Angle

The Angle analysis measures the angle formed by three selected groups along a path or trajectory. It is useful for tracking bending, hinge opening, and local geometric rearrangements.

Adding the plot

1. Open Path Analyzer.
2. Choose Angle in Observable.
3. Choose a Path.
4. Define Group A, Vertex, and Group C.
5. Click Add Time Series or Add Histogram.

Inputs

• Three atom-containing selections are required.
• The middle selection defines the vertex of the angle.
• When the path provides time values, Path Analyzer uses time on the x-axis; otherwise it uses frame indices.

How groups are converted to positions

Path Analyzer converts each selected group to one representative position before computing the angle.

If a group contains one atom, its atomic position is used directly.

If a group contains several atoms, Path Analyzer uses the center of mass of that group.

Views

• Time series: follow the angle along the path.
• Histogram: inspect the distribution of visited angles.

Key equation

If \(\mathbf{p}_A(t)\), \(\mathbf{p}_V(t)\), and \(\mathbf{p}_C(t)\) denote the representative positions of the three selected groups at frame \(t\), Path Analyzer follows

\[ \theta(t)=\arccos\left( \frac{(\mathbf{p}_A-\mathbf{p}_V)\cdot(\mathbf{p}_C-\mathbf{p}_V)} {\|\mathbf{p}_A-\mathbf{p}_V\|\,\|\mathbf{p}_C-\mathbf{p}_V\|} \right) \]

For multi-atom groups, the representative position is the center of mass:

\[ \mathbf{p}_{\mathrm{group}}(t)= \frac{\sum_i m_i\,\mathbf{r}_i(t)}{\sum_i m_i} \]

Tip

• Use single atoms for highly local measurements.
• Use larger groups when you want a coarse-grained structural descriptor.
• If the angle is only one part of a larger motion, combine it later with another saved scalar analysis in Custom scatter or Energy landscape.