The energy density functional described above can be modified to
take account of relativistic effects, such as the retardation
of the Coulomb interaction and
the magnetic interaction between moving electrons. We employ
the modification to the exchange
portion of the local energy density functional that
has been proposed by MacDonald and Vosko
[7].

In this scheme, the exchange energy is partitioned as

where **n** is the number density of electrons.
Here, **DF** refers to the ``Dirac-Fock'' model;
**T** is for ``transverse'' and represents the terms which
are first order in the fine structure constant .

Their corrections are multiplicative, i.e.,

and

where is the non-relativistic exchange energy density. The corrections are given by

and

where:

with being the Fermi velocity;

and

Only the sum,

enters into the final formula