with seaborgium (106) and bohrium (107) have shown that the periodic law becomes valid again in that these elements show the behavior that is expected on the basis of the periodic table. 

Unlike semiempirical methods that are formulated to completely neglect the core electrons, ah initio methods must represent all the electrons in some manner. However, for heavy atoms it is desirable to reduce the amount of computation necessary. This is done by replacing the core electrons and their basis functions in the wave function by a potential term in the Hamiltonian. These are called core potentials, elfective core potentials (ECP), or relativistic effective core potentials (RECP). Core potentials must be used along with a valence basis set that was created to accompany them. As well as reducing the computation time, core potentials can include the effects of the relativistic mass defect and spin coupling terms that are significant near the nuclei of heavy atoms. This is often the method of choice for heavy atoms, Rb and up. 

The Schrodinger equation is a nonreiativistic description of atoms and molecules. Strictly speaking, relativistic effects must be included in order to obtain completely accurate results for any ah initio calculation. In practice, relativistic effects are negligible for many systems, particularly those with light elements. It is necessary to include relativistic effects to correctly describe the behavior of very heavy elements. With increases in computer capability and algorithm efficiency, it will become easier to perform heavy atom calculations and thus an understanding of relativistic corrections is necessary. 

The use of RECP s is often the method of choice for computations on heavy atoms. There are several reasons for this The core potential replaces a large number of electrons, thus making the calculation run faster. It is the least computation-intensive way to include relativistic effects in ah initio calculations. Furthermore, there are few semiempirical or molecular mechanics methods that are reliable for heavy atoms. Core potentials were discussed further in Chapter 10. 

The energy of a Is-electron in a hydrogen-like system (one nucleus and one electron) is —Z /2, and classically this is equal to minus the kinetic energy, 1/2 mv, due to the virial theorem E — —T = 1/2 V). In atomic units the classical velocity of a Is-electron is thus Z m= 1). The speed of light in these units is 137.036, and it is clear that relativistic effects cannot be neglected for the core electrons in heavy nuclei. For nuclei with large Z, the Is-electrons are relativistic and thus heavier, which has the effect that the 1 s-orbital shrinks in size, by the same factor by which the mass increases (eq. (8.2)). 

Indelicato, P. and Lindroth, E. (1992) Relativistic effects, correlation, and QED corrections on Ka transitions in medium to very heavy atoms. Physical Review A, 46, 2426-2436. 

Relativistic effects result if electrons nearby very heavy atomic nuclei are accelerated to such an extent that Einstein s famous theory of relativity begins to take effect,... 

The twin facts that heavy-atom compounds like BaF, T1F, and YbF contain many electrons and that the behavior of these electrons must be treated relati-vistically introduce severe impediments to theoretical treatments, that is, to the inclusion of sufficient electron correlation in this kind of molecule. Due to this computational complexity, calculations of P,T-odd interaction constants have been carried out with relativistic matching of nonrelativistic wavefunctions (approximate relativistic spinors) [42], relativistic effective core potentials (RECP) [43, 34], or at the all-electron Dirac-Fock (DF) level [35, 44]. For example, the first calculation of P,T-odd interactions in T1F was carried out in 1980 by Hinds and Sandars [42] using approximate relativistic wavefunctions generated from nonrelativistic single particle orbitals. 

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