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All electron calculation

Relativistic effects can be included in both the scalar relativistic [18] and the fully relativistic treatment [5,19]. To specify these, there are three options for the keyword, eq.type, as follows:

   eq.type               sch            # sch|sdirac|dirac
where 'sch', 'sdirac', and 'dirac' mean the Schrödinger equation (no relativistic effect), a scalar relativistic treatment, and a fully relativistic treatment of Dirac equation, respectively. In the scalar relativistic treatment, the coupled Dirac equations are averaged with a weight of j-degeneracy, and solved by taking account of both the majority and minority components of radial wave function. Thus, the scalar relativistic treatment includes explicitly kinematic relativistic effects (Darwin and mass velocity terms), and implicitly averaged spin-orbit coupling (no energy splitting). On the other hand, in the fully relativistic treatment, j-dependent Dirac equations are solved including both the majority and minority components of radial wave function. Thus, energy splitting by spin-orbit coupling are also considered. In Table 1 shows eigenvalues of atomic platinum calculated by three different methods.


Table: Eigenvalues (Hartree) of atomic platinum calculated by the Schrödinger equation, a scalar relativistic treatment, and a fully relativistic treatment of Dirac equation within GGA to DFT
state sch sdirac dirac  
      j=l+1/2 j=l-1/2
1s -2612.2560 -2876.3416 -2868.8969  
2s -434.7956 -505.1706 -503.1143  
2p -418.0254 -438.1804 -419.1547 -482.3721
3s -101.2589 -118.6671 -118.0772  
3p -93.3171 -99.1367 -94.8406 -108.7310
3d -78.3951 -77.8404 -76.1768 -79.1659
4s -21.1326 -25.4989 -25.3346  
4p -17.7166 -19.0862 -18.0570 -21.3626
4d -11.4203 -11.2646 -10.9124 -11.5257
4f -3.0221 -2.5775 -2.4568 -2.5821
5s -2.9387 -3.7323 -3.6983  
5p -1.8756 -2.0571 -1.8911 -2.43384
5d -0.2656 -0.2259 -0.2020 -0.24966
6s -0.1507 -0.2074 -0.2079  


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Next: Enhancement or depletion of Up: Relativistic calculation Previous: Relativistic calculation   Contents
2011-09-28