The Primitive Ligand Field Parameterization

The application of the group-product function equations to the ligand-field problem is now straightforward and leads to the primitive parameterization in which we omit contributions from the additional term AH(e) these will be discussed in Sect. 5 below. As already implied in Sect. 3 we choose the optimal number of electrons to put in the M set from chemical arguments since the formal oxidation state of the complex can usually be equated with the best (integral) choice for (the d configuration), and so we can make the partition n = Nj + Nt with 1 9. The functions Pm are then obtained as 

The optimized functions 0 are not therefore eigenfunctions of the full n-electron Hamiltonian, Eq. (2-2), but they are orthogonal and do cause all single excitation matrix elements to vanish, i.e. 

Equation (4-2) is the analogue of Brillouin s theorem for the SCF one-electron molecular orbitals  

We shall now imagine that the optimized function Vlo for the L group of electrons has been obtained, and look in more detail at the variational calculation specified by Eqs. (3-6 a 3-10) when the functions Wmot are expanded in terms of Slater determinants constructed from the M subset of the orthonormal spin-orbital basis f, the ten spin-orbitals of d-orbital character. 

Since there are electrons, there are at most terms in the expansion (4-4). The L group electrons now only enter (3-7 a) through the matrix elements of the density operator derived from their ground state wave function Vlo, pKo - i 2)— 2) for short. The stationary value condition applied to Eq. (3-6 a) can be transformed in the usual way into a matrix eigenvalue equation for the eigenvalues Ewm and the expansion coefficients C in Eq. (4-4) 

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