SCIENCE · INVESTIGATE AND EXPLAIN

Rotate a domain model without changing its molecular shape

Separate the arrangement of all electron domains from the arrangement of bonded nuclei.

Learning outcome: Compare AX3, AX4 and AX3E at two view rotations. Then compare AX5, AX4E and AX3E2, identifying removed equatorial sites. Capture angle ledgers as well as pictures.

Starting recap

Review the electron and formal-charge budget, bond multiplicity, signed interaction energies and the distinction between a model and a measured property.

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Try

AX3E uses four tetrahedral domains but only three bonded sites; ideal pair angles are109.47°, not a measured ammonia angle.

Open the experiment

Predict

Can rotating the picture turn a trigonal pyramid into a genuinely planar molecule?

Your prediction and reason

Experiment

Compare AX3, AX4 and AX3E at two view rotations. Then compare AX5, AX4E and AX3E2, identifying removed equatorial sites. Capture angle ledgers as well as pictures.

Rotate ideal domain and molecular geometry

Worked teaching model · synthetic values · Ideal 2–6-domain templates. Lone pairs occupy equatorial sites in trigonal-bipyramidal cases and opposite sites for square-planar AX4E2. Rotation changes only the view. Actual bond angles may be distorted; the displayed coordinates are not measured molecular structures.

Geometry template: 4 choice View rotation: 30 degrees

Reset keeps your prediction, captures and practice history.

Orthographic projection: bonds toward the viewer use thicker lines; dashed outlined sites are lone-pair domains. Overlap in a view does not merge sites. The table retains depth coordinates. Ideal domain directions are not measured bond angles.

View coordinates on a unit sphere; z positive toward the viewer
Site	x	y	z
bond 1	0.7886751	0.5773503	0.2113249
bond 2	0.2113249	-0.5773503	-0.7886751
bond 3	-0.7886751	0.5773503	-0.2113249
lone-pair domain	-0.2113249	-0.5773503	0.7886751

Axes rescale. Connected samples represent the supplied continuous parameter relationship; stems denote discrete pairs or steps, not a time trajectory.

Numerical plot coordinates

unordered bonded pair index	ideal angle (degrees)
1	109.4712
2	109.4712
3	109.4712

Calculated evidence under the declared representation
Quantity	Value	Unit
Total electron domains	4	domains
Bonded atoms	3	atoms
Lone-pair domains	1	domains
Smallest ideal bond angle	109.4712	degrees
Largest ideal bond angle	109.4712	degrees

AX3E trigonal pyramidal

The domain arrangement includes lone pairs; molecular geometry names only bonded nuclei. All coordinates are ideal templates. Lone-pair and multiple-bond effects can distort actual angles, so a tetrahedral-domain bent model is not a claim that water has a measured 109.47° angle.

AX3E trigonal pyramidal

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Name two arrangements

Electron-domain geometry includes bonding domains and lone-pair domains. Molecular geometry describes positions of bonded nuclei and omits the lone pairs from its name. Three domains give an ideal trigonal plane, four a tetrahedron, five a trigonal bipyramid and six an octahedron. Removing bonded sites from a domain template can produce different molecular shapes with the same total domain count.

Use three-dimensional coordinates

The workbench uses unit vectors from the center. Four tetrahedral directions can be represented by normalized versions of(1,1,1),(1,−1,−1),(−1,1,−1),(−1,−1,1). Any pair has dot product−1/3, yielding an ideal angle about109.47°. Rotating these coordinates for the camera preserves the dot products and therefore every interbond angle. An apparently flat projection does not establish a planar structure.

Place lone pairs consistently

In the trigonal-bipyramidal template, an equatorial site has fewer90° neighbors than an axial site. The elementary lone-pair comparison therefore places the first lone pairs equatorially. AX4E is seesaw, AX3E2 is T-shaped and AX2E3 is linear. In a six-domain template, opposite lone pairs leave AX4E2 square planar; one lone pair gives AX5E square pyramidal.

Do not turn ideal angles into measured claims

Lone-pair and multiple-bond interactions can distort actual angles. The tetrahedral-domain bent template is not a numerical prediction that water has109.47° bonds. Its role is to distinguish the domain arrangement from the bent molecular structure. Actual structure determination requires independent evidence and a model suitable for the species.

Transfer and check

Compare AX2E with AX2E2: both are bent, but one comes from three domains and the other four. Their displayed ideal bonded angles differ,120° versus109.47°. Neither name alone specifies every measured angle. A good retained report includes the domain count, bonded-site count, lone-pair arrangement, view-independent angle calculation and a statement of what is idealized.

Sources and evidence boundary

Conceptual sources checked 30 October 2026: VSEPR and molecular structure. All prose, cases, code and diagrams are original. The supplied models are not measured structures, a performed laboratory investigation or certification of independent mastery. No chemical handling, heating, pressure vessel or cryogenic experiment is requested. Retain predictions, contrasting evidence and a changed-case explanation.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Which angles are ideal templates, and which additional evidence would establish actual distortions?

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Test an electron budget before assigning geometry Next: Determine molecular polarity from vector evidence

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