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Next: 6 Numerical Tests Up: On Convergence Acceleration of Previous: 4 Extrapolation Methods for

5 A Simple Example

  We study as a simple example a charge density

  equation925

corresponding to a two-center product of 1s-ETOs. For the electrostatic potential of this density, we have

equation928

with tex2html_wrap_inline2794 and tex2html_wrap_inline2796 . Here, the addition theorem [117], [78]

equation980

of the exponential function was used that holds for tex2html_wrap_inline2798 . Further, the addition theorem (8) of the spherical harmonics was used. Now, the orthonormality of the spherical harmonics yields

  equation993

The remaining radial integral can be computed with the help of Maple. This approach avoids rounding errors that can easily spoil the calculation of the integral [78]. We note that the result is of the form (17), with

equation1021

Analogously, one obtains for the multipole expansion of this charge density an equation of the form (9),

  equation1041

and for the multipole moments follows

equation1065

which can also be computed advantageously with Maple.


next up previous external
Next: 6 Numerical Tests Up: On Convergence Acceleration of Previous: 4 Extrapolation Methods for

Herbert H. H. Homeier (herbert.homeier@na-net.ornl.gov)