In the equation of the crystal-field theory \(\Delta = \frac{{Q \cdot \langle r^{4} \rangle }}{{\overline{R}{^5} }}\), where Δ is the crystal-field splitting, \(\overline{R}\) is the mean metal–ligand distance in the 3d^N-ion-centered coordination polyhedron and Q is constant, \(\langle r^{4} \rangle\), the mean value of the fourth power of the 3d-electron radius, is assumed to be also constant (Burns 1993). Here, this assumption is proved by means of high-pressure optical absorption spectroscopy on octahedral Fe²⁺ in siderite FeCO₃ in combination with the data of X-ray diffraction structural refinement by Lavina et al. (2010). It is shown that in the pressure range 1·10^–4 to 44.5 GPa or \(\overline{R}\) ranging from 2.15 to 1.97 Å, the value of Q \(\cdot \langle r^{4} \rangle\) does not deviate more than ~ 4% from its average value.

在晶体场理论的方程\（\ Delta = \ frac {{Q \ cdot \ langle r ^ {4} \ rangle}} {{\ overline {R} {^ 5}}} \\）中，其中Δ是晶体场分裂，\（\ overline {R} \）是3d以^N离子为中心的多面体中平均金属-配体距离，Q是常数，\（\ langle r ^ {4} \ rangle \ ），即3 d电子半径的四次方的平均值也假定为常数（Burns 1993）。在此，该假设通过高压光学吸收光谱法对菱铁矿FeCO _3中的八面体Fe ²⁺进行了证明。结合Lavina等人的X射线衍射结构精修数据。（2010）。结果表明，在压力范围1·10 ^–4至44.5 GPa或\（\ overline {R} \）在2.15至1.97Å范围内，Q \（\ cdot \ langle r ^ {4} \ rangle \）与平均值的偏差不超过〜4％。