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Science Poetry

Matter of Degrees

“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 H2O: 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.