Bond-orientational order parameters

Frame.steinhardt(l) returns the local q_l and the Lechner-Dellago average for every atom. The neighbour list is the cutoff list. Degrees 3, 4, 6, 8, and 12 are computed. seams steinhardt uses the mutual four-nearest list, so its means on the mixed frame are not these means.

The runnable copy is docs/tutorials/test_order_parameters.py.

import pydseams as ds

frame = ds.read("input/traj/exampleTraj.lammpstrj", atom_type=2)
q3 = frame.steinhardt(3)

q3["ql"] and q3["ql_bar"] are the per-atom arrays. On this frame the finite means are about 0.374897 and 0.187542.

The local parameter is

\[q_l(i) = \sqrt{\frac{4\pi}{2l+1} \sum_{m=-l}^{l} |q_{lm}(i)|^2}\]

with

\[q_{lm}(i) = \frac{1}{N_b(i)} \sum_{j \in N(i)} Y_{lm}(\hat r_{ij}).\]