Lanthanide heavy atom effect

In this simple case there is no advantage to the pseudopotential calculation (the 3-21G( ) geometry is actually better ), but more challenging calculations on very-heavy-atom molecules, particularly transition metal molecules, rely heavily on ab initio or DFT (Chapter 7) calculations with pseudopotentials. Nevertheless, ordinary nonrelativistic all-electron basis sets sometimes give good results with quite heavy atoms [64]. A concise description of pseudopotential theory and specific relativistic effects on molecules, with several references, is given by Levine [65]. Reviews oriented toward transition metal molecules [66a,b,c] and the lanthanides [66d] have appeared, as well as detailed reviews of the more technical aspects of the theory [67]. See too Section 8.3. 

Relaxation of the rules can occur, especially since the selection rules apply strongly only to atoms that have pure Russell-Saunders (I-S) coupling. In heavy atoms such as lanthanides, the Russell-Saunders coupling is not entirely valid as there is the effect of the spin-orbit interactions, or so called j mixing, which will cause a breakdown of the spin selection rule. In lanthanides, the f-f transitions, which are parity-forbidden, can become weakly allowed as electric dipole transitions by admixture of configurations of opposite parity, for example d states, or charge transfer. These f-f transitions become parity-allowed in two-photon absorptions that are g g and u u. These even-parity transitions are forbidden for one photon but not for two photons, and vice versa for g u transitions [46],... 

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. 

Radii. The filling of the 4f orbitals (as well as relativistic effects) through the lanthanide elements cause a steady contraction, called the lanthanide contraction (Section 19-1), in atomic and ionic sizes. Thus the expected size increases of elements of the third transition series relative to those of the second transition series, due to an increased number of electrons and the higher principal quantum numbers of the outer ones, are almost exactly offset, and there is in general little difference in atomic and ionic sizes between the two heavy atoms of a group, whereas the corresponding atoms... 

Since the centrifugal term is present in the radial Schrodinger equation for all atoms, we must explain why centrifugal effects only dominate the inner valence spectra of fairly heavy atoms. Centrifugal barrier effects are present even in H. However, they act differently in transition elements or lanthanides. 

Relativistic and electron correlation effects play an important role in the electronic structure of molecules containing heavy elements (main group elements, transition metals, lanthanide and actinide complexes). It is therefore mandatory to account for them in quantum mechanical methods used in theoretical chemistry, when investigating for instance the properties of heavy atoms and molecules in their excited electronic states. In this chapter we introduce the present state-of-the-art ab initio spin-orbit configuration interaction methods for relativistic electronic structure calculations. These include the various types of relativistic effective core potentials in the scalar relativistic approximation, and several methods to treat electron correlation effects and spin-orbit coupling. We discuss a selection of recent applications on the spectroscopy of gas-phase molecules and on embedded molecules in a crystal enviromnent to outline the degree of maturity of quantum chemistry methods. This also illustrates the necessity for a strong interplay between theory and experiment. 

The relativistic calculations on the electronic structure of actinide compounds were reviewed by Pyykko (1987). He also reviewed relativistic quantum chemistry in 1988, whereas the relativistic calculations were limited to small molecules containing one heavy atom only (Pyykko 1988). Calculations on the uranyl and neptunyl ions were introduced in the review article. The general information on the computational chemistry of heavy elements and relativistic calculation techniques appear in the book written by Balasubramanian (1997). There are several first-principle approaches to the electronic structure of actinide compounds. The relativistic effective core potential (ECP) and relativistic density functional methods are widely used for complex systems containing actinide elements. Pepper and Bursten (1991) reviewed relativistic quantum chemistry, while Schreckenbach et al. (1999) reviewed density functional calculations on actinide compounds in which theoretical background and application to actinide compounds were described in detail. The Encyclopedia of computational chemistry also contains examples including lanthanide and actinide elements (Schleyer et al. 1998). The various methods for the computational approach to the chemistry of transuranium elements are briefly described and summarized below. 

Ab initio methods for lanthanide and actinide molecules are mostly based on the effective core potential (ECP) method, especially if the molecules in question have several heavy atoms. The philosophy of the ECP method is to replace the chemically unimportant core electrons by an effective core potential and treat the remaining valence electrons explicitly. There are several techniques to derive RECPs which we now briefly describe and refer to the reviews by Christiansen et al. (1985), Krauss and Stevens (1984), Balasubramanian and Pitzer (1987) for further details. 

Effective core potential (ECP) or pseudo-potential approximation, has been proved to be very useful for modeling of heavy atoms in the ab initio methods (Hay and Wadt 1985). In this approximation, core electrons are replaced by an effective potential, thereby reducing the number of electrons to be considered and hence requiring fewer basis functions. The ECP method takes into account the relativistic effect on valence electrons, thus making it applicable to heavy atoms (e.g., second- and third-row transition metals, lanthanides and actinides). It is relatively cheap, works very well, and has very little loss in reliability. 

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