Geometry and molecular topology

Measure distances, angles and dihedrals using the coordinates in your file. Use geometry-based bonds and fragments to check connectivity; they are not quantum-chemical bond orders.

Distance

For Cartesian positions \(\mathbf r_i\) and \(\mathbf r_j\),

\[ d_{ij}=\lVert\mathbf r_i-\mathbf r_j\rVert_2. \]

openWFN presents molecular distances in ångströms.

Bond angle

For angle \(i\)–\(j\)–\(k\), construct \(\mathbf u=\mathbf r_i-\mathbf r_j\) and \(\mathbf v=\mathbf r_k-\mathbf r_j\):

\[ \theta=\cos^{-1}\!\left(\frac{\mathbf u\cdot\mathbf v}{\lVert\mathbf u\rVert\lVert\mathbf v\rVert}\right). \]

Degenerate vectors do not define an angle and should be treated as invalid geometry.

Dihedral

The dihedral is a signed angle between two planes, calculated with atan2. Its sign depends on atom order. Keep all four atom numbers with the result.

Bonds and fragments

Bond detection is a geometric heuristic based on covalent radii and separation, not a quantum bond-order calculation. The resulting adjacency graph defines connected components reported as fragments. It is useful for structure checking, but unusual coordination, metals, weak interactions, and periodic systems may need domain-specific interpretation.

Status: geometric measurements and graph operations are Stable. Bond assignments are explicitly heuristic.