LMTO - Creating Electronic Canonical bands of BCC lattice

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Hello,

I need help with the Canonical band of BCC lattice (Linear Muffin Tin Orbitals method)

I am trying to generate the Canonical (electronic) band for d-d orbital for BCC lattice; this can be done by diagonalizing the Structure constant matrix S(l,m,l',m'), (with l,m, l',m' being the quantum numbers). However, I run into the problem of my matrices being already diagonal, and the eigenvalues (which are the energies) are all doubly and triply degenerate at all k points (along all high symmetry direction), which is not supposed to be.

The formula for S is stated in Andersen (Linear Methods in Band Theory, 1984) - which I used Table I to generate S, with directional cosines l,m, n for BCC lattice being (+_ 1/sqrt3, +-1/sqrt(3), +-1/sqrt(3)) - 8 combinations in all, representing 8 nearest neighbors of the BCC lattice . The 5-by-5 S matrix is generated by taking the sum of each S (over 8 nearest neighbors, transformed to k-space).

Could anyone familiar with LMTO method help me please?
Many thanks,
 

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