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Calculate a few terms in the multipole expansion
aka multipole series
including monopole, dipole, quadrupole, octupole, and hexadecapole.
We use spherical harmonics (Ylm) to account for the angular dependence.
Then we account for the radial dependence.
We apply this to a few configurations with more-or-less
the same symmetry as certain simple molecules:
SO4 CO CO2 XeF4 BCl3 PF5 CF4 SF6
The output format is:
For each molecule there is a headline giving the name of
the molecule, followed by a stanza of results.
In each stanza there are (1+Lmax) lines, one for each L value.
On each line, there are 2L+1 entries, one for each M value.
Each entry is a complex number.
In the margin of each line there is a label giving the
multipole order, i.e. 2^L
with an asterisk if it is the /leading/ order,
i.e. if that line contains the lowest-order non-zero term.
For the examples considered here, all the entries have
zero imaginary part, but this is not true in general.
Example: Try re-orienting the CO dipole along the Y axis.
The inputs model the general shape of the molecule but /not/
its size, so the results are not normalized. This could be
fixed easily.