For the pairwise expansion, I don't see the transformation over rotations via the wigner d matrix explicitly implemented within the code (eqn 7 in the preprint). Is this something that's implicitly being done? Eqn 7 is reproduced below:
$$\rho_{nlm} = \sum_{m'=-l}^l D^l_{mm'}(R) \int_{\mathbb{R}^3} d^3(\boldsymbol{r'})~g({R\left(\boldsymbol{r'} - \boldsymbol{r_{ij}}'\right)} R_{nl}{r'} Y_{lm'}({\hat{r}'})$$
For sanity we should add some tests to test_ellipsoidal_density_projection.py to ensure that rotational invariance is established, both for the pairwise coefficients and the three-body expansion.
For the pairwise expansion, I don't see the transformation over rotations via the wigner d matrix explicitly implemented within the code (eqn 7 in the preprint). Is this something that's implicitly being done? Eqn 7 is reproduced below:
For sanity we should add some tests to
test_ellipsoidal_density_projection.pyto ensure that rotational invariance is established, both for the pairwise coefficients and the three-body expansion.