compute_orientorder

This keyword computes the local, rotationally invariant Steinhardt order parameters \(q_l\) and \(w_l\), as described in [Steinhardt1983] and [Mickel2013]. The results are written to the orientorder.out file.

For an atom \(i\), the parameter \(q_l(i)\) is defined as:

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

where the quantity \(q_{lm}(i)\) is obtained by summing the spherical harmonics over atom \(i\) and its neighbors \(j\):

\[q_{lm}(i)=\frac{1}{N_b}\sum_{j=1}^{N_b}Y_{lm}(\theta({\vec{r}_{ij}}), \phi({\vec{r}_{ij}})).\]

If wl is set to True, the quantity \(w_l\) is computed. This is a weighted average of the \(q_{lm}(i)\) values using Wigner 3-j symbols, yielding a rotationally invariant combination:

\[\begin{split}w_l(i) = \sum \limits_{m_1 + m_2 + m_3 = 0} \begin{pmatrix} l & l & l \\ m_1 & m_2 & m_3 \end{pmatrix} q_{lm_1}(i) q_{lm_2}(i) q_{lm_3}(i).\end{split}\]

If the wl_hat parameter is True, the \(w_l\) order parameter is normalized as:

\[\begin{split}w_l(i) = \frac{ \sum \limits_{m_1 + m_2 + m_3 = 0} \begin{pmatrix} l & l & l \\ m_1 & m_2 & m_3 \end{pmatrix} q_{lm_1}(i) q_{lm_2}(i) q_{lm_3}(i)} {\left(\sum \limits_{m=-l}^{l} |q_{lm}(i)|^2 \right)^{3/2}}.\end{split}\]

If average is True, the averaging procedure replaces \(q_{lm}(i)\) with \(\overline{q}_{lm}(i)\), which is the mean value of \(q_{lm}(k)\) over all neighbors \(k\) of particle \(i\), including atom \(i\) itself:

\[\overline{q}_{lm}(i) = \frac{1}{N_b} \sum \limits_{k=0}^{N_b} q_{lm}(k).\]

Syntax

compute_orientorder <interval> <mode_type> <mode_parameters> <ndegrees> <degree1> <degree2> ... <average> <wl> <wlhat>

  • interval: perform the calculation every interval steps.

  • mode_type: the neighbor selection mode. Currently supports cutoff or nnn (nearest neighbor number).

  • mode_parameters: - for cutoff mode, this is the cutoff distance; - for nnn mode, this is the number of neighbors. Note: if an atom has fewer neighbors than nnn within 6 Å, the result is set to 0.

  • ndegrees: number of spherical harmonic degrees (\(l\)) to compute.

  • degree1..degreeN: individual degree values.

  • average: whether to calculate the averaged Steinhardt order parameter. 1 = True, 0 = False. Defaults to False.

  • wl: whether to compute the \(w_l\) version of the Steinhardt order parameter. Defaults to False.

  • wlhat: whether to compute the normalized \(w_l\) version. Defaults to False.

Examples

  • compute_orientorder 100 cutoff 4.0 3 4 6 8 → Every 100 MD steps, compute three degrees (4, 6, and 8) using a 4 Å cutoff.

  • compute_orientorder 50 nnn 12 2 4 6 0 1 → Every 50 MD steps, compute two degrees (4 and 6) with 12 nearest neighbors. Additionally, compute the \(w_l\) version.

  • compute_orientorder 100 nnn 12 2 4 6 1 1 1 → Every 100 MD steps, compute two degrees (4 and 6) with 12 nearest neighbors. Use the averaged definition, and calculate both the original and the normalized \(w_l\) versions.