Add test; Make sure moments behave correctly when origin is shifted.
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@Ali-Tehrani is already working on this.
Since May 4, 2023.
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Description
For moments, we can use as tests a function (e.g. a Gaussian) that is centered at the origin and also one centered off the origin. The change in solid-harmonic coefficients when you shift the origin of a moment expansion is analytically computable.
- There is code in Julia that shifts the origin of a solid harmonic expansion
There are also some analytic formulas available.
- see page 66
- Ruedenberg found a classical result, which is simplified in Eq. (8) of this reference
- There is also a result in this reference
- A tabulation of the coefficients for translation/rotation is available in the supplementary material of this reference
Originally posted by @PaulWAyers in https://github.com/theochem/grid/issues/13#issuecomment-1212190396
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