Trajectory analysis

Interactive measurements are evaluated in the viewer. Pair-distribution and coordination calculations use PQAnalysis on the server.

Measurements over frames

Select two, three, or four atoms in order, then choose Plot for a distance, angle, or dihedral. The curve loads incrementally; its cursor follows the displayed frame, and selecting a point changes frames.

Periodic measurements use minimum-image geometry by default. A curve keeps the mode chosen when it was created. Choose Pin to retain a measurement and compare compatible pinned curves: distances together, or angular measurements together.

Complete curves export as CSV, SVG, or vector PDF. Frame index is not physical time unless the source supplies time and its unit.

Reference frames and trails

Action	Result
Timeline menu or M	Bookmark the current source/frame identity
Set as reference, then Show displacement	Compare selected atoms with a saved frame
Track	Show selected atom paths over the previous 50 frames and current position

Tracking uses unwrapped motion when available and allows sixteen selected atom images. A reference whose saved source identity no longer matches is cleared. See vacuum and unwrapping limits.

Scalar properties

Numeric frame properties from trajectory metadata or energy/info companions appear under Plot in the timeline menu. Their cursor follows playback; selecting a point navigates to its frame. Units come from the source.

Pair distribution and coordination

Use a file-backed structure or trajectory with all three axes periodic and a finite cell volume. A single frame is sufficient. Every sampled frame must meet the periodic-cell requirement.

Open Pair distribution or Coordination from the timeline menu, selection bar, or command search.

Setting	Meaning
From	Reference atoms, population A
To	Target atoms counted around A, population B
Frames	All, last 100, or last 1,000 when available
Bins	Number of equal-width radial shells
r max · Å	Upper radius in Å; blank uses the backend default

All applies a uniform stride when there are more than 10,000 frames. For another interval or stride, open a slice first:

pqviewer 'trajectory.xyz@100:1000:10'

Results average the sampled frames and are independent of the current playback cursor. They export as CSV, SVG, and vector PDF.

Quantities and normalization

Let F be the sampled frame count, N_A and N_B the population sizes, and H_k the total ordered A-to-B pair count in radial shell k across those frames. Self-pairs are excluded; intramolecular pairs are included.

For shell edges r_k and r_(k+1), PQAnalysis uses:

\[\Delta V_k = \frac{4\pi}{3}\left(r_{k+1}^3-r_k^3\right),\qquad \rho_B = \frac{N_B}{\langle V\rangle},\]

\[g_k = \frac{H_k}{F N_A\rho_B\Delta V_k},\qquad N(r_{k+1}) = \frac{\sum_{j=0}^{k} H_j}{F N_A}.\]

Curve	Radius	Unit
g(r)	Shell centre	Dimensionless
Coordination N(r)	Shell’s outer edge	Neighbors per reference atom

<V> is the arithmetic mean of sampled cell volumes. For changing volumes, this normalizes the accumulated histogram using one mean density; it is not an average of separately normalized per-frame curves.

The target density uses N_B even when A and B overlap. For identical populations in a fixed-volume ideal gas, the finite-population baseline is (N_B - 1) / N_B because self-pairs are excluded. No uncertainty estimate is supplied; correlated frames do not provide independent samples.

Radius and work limits

The backend chooses at most half the shortest supplied lattice-vector length across the sampled cells and clamps larger requested radii to that value. This rule alone does not ensure complete spherical shells in a strongly skewed cell; choose a radius within half of every perpendicular cell-face separation. PQAnalysis images pair displacements by centering fractional components, so this radius restriction matters even when interactive measurements find the shortest Cartesian image.

Bound	Maximum
Atoms in each population	4,096
Sampled frames	10,000
Bins in the interface	2,000, with a minimum of 20
Frame/reference/target pair evaluations	50 million
Reconstructed atom-frames for sliced, ASE, or other non-native sources	5 million

Use a shorter frame preset or smaller populations when a work limit is reached. Three-dimensional shell normalization is unavailable for vacuum, slab, or wire boundary conditions.