Monday, September 13, 2021

Product of Two Gaussians

 


blue β


move blue Gaussian

-α
2
r
e
, SuperscriptBox[\(e\), \(\(-β\) | r - \*SubscriptBox[\(r\), \(0\)]\*SuperscriptBox[\(|\), \(2\)]\)]​
-α
2
r
e
× SuperscriptBox[\(e\), \(\(-β\) | r - \*SubscriptBox[\(r\), \(0\)]\*SuperscriptBox[\(|\), \(2\)]\)]​
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Most current molecular-structure computations make use of Gaussian basis functions (GAUSSIAN 03 software, for example). An essential feature is the fact that the product of two three-dimensional Gaussian functions equals another Gaussian around a shifted center. This greatly simplifies the computation of multicenter integrals. In this Demonstration, contour plots of the three Gaussian functions are shown. The 3D contour plots take some time to respond to the sliders.

Contributed by: S. M. Blinder (March 2011)
Open content licensed under CC BY-NC-SA

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Details

For more information:

S. M. Blinder, Introduction to Quantum Mechanics in Chemistry, Materials Science, and Biology, Burlington, MA: Elsevier Academic Press, 2004 pp. 187–188.

 

https://demonstrations.wolfram.com/ProductOfTwoGaussians/ 

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