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The electronic structure of lanthanide and actinide compounds is oftencharacterized by orbital ordering of localized $f$-electrons.Density-functional theory (DFT) studies of such systems using the currentlyavailable LDA+$U$ method are plagued by significant orbital-dependentself-interaction, leading to erroneous orbital ground states. An alternativescheme that modifies the exchange, not Hartree, energy is proposed as a remedy.We show that our LDA+$U$ approach reproduces the expected degeneracy of $f^1$and $f^2$ states in free ions and the correct ground states in solid PrO$_2$.We expect our method to be useful in studying compounds of $f$- and heavy-$d$elements.

Obtaining correct orbital ground states in $f$ electron systems using a nonspherical self-interaction corrected LDA+$U$ method