Local-scaling density-functional theory for excited states

The local-scaling density-functional method enables us to determine the ground-state electron density directly and variationally through the generation of a parent wave function of a given density. A generalization of the method to excited states is developed by the use of a configuration-interaction-type reference wave function. From a given density which approximates the nth-state density, all the mth-state wave functions (m≤n) are generated in such a manner that they satisfy the wave function and Hamiltonian orthogonalities. The nth-state electron density is determined so as to minimize the Hamiltonian expectation value over the generated nth-state wave function. An illustrative application is presented for the 2 1S state of the helium atom, and simple electron-density functions which compare well with the near-exact density are reported