All electron calculation

Relativistic effects can be included in both the scalar relativistic [14] and the full relativistic treatment [3,15]. 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 full 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 full 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, where electron of 6s state is partially promoted to 6p state.

Table: Eigenvalues (Hartree) of atomic platinum calculated by the Schrödinger equation, a scalar relativistic treatment, and a full relativistic treatment of Dirac equation within GGA to DFT

state	sch	sdirac	dirac
			j=l+1/2	j=l-1/2
1s	-2590.5589	-2830.0886	-2823.3059
2s	-428.9975	-495.0056	-493.0913
2p	-411.3962	-430.9421	-412.3151	-473.9681
3s	-101.5684	-118.0265	-117.5050
3p	-93.5941	-99.3621	-95.2182	-108.6139
3d	-78.0400	-77.5940	-76.0344	-78.8582
4s	-20.8655	-24.9230	-24.7628
4p	-17.5020	-18.8048	-17.7975	-21.0224
4d	-11.2052	-11.0328	-10.6848	-11.2849
4f	-3.1801	-2.7527	-2.6278	-2.7627
5s	-2.9300	-3.6769	-3.6427
5p	-1.8835	-2.0614	-1.8949	-2.43625
5d	-0.2763	-0.2383	-0.2140	-0.26223
6s	-0.1648	-0.2173	-0.2177