Circulant orbitals for atoms and molecules

Circulant orbitals ϕ_n for a closed-shell system are the orbitals obtained when the N canonical orthonormal Hartree-Fock orbitals λ_unk] are subjected to a unitary transformation which is the discrete Fourier transformation: ϕ_n = 1/√N Σ_unk]λ_unk]ω^{(n-1)(unk]-1)}, where ω = exp(2πi/N). Electron densities associated with the orbitals ϕ_n are each close to the average total electron density. The Fock matrix, diagonal for canonical orbitals, for circulant orbitals is a Hermitian circulant matrix, ε_{m, m+q} = 1/N Σ_unk]ε_unk]ω^q(unk]-1), where the ε_unk] are the canonical orbital energies. The states ^Fϕ_n are uniformly distributed on the surface of a sphere in Hilbert space.