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在本篇文章中,我們建議了一種新方法來計算量子力學中的三中心和四中心積分;這方法此以往的好,因為計算簡單,應用廣闊,結果也比較可靠。我們用來計算三中心吸引能的公式[方程(5)]是在任何情况下都是正確的,而用來計算三中心和四中心的排斥能積分公式[方程(18)]在某些情况下是正確的,在另一些情况却能引進一些誤差。在計算非相隣鍵的積分時引進的誤差很小,可以忽略不計;在計算相隣鍵的積分時引進的誤差此較大,但不超過百分之十。我們建議兩種計算A_u和B_u的方法,一種方法是以鍵的一個端點爲原點,嚴格按照球內外的區域積分;另一種方法是以鍵的中點為原點,按照橢圓體的內外區域積分。前一種方法理論上嚴密,然而後一種方法計算簡單,收斂性快,引進的誤差也不大;尤其在計算相隣鍵的三中心排斥能的積分時,似乎後一方法得到的結果還比前一方法好。在本文中,為了容易說明起見,常常引用吸引能和排斥能這兩個名詞,實際我們的方法,是用來計算下列三類積分:它們不僅包括吸引能和排斥能積分,也把交换積分包括在內,甚至可以在更廣泛的意義上看待上列積分。若σ_1,σ_2也是Φ_1和Φ_2的函數時,仍可以用我們的一般展開理論處理,不過要此本文複雜。
In this article, we propose a new method to calculate the triple center and quadruple center points in quantum mechanics. This method is better than ever because of the simple calculation, the broad application and the reliable results. The formula we used to calculate the triplet attraction energy [Equation (5)] is correct in all cases and the formula for calculating the repulsive energy integrals of the three centers and the four centers [Equation (18)] is in some cases The next is correct, but in others it introduces some error. The error introduced when calculating the integrals of non-adjacent keys is small and negligible; the error introduced when calculating the integrals of adjacent keys is large, but not more than 10%. We suggest two methods to calculate A_u and B_u. One method is to use one endpoint of the key as the origin and strictly follow the integral inside and outside the sphere. The other method is to use the middle point of the key as the origin, Area points. The former method is theoretically rigorous. However, the latter method has the advantages of simple calculation, fast convergence and little error introduced. Especially when calculating the integral of the three-center repulsion energy of adjacent bonds, it seems that the latter method is still better than the former method A good method. In this paper, we often refer to the two terms “attraction energy” and “repulsion energy” for ease of explanation. In fact, our method is to calculate the following three types of points: they include not only the energy of attraction and repulsion, but also the exchange of points Included, even in the broader sense of the above points. If σ_1, σ_2 are also functions of Φ_1 and Φ_2, we can still use our general expansion theory, but this article is complicated.