Chapter 1 Point Group Symmetry.

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Presentation transcript:

Chapter 1 Point Group Symmetry

Symmetry Elements E: Identity operation Cn: Proper rotation

Symmetry Elements i: Inversion sh: Horizontal Mirror Plane sv: Vertical Mirror Plane

Symmetry Elements Sn: Improper rotation: combination Cn and sh S2 is equivalent to inversion (i)

Symmetry Groups Groups with no proper rotation axis C1: Only E (i.e. no symmetry elements) Cs: E and s Ci: E and i Sn: E, Sn (S1 = Cs; S2 = Ci) Groups with one proper rotation axis Cn: E, Cn only Cnv: E, Cn, and n sv (linear unsymmetrical molecules are C∞v) Cnh: E, Cn, and sh Dihedral Groups: Groups with n C2 axes  to Cn Dn: E, Cn, and n C2 axes  to Cn Dnh: E, Cn, n C2 axes, and sh (linear symmetrical molecules are D∞h) Dnd: E, Cn, n C2 axes, and n sv Cubic Groups: Groups with more than one Cn (n ≥ 3) Td: symmetry of a regular tetrahedron: 4 C3 Oh: symmetry of a regular octagon: 6 C4 Ih: symmetry of a regular icosahedron: 12 C5

Symmetry Decision Tree Linear? Find principal axes C∞v or D ∞h More than one Cn (n ≥ 3) Cubic T, O, I Cs, Ci or C1 Cn is the principal axis? nC2  to Cn? S2n colinear w/ Cn? n vertical mirror planes S2n sh? sv? Dnd Dnh Dn Cn Cnv Cnh Yes No None Physical Chemistry, Joseph H. Noggle, 2nd ed., Scott Foresman & Co, Glenview, IL, 1996, pg 840.