Relativistic generalized gradient approximation

The RGGA reaches the same level of accuracy in the relativistic regime as the nonrelativistic GGA does for light atoms. An improvement is also observed for Vx (see Fig.2) and thus the single particle-energies. In the case of magnetic systems the RGGA (148) can be combined with the relation (141). 

The correlation functional requires a slightly different scheme, as, on the one hand, the RLDA is not known completely, and, on the other hand, some GGAs for Ec [173] are not based on the LDA. Therefore only one overall correction factor for the complete GGA has been used, 

In contrast to the RLDA, the RGGA allows an examination of the importance of the relativistic ingredients of [ ] for the properties of molecules and solids. This question has been investigated both for noble metal compounds [195,196] and for metallic Gold and Platinum [39] within the framework of LAPW calculations [99]. Prototype results for Cu2 and Au2 are given in Table 9. It turns out that even for Au, which usually exhibits the effects of relativity most clearly 

On the other hand, a comparison of the (R)GGA results in Tables 9 and 10 with experiment reveals the limitations of the semi-local GGA concept for 

Lattice constant and cohesive energy coh of Au and Pt obtained from LAPW calculations with relativistic and nonrelativistic LDA and PW91-GGA [39] in comparison to experiment [198,199]. 

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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. 

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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