原子的解析波函数——Ⅱ.第二周期元素的正常态原子与离子的解析波函数与能量积分的计算

我们在文献1]中设计了一套五个参数的变分波函数用来计算了周期表中前面十个原子的能量,所得结果比过去一些作者用四参数波函数所算得的结果为好。我们在过去计算经验的基础上,另外找到了一套特别简单的解析波函数,其形式为1s电子:ψ₁(r)=N₁e^-μar,2s电子:ψ₂(r)=N₂(μr)e^-μr-Ne^-μar],2p电子:ψ₃(r)=N₃(μr)cosθe^-μr,ψ₄(r)=N₄(μr)sinθe^iφ-μr,ψ₅(r)=N₅(μr)sinθe^-iφ-μr,式中的α与μ为变分参数;N₁,N₂,N₃,N₄,N₅为归一化因子;N为正交化系数。μ可用解析法来决定,因而只有一个参数α要由数值法来决定。我们用这样的波函数算出了第二周期元素的正常态原子和离子(共有八十几个原子态)的各电子的各种能量积分值及总能量值,并确定了波函数的最佳参数值。其结果与五参数波函数的计算结果相比,一般相差在万分之一至千分之一的范围内,并比最近有些作者用一种三参数波函数所算的结果还好。根据这些结果,我们还讨论了Slater近似计算法的可靠程度和适用范围。

THE ANALYTIC WAVE FUNCTIONS FOR ATOMS——II. THE ANALYTIC WAVE FUNCTIONS AND ENERGIES FOR THE ATOMS AND IONS OF ELEMENTS OF THE SECOND PERIOD

The energies of the atoms and ions of the elements of the second period in the periodic table are calculated with a set of simple variational wave functions. The form of the wave functions used is as follows: 1s:ψ₁(r)=N₁e^-μar, 2s:ψ₂(r)=N₂(μr)e^-μr-Ne^-μar], 2p:ψ₃(r)=N₃(μr)cosθe^-μr,ψ₄(r)=N₄(μr)sinθe^iφ-μr,ψ₅(r)=N₅(μr)sinθe^-iφ-μr.There are only two parameters in all. The parameter ft is a scale factor, the best value of which can be determined analytically, leaving but only one parameter a to be determined numerically. N₁, N₂, N₃, N₄, and N₅ are normalization factors. The constant N is fixed so that ψ₂ is orthogonal to ψ₁. The results of this calculation are better than those calculated by Кириллова, Веселов и Братцев with their wave functions containing three parameters and are very close to those calculated in a previous paper by us with wave functions containing five parameters.