Relativistic generalized gradient

Full potential linearized-augmented-plane-wave calculations for 5d transition metals using the relativistic generalized gradient approximation... 

Philipsen, P.H.T. and Baerends, E.J. (2000) Relativistic calculations to assess the ability of the generalized gradient approximation to reproduce trends in cohesive properties of solids. Physical Review B - Condensed Matter, 61, 1773-1778. 

P. H. T. Philipsen and E. J. Baerends, Relativistic Calculations to Assess the Ability of the Generalized Gradient Approximation to Reproduce Trends in Cohesive Properties of Solids, Phys. Rev. B 61 (2000), 1773. 

In spite of the impressive progress which has been achieved with conventional ab-initio methods as the Configuration-Interaction or Coupled-Cluster schemes in recent years density functional theory (DFT) still represents the method of choice for the study of complex many-electron systems (for an overview of DFT see [1]). Today DFT covers an enormous variety of fields, ranging from atomic [2,3], cluster [4,5] and surface physics [6,7] to the material sciences [8-10]. and theoretical biophysics [11-13]. Moreover, since the introduction of the generalized gradient approximation DFT has become an accepted method also for standard quantum chemical applications [14,15]. Given this tremendous success of nonrelativistic DFT the question for a relativistic extension (RDFT) arises quite naturally in view of the large number of problems in which relativistic effects play an important role (see e.g. Refs.[16,17]). 

E. Engel, S. Keller, R. M. Dreizler. Generalized gradient approximation for the relativistic exchange-only energy functional. Phys. Rev. A, 53(3) (1996) 1367-1374. 

These lectures present an introduction to density functionals for non-relativistic Coulomb systems. The reader is assumed to have a working knowledge of quantum mechanics at the level of one-particle wavefunctions (r) [1]. The many-electron wavefunction f (ri,r2,..., rjv) [2] is briefly introduced here, and then replaced as basic variable by the electron density n(r). Various terms of the total energy are defined as functionals of the electron density, and some formal properties of these functionals are discussed. The most widely-used density functionals - the local spin density and generalized gradient... 

As the hopes placed in the GEA did not materialize (in the non-relativistic case), one turned to the construction of generalized gradient approximations (GGA). These are based on the following philosophy (i) Use available exact results for atoms (x-only or on the basis of Cl calculations) and fit them to a functional of the form... 

Usually, self-consistent, all-electron calculations are performed within the relativistic local density approximation (LDA). The general gradient approximation (GGA), also in the relativistic form, RGGA, are then included perturbatively in E p,m). The accuracy depends on the adequate knowledge of the potential, whose exact form is, however, unknown. There is quite a number of these potentials and their choice is dependent on the system. Thus, PBE is usually favored by the physics community, PBEO, BLYP, B3LYP, B88/P86, etc., by the chemical community, while LDA is still used extensively for the solid state. 

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