Expectations of the Kohn-Sham operator in a natural-orbital functional environment: An adiabatic response theory with single and double excitations

A combined adiabatic approach is proposed in which orbital expectations of the Kohn-Sham operator (KSEs) are embedded into the matrix environment of time-dependent phase-including natural-orbital functional theory (TDPINOFT). Analytical diagonalization of a model molecular matrix eigenvalue problem shows that the resultant TDNOFT-KSE combines strong sides of both adiabatic time-dependent density functional theory (TDDFT) and TDPINOFT. Around the equilibrium, like in TDDFT, the energy of a single excitation of the model is evaluated with the KSEs. In its turn, the TDPINOFT environment provides an effective Hartree-exchange-correlation (Hxc) kernel, which properly diverges in the bond dissociation limit. This environment also generates a double excitation, the energy of which is related to the ratio of fractional occupation numbers of the natural orbitals.