LMTO - Creating Electronic Canonical bands of BCC lattice

[espoir]

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,

 

[eljose79]

Hello,

I am familiar with the LMTO method and would be happy to assist you with generating the Canonical band for d-d orbital for BCC lattice. It sounds like you have correctly followed the formula for generating the Structure constant matrix S and have accounted for the directional cosines for the BCC lattice. However, it is possible that there may be errors in your calculations or in the data used to generate the matrix.

One suggestion I have is to double check your calculations and make sure that all the values used to generate the S matrix are correct. It is also possible that there may be an error in the data you used to generate the matrix, so it may be helpful to cross-reference with other sources or to consult with other scientists who have used the LMTO method for BCC lattice.

Another suggestion is to try using a different set of directional cosines for the BCC lattice. While the ones you have used are commonly used, there may be slight variations depending on the specific data and calculations being used. Experimenting with different directional cosines may help to identify any potential errors in your calculations.

I hope this helps and if you have any further questions, please don't hesitate to reach out. Good luck with your research!