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Manuscript Title: High speed evaluation of F0(x). | ||

Authors: L.L. Shipman, R.E. Christoffersen | ||

Program title: DFZERO | ||

Catalogue identifier: ACAA_v1_0Distribution format: gz | ||

Journal reference: Comput. Phys. Commun. 2(1971)201 | ||

Programming language: Fortran. | ||

Computer: GE-635. | ||

Operating system: GECOS III. | ||

RAM: 1K words | ||

Word size: 36 | ||

Keywords: Quantum chemistry, 1s-type orbital, Molecular physics, Gaussian orbital, Integral evaluation, Electronic energy, Chebyshev series, Asymptotic expansion, Molecular integral. | ||

Classification: 16.10. | ||

Nature of problem:Much physical insight into the fundamental nature of molecules arises directly and indirectly from the calculation of the electronic energy. However, the ease of evaluating the various integrals that arise in the calculation of the electronic energy is strongly basis set dependent. The use of spherical Gaussian basis orbitals allows major simplifications to occur in the integral evaluations, for all of the integrals that are required can be evaluated analytically, and require only the auxiliary function, F0(x) = exp(-xu**2)du integrated from u=0 to 1 for values of x > and = 0. Consequently, efficient and accurate evaluation of F0(x) is essential, if practical procedures for energy evaluation are to be developed. | ||

Solution method:The argument range 0<=x is divided up into four intervals; 0<= x <6.125, 6.125 <= 14, 14<= x < 28, and 28 <= x. In the first three intervals an eight-term, rearranged Chebyshev series (power series) is used to approximate F 0(x). In the last interval an asymptotic approximation is used to evaluate F 0(x). | ||

Restrictions:The relative error is less than 4 X 10**-13. DFZERO would not be useful for calculations in which a greater degree of accuracy is desired. Also DFZERO evaluates F 0(x) for only positive or zero arguments. | ||

Unusual features:Speed in evaluation is coupled with a compact high speed store requirement. Rearranged Chebyshev series coefficients are introduced in DATA statements, so there is no overhead time required for their calculation before DFZERO can be called. |

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