Multiplets ensemble exchange potential

In a previous paper [16] the ensemble exchange potentials are studied for the following multiplets D, S for the atoms O and S and and... 

It was emphasized in the theory of Gross, Oliveira and Kohn [7] that the ensemble exchange potential depends on w. In a previous paper [16] it was shown that the ensemble exchange factor for multiplets is different for different values of w. 

The fact that the exact exchange potential has similar behaviour for the ensemble of multiplets suggests that approximations might also be similar. Probably, a small change in the ground-state exchange functionals might lead... 

The method of fractionally occupied states can be used to treat the multiplet problem, too. However, the exchange energy and potential are not known even for the ground state. They are unknown for the ensemble of excited states, too. 

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