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High Quality Content by WIKIPEDIA articles! Restricted open-shell Hartree-Fock (ROHF) is a variant of Hartree-Fock theory for open shell molecules. It uses doubly occupied molecular orbitals as far as possible and then singly occupied orbitals for the unpaired electrons. This is the simple picture for open shell molecules but it is difficult to implement. Where F is the so-called Fock matrix, C is a matrix of coefficients, S is the overlap matrix of the basis functions, and is the (diagonal, by convention) matrix of orbital energies. Unlike restricted Hartree-Fock theory for closed shell molecules, the form of the Fock matrix is not unique. Different so-called canonicalisations can be used leading to different orbitals and different orbital energies, but the same total wavefunction, total energy, and other observables. Developing post-Hartree-Fock methods based on a ROHF wave function is inherently more difficult than using a UHF wave function, due to the lack of a unique set of molecular orbitals.

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