  We apply the optimized effective potential method (OPM) to the multiplet
energies of the 3d$^n$ transition metal atoms, where the orbital dependence of
the energy functional with respect to orbital wave function is the
single-configuration HF form. We find that the calculated OPM exchange
potential can be represented by the following two forms. Firstly, the
difference between OPM exchange potentials of the multiplet states can be
approximated by the linear combination of the potentials derived from the
Slater integrals $F^2({\rm 3d,3d})$ and $F^4({\rm 3d,3d})$ for the average
energy of the configuration. Secondly, the OPM exchange potential can be
expressed as the linear combination of the OPM exchange potentials of the
single determinants.
