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CHAPTER 11 Molecular Symmetry

I. Molecular Symmetry

A. Symmetry Operations and Elements.

1. Symmetry operation = an action that leaves the object looking unchanged.

2. Symmetry element = a point, axis, or plane with respect to which the

symmetry operation is performed. 3. point group = classification grouping of molecule’s symmetry. E.g.

H2O belongs to group C2v. 4. Five kinds of symmetry operations (related to 5 symmetry element).

a. identity operation – doing nothing (element E) b. n-fold rotation (operation) around n-fold axis (element Cn) rotation of 360/n degrees H2O is said to have 2-fold axis; ammonia has 3-fold axis.

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A cube has: ____ C2 axes ____ C3 axes ____ C4 axes

c. Reflection (operation) through a plane of symmetry or mirror

plane. (element σ) Can either be parallel to principal axis of rotation (called vertical

plane σv) or perpendicular (called horizontal plane σh).

Water has two vertical planes of symmetry Benzene has horizontal plane σh (perpendicular to 6-fold axis)

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σd = dihedral plane – a vertical plane that bisects the angle between two C2 axes perpendicular to principle axis.

d. Inversion (operation) through center of symmetry i.

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e. Improper rotation about an axis of improper rotation Sn = n-fold rotation followed by a horizontal reflection.

methane Staggered ethane

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B. Symmetry Classes of Molecules (Schoenflies system). -classified into point groups by the kinds of symmetry elements they

possess.

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1. Groups Cl, Ci, Cs. C1 – no symmetry elements except identity Ci – has the inversion only Cs – a plane of reflection only

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2. Groups Cn, Cnv, Cnh. Cn – has n-fold rotational axis

Cnv – n-fold rotational axis plus n vertical planes σv of reflection Cnh – n-fold rotational axis plus horizontal plane σh

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3. Groups Dn, Dnh, Dnd. Dn – n-fold rot axis Cn plus n 2-fold axis perpendicular to Cn Dnh – n-fold rot axis Cn plus n 2-fold axis perpendicular to Cn plus

horizontal plane σh Dnd - n-fold rot axis Cn plus n 2-fold axis perpendicular to Cn plus n-

dihedral mirror plane σd 4. Sn – possesses no other symmetry but has one n-fold improper axis (Sn axis). But S2 = Ci (already classified)

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5. The cubic groups tetrahedral - T, Td, Th octahedral - O, Oh Icosahedral - I Methane is Td SF6 is Oh

C. Consequences of Symmetry.

1. Polarity – only groups belonging to Cn, Cnv, Cs may have a permanent dipole moment.

2. Chirality – optically active (rotates the plane of polarized light). -all molecules possessing a center of inversion i are non-chiral and

hence optically inactive. -others may or may not be chiral

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NOTES: