Open-shell Pseudohamiltonians

Open-shell Pseudohamiltonians.—The majority of atoms do not have valence structures which can be represented by the fully closed-shell wavefunction of equation (14), and consequently ab initio pseudopotentials cannot be derived directly from the theory outlined above. Acceptable wavefunctions for such atoms require either more than one determinant or the use of the symmetry-equivalenced or generalized Hartree-Fock method, and usually include partially filled shells. The total all-electron wavefunction may be symbolically expressed in terms of four subspaces, 

McWeeny and B. T. Sutcliffe, Methods of Molecular Quantum Mechanics , Academic Press, New York, 1969. 

Saunders and M. F. Guest, ATMOL 3 User Note No. 9, Atlas Computing Division, Rutherford Laboratory. 

The general matrix representation for the hamiltonian in the AO basis is then35 

If the valence-electron wavefunction is also symbolically expressed, 

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