Describe bending vibrations

Start with H₂O at 104.5°. Move both H atoms in the molecular plane so the angle becomes 110° while O–H lengths stay nearly fixed.

GCE A-Level H3 Chemistry 9813-2027

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Learning objectives

Describe bending vibrations

Watch an angle open and close

Start with H₂O at 104.5°. Move both H atoms in the molecular plane so the angle becomes 110° while O–H lengths stay nearly fixed.

The changing internal coordinate is the H–O–H angle, so the motion is bending.

Bending families

Bending changes bond angle with little bond-length change. Scissoring and rocking are in-plane; wagging and twisting are out-of-plane descriptions for multi-atom groups.

For linear CO₂ the bend is doubly degenerate: two perpendicular bending planes share one vibrational frequency near 667 cm⁻¹.

Dipole change during a bend

At equilibrium CO₂ is linear and non-polar, but a bent instantaneous geometry has bond dipoles that no longer cancel.

The oscillating dipole makes the degenerate bending frequency IR active even though the equilibrium molecule has no permanent dipole.

CO₂ bending planes

One CO₂ bend moves both O atoms above and below the molecular axis in the page; the equal-energy partner bends perpendicular to the page.

The two modes are distinct motions but degenerate, so they contribute one absorption frequency near 667 cm⁻¹.

Try this

Explain why two CO₂ bending motions give one IR band.

Check your answer

A strong answer gives perpendicular bending planes, equal energy/degeneracy and one shared absorption frequency.

Distinguish CH₂ bends

In scissoring the two C–H bonds move toward and away from each other in the molecular plane.

In rocking both H atoms move in the same in-plane direction; neither description requires C–H stretching.

Try this

Describe the arrow difference between CH₂ scissoring and rocking.

Check your answer

Scissoring uses opposing in-plane H motions; rocking uses same-direction in-plane motion.

Transfer to out-of-plane motion

Wagging and twisting are the out-of-plane counterparts of rocking and scissoring.

Use the in-plane pair you have just drawn to decide how the two H atoms move relative to the H–C–H plane in each.

Try this

Sketch and label wagging and twisting of a CH₂ group.

Check your answer

In wagging both H atoms move together above, then below, the plane; in twisting one moves above as the other moves below. The sketches must show that together-versus-opposite difference and keep C–H lengths approximately fixed.

Bending is not a weak stretch

Bending and stretching are different normal-coordinate patterns, not merely low- and high-energy versions of the same motion.

A bend is identified by angle change; a stretch by bond-length change.

Try this

Better reasoning: “The 667 cm⁻¹ CO₂ band is a slow C=O stretch.”

Check your answer

Replace slow stretch with the doubly degenerate angle-changing bend and state its changing dipole.

Check bending before mode counting

After the check questions, try the OCS case without notes. Return later for a different NH₂Cl question.

Try this next: predict simple-molecule mode counts.

Try this

Use fixed arrows to distinguish CO₂ bending from stretching.

Check your answer

A complete response changes the O=C=O angle, keeps C=O lengths nearly fixed and links the bend to the 667 cm⁻¹ band.