Density functional theory relativistic, review

The Douglas-Kroll approach to relativistic electronic structure theory in the framework of density functional theory was reviewed focussing on recent method developments and illustrative applications which demonstrate the capabilities of this approach. Compared to other relativistic methods, which often are only applied to small molecules for demonstration purposes, the DK approach has been used in a variety of fields. Besides the very popular pseudopotential approach, which accounts for relativistic effects by means of a potential replacing the core electrons, until now the scalar relativistic variant of the second-... 

During the last 10-20 years, a large number of efficient theoretical methods for the calculation of linear and nonlinear optical properties have been developed— this development includes semi-empirical, highly correlated ab initio, and density functional theory methods. Many of these approaches will be reviewed in later chapters of this book, and applications will be given that illustrate the merits and limitations of theoretical studies of linear and nonlinear optical processes. It will become clear that theoretical studies today can provide valuable information in Are search for materials with specific nonlinear optical properties. First, there is the possibility to screen classes of materials based on cost and time effective calculations rather then labor intensive synthesis and characterization work. Second, there is Are possibility to obtain a microscopic understanding for the performance of the material—one can investigate the role of individual transition channels, dipole moments, etc., and perform systematic model Improvements by inclusion of the environment, relativistic effects, etc. 

A different approach to the solution of the electron correlation problem comes from density functional theory (see Chapter 4). We hasten to add that in a certain approximation of relativistic density functional theory, which is also reviewed in this book, exchange and correlation functionals are taken to replace Dirac-Fock potentials in the SCF equations. Another approach, which we will not discuss here, is the direct perturbation method as developed by Rutkowski, Schwarz and Kutzelnigg (Kutzel-nigg 1989, 1990 Rutkowski 1986a,b,c Rutkowski and Schwarz 1990 Schwarz et al. 1991). 

An overview of relativistic density functional theory (RDFT) is presented with special emphasis on its field theoretical foundations and the construction of relativistic density functionals. A summary of quantum electrodynamics (QED) for bound states provides the background for the discussion of the relativistic generalization of the Hohenberg-Kohn theorem and the effective single-particle equations of RDFT. In particular, the renormalization procedure of bound state QED is reviewed in some detail. Knowledge of this renormalization scheme is pertinent for a careful derivation of the RDFT concept which necessarily has to reflect all the features of QED, such as transverse and vacuum corrections. This aspect not only shows up in the existence proof of RDFT, but also leads to an extended form of the single-particle equations which includes radiative corrections. The need for renormalization is also evident in the construction of explicit functionals. 

Recent advances in electronic structure theory achieved in our group have been reviewed. Emphasis is put on development of ab initio multireference-based perturbation theory, exchange and correlation functionals in density functional theory, and molecular theory including relativistic effects. 

The collection presented here is far from being complete. Extended bibliographies including more than 10.000 references on relativistic theory in chemistry and physics have been published by Pekka Pyykko [32-34]. We took much advantage of his careful and patient work when preparing this chapter. Specialized on solid state effects are recent reviews on magnetooptical Kerr spectra [35] and on density functional theory applied to 4f and 5f elements and metallic compounds [24]. 

Abstract. The 1/Z expansion will first be used to discuss the scaling properties of the ground-state energy of heavy (non-relativistic) neutral atoms with atomic number Z. The question will be addressed as to what order in Z electron correlation first enters the expansion. The density functional theory (DFT) invoked above will be utilized then to treat, but now inevitably more approximately, the correlation energy in a variety of molecules. Finally, recent studies at Hartree-Fock level on almost spherical B and C cages will be reviewed. For buckminsterfullerene, the role of electron correlation will then be assessed using the Hubbard Hamiltonian, as in the study of Flocke et al. 

First of all, a few words on the scope of this review seem to be appropriate. For simplicity, all explicit formulae in this chapter will be given for spin-saturated systems only. Of course, the complete formalism can be extended to spin-density functional theory (SDFT) and all numerical results for spin-polarized systems given in this paper were obtained by SDFT calculations. In addition, the discussion is restricted to the nonrelativistic formalism - for its relativistic form see Chap. 3. The concept of implicit functionals has also... 

The programs that use only the density functional theory and the programs for relativistic calculations at the level of Dirac theory and beyond are reviewed in other chapters. 

Autschbach has outlined some basic concepts of relativistic quantum chemistry and recent developments of relativistic methods for the calculation of the molecular properties, including important for NMR spectroscopy, nuclear magnetic resonance shielding, indirect nuclear spin-spin coupling and electric field gradients (nuclear quadrupole coupling). The author analysed the performance of density functional theory (DFT) and its applications for heavy-element systems. Finally, the author has reviewed selected applications of DFT in relativistic calculation of magnetic resonance parameters. 

In this chapter we will provide a critical review of the use of 2- and 4-component relativistic Hamiltonians combined with all-electron methods and appropriate basis sets for the study of lanthanide and actinide chemistry. These approaches provide in principle the more rigorous treatment of the electronic structure but typically demand large computational resources due to the large basis sets that are required for accurate energetics. A complication is furthermore the open-shell nature of many systems of practical interest that make black box application of conventional methods impossible. Especially for calculations in which electron correlation is explicitly considered one needs to find a balance between the appropriate treatment of the multi-reference nature of the wave function and the practical limitations encountered in the choice of an active space. For density functional theory (DFT) calculations one needs to select the appropriate density functional approximation (DFA) on basis of assessments for lighter elements because little or no high-precision experimental information on isolated molecules is available for the f elements. This increases the demand for reliable theoretical ( benchmark ) data in which all possible errors due to the inevitable approximations are carefully checked. In order to do so we need to understand how f elements differ from the more commonly encountered main group elements and also from the d elements with which they of course share some characteristics. 

For this kind of confinement, the solution of the non-relativistic time independent Schrodinger equation has been tackled by different techniques. For confined many-electron atoms the density functional theory [6], using the Kohn-Sham model [7], has given some estimations of the non-classical effects [8-11], through the exchange-correlation functional. An elementary review of this subject can be found in Ref [12], where numerical techniques are discussed to solve the Kohn-Sham equations. Furthermore, in this reference, some chemical predictors are analyzed as a function of the confinement radii. 

The presently available explicit approximations for the relativistic xc-energy functional are presented in Section 4. Both implicit functionals (as the exact exchange) and explicit density functionals (as the RLDA and RGGA) are discussed (on the basis of the information on the RHEG in Appendix C and that on the relativistic gradient expansion in Appendix E). Section 4 also contains a number of illustrative results obtained with the various functionals. However, no attempt is made to review the wealth of RDFT applications in quantum chemistry (see e.g.[74-88]) and condensed matter theory (see e.g.[89-l(X)]) as well as the substantial literature on nonrelativistic xc-functionals (see e.g.[l]). In this respect the reader is referred to the original literature. The review is concluded by a brief summary in Section 5. 

M = O, F, K, Ca, Mn, Cs, Ba, La, Eu and U. They employed relativistic ECPs for the metal atom and restricted Hartree-Fock (RHF) level of theory to study these complexes. There are other theoretical calculations based on the density functional method by Rosen and Wastberg (1988) as well as Ballster etal. (1990). The recent study of Chang et al. (1991) on La Cgo showed that the lanthanum atom donates two electrons from the 6s orbital to the carbon cage. This, in fact, provided the basis to explain the unusual stability of La Cg2 observed by Chai et al. (1991). In this section we review recent theoretical and experimental developments so as to gain insight into these unusual carbon cages containing a lanthanide or actinide atom inside. 

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