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根据自由离子的多重态理论,多电子谱项的能级可以用Slater-Condon参数F~k,G~k来表示.对第一过渡系元素的d~N组态,则可进一步表示为Racah静电参量A,B,C的形式.这些参量一方面可由原子谱项能级的实验数据来拟合,另一方面则可由轨道径向波函数计算.在第一过渡系离子的中心场近似下,计算这些参量时常用到比较简便的Slater径向波函数(STO),但它不够准确;Watson由多个STO线性组合,再由Hartree-Fock方法得到的自洽径函(WTO),结果改进很多,但形式又过于复杂,不便使用;后来,Richardson等将这种自洽波函数进一步简化,特别是对3d轨道,简化为双Slater函数形式.随后,这种双ξ径向波函数得到众多研究和应用.
According to the multiple ion theory of free ions, the energy levels of multiple electron spectra can be expressed as Slater-Condon parameters F ~ k, G ~ k. The d ~ N configuration of the first transition element can be further expressed as Racah Electrostatic parameters A, B, C. These parameters can be fitted on the one hand by the experimental data of the energy levels of the atomic spectra and on the other hand by the radial wave function of the orbital.When the central field of the first transitional ion is approximated The simplest Slater Radial Wave Function (STO) is often used in the calculation of these parameters, but it is not accurate enough. The Watson is a self-consistent function derived from the linear combination of several STO and then the Hartree-Fock method. The result is improved Many, but the form is too complicated, inconvenient to use; Later, Richardson such a further simplification of this self-consistent wave function, especially for the 3d orbit, reduced to the form of double Slater function .Then, this double ξ radial wave function is many Research and application.