Bond-breaking excitations with diverging coupling matrix of response density functional theory from highest-level functionals

Bond-breaking excitations ω_α are the problematic case of adiabatic time-dependent density functional theory (TDDFT). The calculated ω_α erroneously vanishes with the bond elongation, since the Hartree-exchange-correlation kernel and the corresponding response coupling matrix K of standard approximations lack the characteristic divergence in the dissociation limit. In this paper an approximation for K is proposed constructed from the highest-level functionals, in which both occupied and virtual Kohn-Sham orbitals participate with the weights w_p. The latter provide the correct divergence of K in the limit of dissociating two-electron bond. The present K brings a decisive contribution to the energy of the ¹Σ_u ⁺ in the prototype H₂ molecule calculated for various H-H separations. At shorter separations it improves ω_α compared to the zero-order TDDFT estimate, while at the largest separation it reproduces near-saturation of the reference excitation energy.