Abstract
We demonstrate a crucial role of fractional occupation numbers (FONs) of natural orbitals (NOs) in the description of double excitations in time-dependent NO functional theory (TDNOFT). An analytical dependence of the double excitation energy ωα on the ratio of the FONs is derived in a model from the matrix diagonalization problem. In the large ratio Heitler-London limit the derived formula reproduces the correct asymptotics of ωα of the ionic state of double excitation character. In the small ratio Møller-Plesset, MP limit the reverse relation of static MP perturbation theory emerges in the dynamical response theory to provide ωα.
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