The following is its matrix form: Here the order of matrix elements is m = 1 , 2, and then l = 3 ↑ , 3 ↓ , 4 ↑ , 4 ↓ etc.., V$_{±}$$_{x}$ = V e ± ik$_{x}$a 0 , V$_{±}$$_{y}$ = V e ± ik$_{y}$b 0 and s$_{i}$ = sin δθ$_{i}$ , c$_{i}$ = cos δθ$_{i}$ . It can be diagonalized and the eigen values are where ε$_{p}$ is six-fold degenerate and − → R$_{nn}$ and δθ$_{nn}$ = 2 δθ$_{l}$ are the position vector and spin angle difference between two nearest neighboring transition element 8 E$_{1}$$_{±}$ = ε$_{d}$ + ε$_{p}$ 2 + √ ( ε$_{d}$ − ε$_{p}$ 2 ) 2 + 4 V 2 ± V 2 ∣ ∑ n.n. cos δθ$_{nn}$e 2 i − → k · − → R$_{nn}$ ∣ (9a) E$_{2}$$_{±}$ = ε$_{d}$ + ε$_{p}$ 2 − √ ( ε$_{d}$ − ε$_{p}$ 2 ) 2 + 4 V 2 ± V 2 ∣ ∑ n.n. cos δθ$_{nn}$e 2 i − → k · − → R$_{nn}$ ∣ (9b) E$_{3}$ = ε$_{p}$ (9c)       ε$_{d}$ 0 V$_{+}$$_{x}$c$_{3}$ − V$_{+}$$_{x}$e $^{iφ}$s$_{3}$ − V$_{−}$$_{x}$c$_{4}$ − V$_{−}$$_{x}$e $^{iφ}$s$_{4}$ V$_{−}$$_{y}$c$_{5}$ V$_{−}$$_{y}$e $^{iφ}$s$_{5}$ − V$_{+}$$_{y}$c$_{6}$ 0 ε$_{d}$ V$_{−}$$_{x}$c$_{3}$ V$_{−}$$_{x}$e + $^{iφ}$s$_{3}$ − V$_{+}$$_{x}$c$_{4}$ V$_{+}$$_{x}$e $^{iφ}$s$_{4}$ V$_{+}$$_{y}$c$_{5}$ − V$_{+}$$_{y}$e $^{iφ}$s$_{5}$ − V$_{−}$$_{y}$c$_{6}$ − V$_{−}$$_{x}$c$_{3}$ V$_{+}$$_{x}$c$_{3}$ ε$_{p}$ 0 0 0 0 0 0 − V$_{−}$$_{x}$e − $^{iφ}$s$_{3}$ V$_{+}$$_{x}$e − $^{iφ}$s$_{3}$ 0 ε$_{p}$ 0 0 0 0 0 − V$_{+}$$_{x}$c$_{4}$ − V$_{−}$$_{x}$c$_{4}$ 0 0 ε$_{p}$ 0 0 0 0 − V$_{+}$$_{x}$e − $^{iφ}$s$_{4}$ V$_{−}$$_{x}$e − $^{iφ}$s$_{4}$ 0 0 0 ε$_{p}$ 0 0 0 V$_{+}$$_{y}$c$_{5}$ V$_{−}$$_{y}$c$_{5}$ 0 0 0 0 ε$_{p}$ 0 0 V$_{+}$$_{y}$e − $^{iφ}$s$_{5}$ − V$_{−}$$_{y}$e − $^{iφ}$s$_{5}$ 0 0 0 0 0 ε$_{p}$ 0 − V$_{−}$$_{y}$c$_{6}$ − V$_{+}$$_{y}$c$_{6}$ 0 0 0 0 0 0 ε$_{p}$ V$_{−}$$_{y}$e − $^{iφ}$s$_{6}$ − V$_{+}$$_{y}$e − $^{iφ}$s$_{6}$ 0 0 0 0 0 0 0 (8)