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The full relativistic KS equations
is be transformed into an equation for the large component only
and averaged over spin-orbit components. In atomic units
(Rydberg:
= 1, m = 1/2, e2 = 2):
- +  + M(r) V(r) - ε Rnl(r) |
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-    + 〈κ〉 = 0, |
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(12) |
where
α = 1/137.036 is the fine-structure constant,
〈κ〉 = - 1 is the degeneracy-weighted average value
of the Dirac's κ for the two spin-orbit-split levels, M(r) is
defined as
M(r) = 1 -  V(r) - ε .
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(13) |
The charge density is defined as in the nonrelativistic case:
n(r) = Θnl .
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(14) |