Actinides relativistic effects

We should note that the Schrodinger equation is non-relativistic since we derived it from the non-relativistic expression for the energy eqn (2.26). The Dirac equation is the relativistic analogue that is based on the relativistic expression for the energy, namely eqn (26). It led directly to the novel concept of electron spin. Since the valence electrons, which control the cohesive and structural properties of materials, usually travel with velocity v c, they are adequately described by the Schrodinger equation. For the heavier elements, such as the lanthanides and actinides, relativistic effects can be included perturbatively when necessary. Photons, the quanta of the... 

Intermolecular interactions by Perturbation Theory Lanthanides and Actinides Relativistic Effective Core Potential... 

Hay, P. J., Martin, R. L., 1998, Theoretical Studies of the Structures and Vibrational Frequencies of Actinide Compounds Using Relativistic Effective Core Potentials With Hartree-Fock and Density Functional Methods ... 

The methods used to describe the electronic structure of actinide compounds must, therefore, be relativistic and must also have the capability to describe complex electronic structures. Such methods will be described in the next section. The main characteristic of successful quantum calculations for such systems is the use of multiconfigurational wave functions that include relativistic effects. These methods have been applied for a large number of molecular systems containing transition metals or actinides, and we shall give several examples from recent studies of such systems. 

Relativistic effects are more pronounced for the actinides because of their higher nuclear charge. As a result, the s and p orbitals screen the charge of the nucleus better and the d and f orbitals expand, and are destabilized 2,3). The shielding of the 5/ orbitals by filled outer s and p orbitals is thus not as effective, and actinide ions form more covalent bonds and are found in higher oxidation states, at least at the beginning of the 5/ series. 

Early band structure calculations for the actinide metals were made both with and without relativistic effects. As explained above, at least the mass velocity and Darwin shifts should be included to produce a relativistic band structure. For this reason we shall discuss only the relativistic calculations. There were some difficulties with the f-band structure in these studies caused by the f-asymptote problem , which have since been elegantly solved by linear methods . Nevertheless the non-self-consistent RAPW calculations for Th through Bk indicated some interesting trends that have also been found in more recent self-consistent calculations ... 

Experimental investigations of spectroscopic and other physical-chemical properties of actinides are severely hampered by their radioactive decay and radiation which lead to chemical modifications of the systems under study. The diversity of properties of lanthanide and actinide compounds is unique due to the multitude of their valency forms (which can vary over a wide range) and because of the particular importance of relativistic effects. They are, therefore, of great interest, both for fundamental research and for the development of new technologies and materials. The most important practical problems involve storage and processing of radioactive waste and nuclear fuel, as well as pollution of the environment by radioactive waste, where most of the decayed elements are actinides. 

Relativistic effects cannot be neglected if heavier systems are studied we have discussed the major relativistic effects on calculated NMR shieldings and chemical shifts in this chapter. Besides relativistic effects, electron correlation has to be included for even a qualitatively correct treatment of transition metal or actinide complexes. So far, DFT based methods are about the only approaches that can handle both relativity and correlation, and DFT is, for the time being, the method of choice for these heavy element compounds. In this chapter, we have presented results from two relativistic DFT methods, the Pauli- (QR-) and ZORA approaches. 

K. Balasubramanian, Relativistic effects and electronic structure of lanthanide and actinide molecules 29... 

The data of Table 4 and Figure 10 show that the IR of the 4d and 5d elements are almost equal due to the lanthanide contraction which is 86% a non-relativistic effect, while the IR of the transactinides are about 0.05 A larger than the IR of the 5d elements due to an orbital expansion of the 6p3/2 orbitals being the outer orbitals for the maximum oxidation state. The IR of the lighter 6d elements are however smaller than the IR of the actinides since the latter undergo the actinide contraction of 0.030 A which is mostly a relativistic effect [13,105]. 

For the computational investigation of molecular systems containing heavy atoms, such as transition metals, lanthanides, and actinides, we could neglect neither relativity nor electron correlation. Relativistic effects, both spin-free and spin-orbit, increase with the nuclear charge of atoms. Therefore, instead of the nonrelativistic Schrodinger equation, we must start with the Dirac equation, which has four-component solutions. For many-electron systems, the four-component Hamiltonian is constructed from the one-electron Dirac operator with an approximated relativistic two-electron operator, such as the Coulomb, Breit, or Gaunt operator, within the nopair approximation. The four-component method is relativistically rigorous, which includes both spin-free and spin-orbit effects in a balanced way. However it requires much computational time since it contains more variational parameters than the approximated, one or two-component method. 

The electronic structures and bonding ia-,actinide compounds cannot be reliably treated without the inclusion of relativistic effects. A specific example is provided by uranocene, (QHg U,19 but there are many others.20 21... 

A important relativistic effect is that 5f orbitals of actinides are larger and their electrons more weakly bound than predicted by non-relativistic calculations, hence the 5f electrons are more chemically available . This leads to ... 

N. Kaltsoyannis, Chem. Soc. Rev., 2003,32,9 (computational actinide chemistry, including relativistic effects). 

Ionic Radii and the Actinide Contraction - A Partial Relativistic Effect... 

SCF calculations also frequently neglect relativistic effects, which may well be important, especially for third row transition metal and actinide compounds. 

Our results therefore clearly demonstrate that there are marked qualitative as well as quantitative differences between the predictions of the NRL and DF SCF calculations for the nature of bonding, total energies, orbital energies, dissociation energies etc., for the diatomics involving actinides due to very significant relativistic effects in such systems. 

We also conclude from our ab initio DF SCF calculations that the 5d, 6d and 5f DFAOs (and their associated electrons) are definitely involved (due to relativistic effects in the electronic structure and bonding of the diatomics of the heavy third-row transition elements and actinides, and they present the formidable dual challenge to quantum chemists of the accurate calculation of the relativistic and electron correlation effects for such systems. 

Valence electrons in atoms and molecules have a finite (albeit small) probability of being close to the nuclei and they can as a consequence acquire high instantaneous velocities.In fact,the velocities for the valence electrons can approach that of light as they pass in close proximity to heavier nuclei with Z >72.It is for this reason not too surprising that relativistic effects become of importance for the chemical properties of compounds containing 5d-block elements in the third transition series or 5f-block elements in the actinide series. 

We shall finally probe the degree to which relativistic effects might be of importance for bond energies in compounds involving actinides, by representing results from calculations on RMCI3 with M=Th,U and R=H,CH3. 

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. 

With respect to the chemical properties of the actinides, a new effect becomes noticeable with increasing atomic number Z, the influence of the positive nuclear charge on the electrons increases in such a way that their velocity approaches the velocity of light, which leads to relativistic effects. The valence electrons are more effectively screened from the nuclear charge, with the result of stabilization of the spherical 7s and 7pi/2 orbitals and destabilization of the 6d and 5f orbitals. 

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