= Torsional strain
<Torsional strain> is an increase in the <energy> of a <molecule> associated with an unfavourable <torsion angle>, relative to a stated reference <conformation>. Rotation about a bond can change the relative orientations of substituents without changing which <atoms> are bonded. The IUPAC definition of strain explicitly includes unfavourable <dihedral angles> alongside bond-length and bond-angle distortions.<Compendium of Chemical Terminology (Gold Book), second edition>[Strain, entry S06037, DOI10.1351/goldbook.S06037]{ref}
Consider <ethane> viewed along its central carbon–carbon bond. An <eclipsed conformation> aligns projected carbon–hydrogen bonds, whereas a <staggered conformation> places them between one another. An idealized threefold <potential energy> model is
$$
V(\phi)=\frac{V_3}{2}\left[1+\cos(3\phi)\right],\qquad V_3>0,
$$
with $\phi=0$ chosen eclipsed. It gives $V(0)=V_3$ and $V(\pi/3)=0$: a finite rotational barrier separates equivalent minima. The model is a teaching parametrization; $V_3$ must be obtained independently rather than read from the drawing.
The 1937 paper by <J. D. Kemp> and <K. S. Pitzer> explicitly connected the <entropy> of <ethane> and the <third law of thermodynamics> with hindered methyl-group rotation.<The Entropy of Ethane and the Third Law of Thermodynamics. Hindered Rotation of Methyl Groups by J. D. Kemp and Kenneth S. Pitzer>[Verified original title, JACS59, pp.276–279]{ref} This historical connection shows why internal rotation is a measurable molecular degree of freedom, not simply unrestricted motion around a single bond. In a ring, geometric closure can restrict accessible <torsion angles>; <ring strain> can therefore include <torsional strain> as well as other contributions. Assigning a separate torsional energy is model-dependent, rather than a complete account of every electronic interaction.
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