Comment on calculations of excited states by the density functional theory

Valone and Capitani [Phys. Rev. A 23 (1981) 2127] proposed a method for calculating a single selected excited state by finding the ground state energy of the square of a shifted Hamiltonian. Here we prove that this approach can not enable one to calculate excited states on the basis of the Hohenberg and Kohn density functional theory. The justification for the use of the density functional theory for a single excited state on the basis of Katoʹs cusp theorem is briefly discussed.