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and φ . We now made the following transformation 

where − → R$_{i,l}$ = − → R$_{i}$ + − → r l with − → r l being the position vector of the l -th oxygen atom in the basis without bond-bending. The Hamiltonian becomes 

where d$_{jm}$ = c$_{djm}$ , δθ$_{l}$ = a$_{0}$q$_{x}$/ 2, η$_{l}$ = 1 for l = 3 , 4 and δθ$_{l}$ = b$_{0}$q$_{y}$/ 2, η$_{l}$ = − 1 for l = 5 , 6. a$_{0}$ and b$_{0}$ are, respectively, the distance between transition metal ions along x and y direction. The Hamiltonian in momentum space is 

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