3.1.7. horton.moments – Auxiliary routines related to multipole moments¶
This module fixes all the conventions with respect to multipole moments. Some of the code below may (in some way) reoccur in the low-level routines. In any case, such low-level code should be consistent with the conventions in this module. See for example, horton.gobasis.cext.cart_to_pur_low.
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horton.moments.get_cartesian_powers(lmax)¶ Return an ordered list of power for x, y and z up to angular moment lmax
Arguments:
- lmax
- The maximum angular momentum (0=s, 1=p, 2=d, …)
Returns: an array where each row corresponds to a multipole moment and each column corresponds to a power of x, y and z respectively. The rows are grouped per angular momentum, first s, them p, then d, and so on. Within one angular momentum the rows are sorted ‘alphabetically’, e.g. for l=2: xxx, xxy, xxz, xyy, xyz, xzz, yyy, yyz, yzz, zzz.
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horton.moments.get_ncart(l)¶ The number of cartesian powers for a given angular momentum, l
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horton.moments.get_ncart_cumul(lmax)¶ The number of cartesian powers up to a given angular momentum, lmax.
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horton.moments.rotate_cartesian_multipole(rmat, moments, mode)¶ Compute rotated Cartesian multipole moment/expansion.
Arguments:
- rmat
- A (3,3) rotation matrix.
- moments
- A multipole moment/coeffs. The angular momentum is derived from the length of this vector.
- mode
- A string containing either ‘moments’ or ‘coeffs’. In case if ‘moments’, a Cartesian multipole moment rotation is carried out. In case of ‘coeffs’, the coefficients of a Cartesian multipole basis are rotated.
Returns: rotated multipole.
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horton.moments.rotate_cartesian_moments_all(rmat, moments)¶ Rotate cartesian moments
Arguments:
- rmat
- A (3,3) rotation matrix.
- moments
- A row vector with a series of cartesian multipole moments, starting
from l=0 up to l=lmax. Items in this vector should follow the same
order as defined by the function
get_cartesian_powers.
Returns: A similar vector with rotated multipole moments
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horton.moments.get_npure(l)¶ The number of pure functions for a given angular momentum, l
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horton.moments.get_npure_cumul(lmax)¶ The number of pure functions up to a given angular momentum, lmax.