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a planar crystal on the xy-plane. For bonds along x(y)-direction, p$_{y}$$_{(}$$_{x}$$_{)}$-orbital of the oxygen atoms and the xy-orbital of the transition element ions form π - bond. The p$_{z}$-orbitals are ignored because they do not give rise to polarization in z-direction.orbitals are considered. Thus, we have the Hamiltonian: 

<img src='content_image/313325.jpg'>

where V ′ = V ( pdπ ) and l = 1 , 2 for the oxygen atoms on x-axis and y-axis respectively. Making a transformation similar to that in eqs (5), we obtain the Hamiltonian in momentum space: 

<img src='content_image/313324.jpg'>

Now δθ$_{l}$$_{=3}$$_{,}$$_{4}$ = q$_{x}$a$_{0}$/ 2 and δθ$_{l}$$_{=5}$$_{,}$$_{6}$ = q$_{y}$b$_{0}$ . We can solve for eigen values 

<img src='content_image/313323.jpg'>

<img src='content_image/313321.jpg'>

where ε$_{p}$ is two-fold degenerate. The eigen vectors are 

<img src='content_image/313322.jpg'>

<img src='content_image/313320.jpg'>

