Degeneracy matrix rank

Electron-electron interaction is significant in studies where spin-orbital degeneracy, or near degeneracy, is present. The atomic d-orbitals have a common radial factor and their 15 distinct products give rise to 120 density-density integrals. These are expressed in terms of three basic ones, F0, F2, and F4 in the Slater-Condon formulation. The 100 spin-orbital densities are linear combination of the orbital ones and the 100 by 100 interaction integral matrix has a rank of 15 and is expressed by the Slater-Condon parameters. 

The quantity v may be greater than v because of homogeneous catalysis by an element which does not appear in equation (T) or because the additional species in (T ) remove a degeneracy which had reduced the rank of the matrix of coefficients for equation (T). The multiplicity, 0, of the exact stoichiometric change is given by... 

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