*“A molecule’s turning rotations;*

*Its stretching and bending vibrations—*

*To calculate, heed them:*

*The degrees of freedom.*

*(Forget not three types of translation!)”*

The 10 April 2022 limerick addressed a concept related to molecular motions and energetics. The main idea here is that a molecule can undergo 3N types of motion, where N is the number of atoms in a molecule. The types of motion are more precisely termed “degrees of freedom” in chemistry analyses.

**“A molecule’s turning rotations; /**

**Its stretching and bending vibrations…”**

We can consider water as a sample molecule. Water, with its V-shape, has the formula H_{2}O: thus, three atoms and nine (3N) degrees of freedom.

We can think of the ways that a water molecule could move. It could “translate” (move in space) in three dimensions: the x, y, and z axes in a Cartesian system. As we look at a water molecule, we see that it could also “rotate” in three ways: first, so that the H atoms spin to the “left and right” around the O atom; second, in the direction perpendicular to the first direction (so the H atoms spin “over and under” relative to the O atom); third, within the plane of the screen itself.

The possible “vibrations” correspond to the remaining number of degrees of freedom possible for water as a non-linear molecule. These can be calculated via the equation 3N-6 (since six degrees of freedom are already occupied: three translations and three rotations).

From that equation, we can confirm that water has three vibrational modes: a symmetric stretch, in which both O-H bonds stretch and compress at once; an asymmetric stretch, in which the O-H bonds alternate their motion; and a bending mode, in which the molecule’s H-O-H bond angle changes.

**“To calculate, heed them: /**

**The degrees of freedom. /**

**(Forget not three types of translation!)”**

The concept of degrees of freedom facilitates many calculations in chemistry, such as those related to infrared spectroscopy.

Interestingly, this essay is slightly misaligned with the poem: the “three types of translations” provide the poetic punchline, but it doesn’t work to omit that prose-based explanation until the end.

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