The multistate matrix density D(r) can be sufficiently represented by N 2 nonorthogonal (necessary) determinants. In a departure from Kohn-Sham DFT for the ground state, we introduce in MSDFT an "active space" of N interacting states {Φ A ; A = 1, ..., N}, each of which is written as a linear combination of N nonorthogonal determinants, Φ A = ∑ N p a pA ψ pA , to completely represent D(r) of the real (fully interacting) system. Its matrix elements are computed from one-electron orbitals {χ is the overlap between two Slater determinants of the corresponding (n e -1) orbitals. Unlike the diagonal state densities, the transition density D AB (r) with A = B can be positive, negative or complex.