The Journal of Physical Chemistry Letters
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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.