CRCU

Chemical Research in Chinese Universities ›› 1986, Vol. 2 ›› Issue (1): 76-84.

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OPTIMAL SCHEME FOR SEQUENTIAL COMPUTATIONS OF Fm(z) INTEGRALS IN AB INITIO CALCULATIONS----COMBINATORY USE OF UPWARD AND DOWNWARD RECURSIONS

Liao Muzhen1, Wu Guoshi1, Chen Kaixian2, Liu Honglin3, Chen Nianyi3   

  1. 1. Department of Chemistry and Chemical Engineering, Tsinghua University, Beijing;
    2. Shanghai Institute of Materia Medica, Academia Sinica, Shanghai;
    3. Shanghai Institute of Metallurgy, Academia Sinica, Shanghai
  • Received:1986-10-13 Online:1986-06-24 Published:2011-09-07

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Abstract: The quantitative rules of the transfer and variation of errors,when the Gaussian integral functions Fm(z) are evaluated sequentially by recurring,have been expounded.The traditional viewpoint to negate the applicability and reliability of upward recursive formula in principle is amended.An optimal scheme of upward-and downward-joint recursions has been developed for the sequential Fm(z) computations.No additional accuracy is needed with the fundamental term of recursion because the absolute error of Fm(z) always decreases with the recursive approach.The scheme can be employed in modifying any of existent subprograms for Fm(z) computations.In the case of p-d-f-and g-type Gaussians,combining this method with Schaad’s formulas can reduce,at least,the additive operations by a factor 40%;the multiplicative and exponential operations by a factor 60%.