Add test; Make sure moments behave correctly when origin is shifted. - Githubissues

theochem / grid

Python library for numerical integration, interpolation, and differentiation on (molecular) grids.

https://grid.qcdevs.org/

GNU Lesser General Public License v3.0

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Add test; Make sure moments behave correctly when origin is shifted. #159

Open PaulWAyers opened 1 year ago

PaulWAyers commented 1 year ago

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