Efficient random phase approximation for diradicals

We apply the analytically solvable model of two electrons in two orbitals to diradical molecules, characterized by two unpaired electrons. The effect of doubly occupied and empty orbitals is taken into account by means of random phase approximation (RPA). We show that in the static limit, the direct RPA leads to the renormalization of the parameters of the two-orbital model. We test our model by comparing its predictions for singlet-triplet splitting with the results of several multi-reference methods for a set of thirteen molecules. We find that for this set, the static RPA results are close to those of the NEVPT2 method with two orbitals and two electrons in the active space.