Fock matrix high-spin open-shell

We conclude that, for closed-shell and high-spin states, second-order optimizations can be carried out in the AO basis at a cost of n for each trial-vector transformation (10.8.8). For other open-shell CSF states, it is more difficult to simplify the construction of the Q matrix in order to carry out a second-order optimization in the AO basis. However, with the possible exception of the two-electron open-shell singlet state (10.1.7), Hartree-Fock wave functions for oth than high-spin states are of little interest except for systems of high spatial symmetry. In Exercise 10.7, an STO-3G Hartree-Fock wave function for HeH is calculated using Newton s method. 

For open shells, the identification of the Fock-matrix elements is more difficult. For high-spin states, it is straightforward to identify the elements that correspond to the nonredundant rotations since these rotations mix orbitals of different occupations. The identification of the elements that correspond to redundant rotations is less straightforward, hi some cases, such as for the two-electron singlet state, an unambiguous identification cannot be made since rotations between singly occupied orbitals are not redundant. 

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