Circulant orbitals for atoms and molecules

1 March 1981

journal article
Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences

Vol. 78 (3) , 1323-1326
https://doi.org/10.1073/pnas.78.3.1323

Abstract

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 ^F ϕ _n are uniformly distributed on the surface of a sphere in Hilbert space.

Keywords

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