ions. The eigen vectors are where A$_{m}$$_{1(2)}$$_{±}$ are normalization constants, − → r lm = − → r l − − → r $_{m}$, and Note that ψ$_{pl}$ = ψ$_{px}$ for l = 3 , 4 and ψ$_{pl}$ = ψ$_{py}$ for l = 5 , 6. The eigen vectors of ε$_{p}$ do not concern us because they are non-bonding states. If there is no bond-bending, then there are only π -bonding for xy-orbitals. It turns out that the eigen vectors have very similar forms as those in eqs. (9). They are shown in Appendix. We now introduce the spin-orbit interaction in eq. (4). Its effect can be ex- pressed in the following relations 9 0.0.4 4. Spin-orbit interaction and polarization − → l · − → s | xy, ↑〉 = i | zx, ↓〉 + | yz, ↓〉 − i | x 2 − y $^{2}$, ↑〉 (12a) A$_{m}$$_{1}$$_{±}$ A$_{m}$$_{2}$$_{±}$ = ± ∑ n.n. cos δθ$_{nn}$e 2 i − → k · − → R$_{nn}$ ∣ n.n. cos δθ$_{nn}$e 2 i − → k · − → R$_{nn}$ ∣ . (11) ψ$_{1+}$$_{,}$ − → k , − → q ( − → r ) = ∑ j,m e i − → k · − → $^{R$_{j,m}$}$A$_{m}$$_{1+}$ [ ψ$_{d}$ ( − → r − − → R$_{j,m}$ )+ ∑ l V ( − 1) $^{l}$ei − → k · − → r lm E$_{1+}$ − ε$_{p}$ ψ$_{pl}$ ( − → r − − → R$_{j,l}$ ) ] ( cos θ$_{j,m}$ e $^{iφ}$sin θ$_{j,m}$ ) (10a) ψ$_{1}$$_{−}$$_{,}$ − → k , − → q ( − → r ) = ∑ j,m e i − → k · − → $^{R$_{j,m}$}$A$_{m}$$_{1}$$_{−}$ [ ψ$_{d}$ ( − → r ψ$_{pl}$ )+ ∑ l V ( − 1) $^{l}$ei − → k · − → r lm E$_{1}$$_{−}$ − ε$_{p}$ ψ$_{pl}$ ( − → r − − → R$_{j,l}$ ) ] ( cos θ$_{j,m}$ e $^{iφ}$sin θ$_{j,m}$ ) (10b) ψ$_{2+}$$_{,}$ − → k , − → q ( − → r ) = ∑ j,m e i − → k · − → $^{R$_{j,m}$}$A$_{m}$$_{2+}$ [ ψ$_{d}$ ( − → r − − → R$_{j,m}$ )+ ∑ l V ( − 1) $^{l}$ei − → k · − → r lm E$_{2+}$ − ε$_{p}$ ψ$_{pl}$ ( − → r − − → R$_{j,l}$ ) ] ( cos θ$_{j,m}$ e $^{iφ}$sin θ$_{j,m}$ ) (10c) ψ$_{2}$$_{−}$$_{,}$ − → k , − → q ( − → r ) = ∑ j,m e i − → k · − → $^{R$_{j,m}$}$A$_{m}$$_{2}$$_{−}$ [ ψ$_{d}$ ( − → r − − → R$_{j,m}$ )+ ∑ l V ( − 1) $^{l}$ei − → k · − → r lm E$_{2}$$_{−}$ − ε$_{p}$ ψ$_{pl}$ ( − → r − − → R$_{j,l}$ ) ] ( cos θ$_{j,m}$ e $^{iφ}$sin θ$_{j,m}$ ) (10d)