l  The spin−orbit coupling, which will mix the ²E_g and ⁴T_2g states, relaxed the spin selection rule. Besides, since a strong electric dipole transition occurs between the states with opposite parity, the ²E_g → ⁴A_2g transition can gain electric dipole intensity if the Mn⁴⁺ ion is located in a non-centrosymmetric site (absence of inversion symmetry). In this case, the static crystal field can contain odd parity components which can mix high energy states of odd parity. This relaxes the parity selection rule.

参考文献：M.G. Brik, W.W. Beers, W. Cohen, S.A. Payne, N.J. Cherepy, M. Piasecki, A.M. Srivastava. On the Mn⁴⁺ R-line emission intensity and its tunability in solids. Opt. Mater. 91 (2019) 338–343.

l  实验中观察到 d-d 跃迁，是由于电子运动和分子振动间相互作用即振动的波函数和电子的波函数混杂引起的。定性地看，电子跃迁发生在配合物的振动瞬间，这些振动破坏了分子的对称性；当这种振动发生时，状态失去“g”特性，使电子跃迁变成了少量的宇称允许。

l  自旋禁阻跃迁如ΔS=±1所观察到的强度很弱，约为允许跃迁的百分之一。自旋-轨道耦合作用使得可观察到自旋禁阻的²E_g→⁴A_2g跃迁。自旋-轨道耦合作用使得²G和4F谱项内具有相同总角动量J的能态间彼此混合，这种少量的混杂使得ΔS=0选律不再完全适用。

参考文献：姬海鹏.Mn4+离子光谱学基础. 发光学报, 2022, 43: 1175-1187.