从头计算中Fm(z)积分系列计算的最优方案——向上和向下结合的递推法

Optimal Scheme of Fm(z) Integral Sequence Calculations in ab initio Method --Combination of Upward with Downward Recurrence Method

本文阐明了量子化学从头计算中的Gauss积分函数Fm(z)用递推公式计算时误差传递和变化的定量规律.提出了向上和向下递推相结合进行Fm(z)系列计算的最优方案,它保证绝对误差在递推过程中只减不增,对递推基项无附加的精度要求,可用于改进各种Fm(z)程序.本法与Schaad公式相结合,用于P、d、f和g型Gauss函数的计算,可分别节约加法运算40%以上和乘法、指数运算60%以上.

In this paper the quantitative rules of error transfer and change of Gaussian integral function Fm(z) sequence calculation by recurrence formula in ab initio method are expounded. The optimal scheme of Fm(z) integral sequence calculations by conbination of upward with downward recurrence is proposed. This method assures that the absolute derivations only decrease without increasing in recurrence process, and hence the subsidiary precision prescrible is not need for the recurrence founda-tional term. As a result it can be applied to improvement of the exsitent serious Fm(z) computer programs. Combination of this method with Schaad’s formula being used to p,d,f type Gaussian function calculations, the additive operation and the multiplication and exponential operation decrease by above 40% and above 60% specifically.