•The shape of CT excitation curves is characteristic for a particular acceptor.•The energy of the CT orbital as a function of R provides this shape.•The height of the curve is determined with the IP of the donor.A simple nature of charge-transfer (CT) in the prototype complexes Dp-F2 (Dp=NH3, H2O) manifests itself in a very close shape of their CT excitation energy curves ωCT(R) along the donor-acceptor separation R. It affords a simple orbital description in terms of the CT orbitals (CTOs) obtained with a transformation of the virtual orbitals of the standard local density approximation (LDA). The transferable energy of the relevant CTO as a function of R closely approximates the common shape of ωCT(R), while the height of the individual curve is determined with the ionization potential of Dp.Download high-res image (69KB)Download full-size image

•The energy of double excitation is analytically related to the ratio of FONs.•In Heitler–London limit the formula reproduces the ionic excitation energy.•In Moeller-Plesset (MP) limit it turns to the reversed MP perturbation formula.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.Download high-res image (35KB)Download full-size image

•A transformation of the virtual KS orbitals is proposed to a set of charge-transfer orbitals (CTOs) adapted to description of CT excitations.•The CTO scheme offers a simple estimate of the CT excitation energy with an orbital energy difference.•This estimate reproduces well the reference values of the configuration interaction (CI) method in a wide range of donor-acceptor separations in the paradigmatic He-BeHe-Be complex.•CTO-based orbital energy and shape indices are proposed to assess the suitability of the CT description with virtual orbitals of a given basis set.•Both indices yield correct trends for the KS and HF orbitals.A transformation of the virtual Kohn-Sham orbitals is proposed to a set of charge-transfer orbitals (CTOs) adapted to description of CT excitations. The CTO scheme offers a simple estimate of the CT excitation energy with an orbital energy difference. This estimate reproduces well the reference values of the configuration interaction (CI) method in a wide range of donor-acceptor separations in the paradigmatic He-BeHe-Be complex. CTO-based orbital energy and shape indices are proposed to assess the suitability of the CT description with virtual orbitals of a given basis set. Both indices yield correct trends for the Kohn-Sham and Hartree-Fock orbitals.