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|diracwhere '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.

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 |