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Chemistry · Glossary

What is Improper rotation axis?

Definition 4.5 University Chemistry — Year 3 · Chapter 4 — Symmetry and Point Groups

An improper rotation axis SnS_n is a line about which a rotation by 2π/n2\pi/n followed by reflection in the plane perpendicular to it is a symmetry operation. S1=σS_1 = \sigma and S2=iS_2 = i.

Symmetry elements. H2O: the C_2 axis (dashed) and two vertical mirror planes. NH3 and BF3 seen down their principal axis (triangle glyph): thick lines are mirror planes seen edge-on; in BF3 the thick circle marks the horizontal mirror plane (the plane of the page) and the lens glyphs the three C_2 axes lying in it.
Symmetry elements. HX2O\ce{H2O}: the C2C_2 axis (dashed) and two vertical mirror planes. NHX3\ce{NH3} and BFX3\ce{BF3} seen down their principal axis (triangle glyph): thick lines are mirror planes seen edge-on; in BFX3\ce{BF3} the thick circle marks the horizontal mirror plane (the plane of the page) and the lens glyphs the three C2C_2 axes lying in it.

Examples

Example 4.6 (Elements of four molecules)

HX2O\ce{H2O}: EE, a C2C_2 axis bisecting the H–O–H angle, and two vertical planes, the molecular plane and the plane perpendicular to it. NHX3\ce{NH3}: EE, a C3C_3 through N (operations C3C_3 and C32C_3^2), and three σv\sigma_v, each containing one N–H bond. BFX3\ce{BF3}: a C3C_3, three C2C_2 along the B–F bonds, σh\sigma_h (the molecular plane), three σv\sigma_v, and an S3S_3. CHX4\ce{CH4}: four C3C_3 along the C–H bonds, three C2C_2 bisecting H–C–H angles, which are also S4S_4 axes, and six σd\sigma_d, each containing two C–H bonds (figure below).

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