Chapter 4 - Symmetry and Group Theory Flashcards

1
Q

symmetry elements

A

mirror planes, axes of rotation, inversion centers, etc

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2
Q

symmetry opration

A

the actual reflection/rotation/inversion operation

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3
Q

Identity operation

A

E, no change in molecule

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4
Q

Rotation operation

A

Cn, rotation through 360º/n

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5
Q

Reflection operation

A

σ, reflection through mirror plane

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6
Q

Inversion operation

A

i, each point moves through the center of the molecule to a position opposite the original position and as far from the central point as where it started

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7
Q

Rotation-reflection operation

A

Sn, aka improper rotation: rotation of 360º/n followed by reflection through a plane perpendicular to a axis of rotation

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8
Q

E

A

Identity operation, no change

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9
Q

Cn

A

Rotation operation, 360/nº each time

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10
Q

σ

A

Reflection operation through mirror plane

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11
Q

σh

A

Horizontal reflection operation when the plane is perpendicular to the principal axis of rotation

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12
Q

σv/σd

A

Vertical reflection operation when the plane contains the principal axis of rotation

σd: Dihedral passes through fewer atoms (dihedral to the angle of the bonds). Dihedral, same plane as v but related by half a rotation of the principle axis

σv: Vertical, parallel to/passing through the principal axis (primary rotation axis)

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13
Q

i

A

Inversion, each point moves through the center of the molecule to a position opposite the original position and as far from the central point as where it started

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14
Q

Sn

A

Rotation-reflection/improper-rotation operation, rotation of 360º/n followed by reflection through a plane perpendicular to a axis of rotation

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15
Q

Principal axis

A

The Cn axis with the largest value of n

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16
Q

Point group

A

a set of symmetry operations that best describes the molecule’s overall symmetry

17
Q

Groups of low symmetry

A

C1 - no symmetry other than the identity operation

Cs - only one mirror plane

Ci - only an inversion center

18
Q

Groups of high symmetry

A

C∞v - Linear molecule with an infinite number of rotations and an infinte number of reflection planes containing the rotation axis (e.g. H-Cl). Do not have a center of inversion.

D∞h - Linear molecule with an infinite number of rotations and an infinite number of reflection planes containing the rotation axis.

19
Q
A

d orbital: z2

20
Q
A

d orbital x2-y2

24
Q

σ-bond

A

orbitals are symmetric to rotation about the line connecting the nuclei

no nodes that include the line between nuclei

25
π-bond
a change in sign in the wave function with C2 rotation about the bond axis one node including the line between nuclei
26
δ-bond
change in sign on C4 rotation about the bond axis two nodes including the line between nuclei
27
28
Identify rotation axes
29
What is the difference between dihedral and vertical mirror planes?
σd: Dihedral passes through fewer atoms (dihedral to the angle of the bonds). Dihedral, same plane as v but related by half a rotation of the principle axis σv: Vertical, parallel to/passing through the principal axis (primary rotation axis)
30