where µ, ν are atomic orbitals indices, D is a matrix with (in general) three translation vectors as columns, l is a vector indexing the cells along each translation vector, with 0 the center cell, and e -iDl⋅p is the translation operator. In real space, the matrix in Eq. 9 is pure imaginary as for molecules. Due to the presence of the translation operator, the magnetic dipole matrix is not Hermitian, i.e. m 0l µν ≠ m 0-l νµ :