Noninteracting v -Representable Subspaces of Orbitals in the Kohn-Sham Method.

The notion of noninteracting v -representability is extended from electron densities to finite-dimensional linear subspaces of orbitals. Unlike electron densities, orbital subspaces can be tested for noninteracting v -representability using a transparent necessary condition: the subspace must be invariant under the action of some one-electron Kohn-Sham Hamiltonian. This condition allows one to determine in principle, and sometimes in practice, whether a given one-electron basis set can represent an N -electron density within the Kohn-Sham method and to find the corresponding Kohn-Sham effective potential v if it exists. If the occupied Kohn-Sham orbitals form linearly independent products, then their subspace is determined by the corresponding ground-state electron density. This means that the Kohn-Sham effective potential corresponding to certain finite-basis-set electron densities can be deduced from the basis set itself.