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Chapter 4. Molecular Symmetry 근근근

Chapter 4. Molecular Symmetry 근정전. Chapter 4. Molecular Symmetry 청와대 본관

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Page 1: Chapter 4. Molecular Symmetry 근정전. Chapter 4. Molecular Symmetry 청와대 본관

Chapter 4. Molecular Symmetry

근정전

Page 2: Chapter 4. Molecular Symmetry 근정전. Chapter 4. Molecular Symmetry 청와대 본관

Chapter 4. Molecular Symmetry

청와대 본관

Page 3: Chapter 4. Molecular Symmetry 근정전. Chapter 4. Molecular Symmetry 청와대 본관

Chapter 4. Molecular Symmetry

청와대 영빈관

Page 4: Chapter 4. Molecular Symmetry 근정전. Chapter 4. Molecular Symmetry 청와대 본관

Chapter 4. Molecular Symmetry

청와대 본관

Page 5: Chapter 4. Molecular Symmetry 근정전. Chapter 4. Molecular Symmetry 청와대 본관

Chapter 4. Molecular Symmetry

청와대 본관

Page 6: Chapter 4. Molecular Symmetry 근정전. Chapter 4. Molecular Symmetry 청와대 본관

Chapter 4. Molecular Symmetry

청와대 본관

Page 7: Chapter 4. Molecular Symmetry 근정전. Chapter 4. Molecular Symmetry 청와대 본관

Chapter 4. Molecular Symmetry

Page 8: Chapter 4. Molecular Symmetry 근정전. Chapter 4. Molecular Symmetry 청와대 본관

Chapter 4. Molecular Symmetry

Page 9: Chapter 4. Molecular Symmetry 근정전. Chapter 4. Molecular Symmetry 청와대 본관

Chapter 4. Molecular Symmetry

H2O

Page 10: Chapter 4. Molecular Symmetry 근정전. Chapter 4. Molecular Symmetry 청와대 본관

Symmetry Operation and Symmetry Elements

• Symmetry Operation:A well-defined, non-translational movement of an object that produces a new orientation that is indistinguishable from the origina

l object.• Symmetry Element:A point, line or plane about which the symmetry opera

tion is performed.

180o rotation: symmetry operation

line: symmetry element

Page 11: Chapter 4. Molecular Symmetry 근정전. Chapter 4. Molecular Symmetry 청와대 본관

Four kinds of Symmetry Elements and Symmetry Operations Required in

Specifying Molecular Symmetry

• Proper (rotation) axis (Cn)

• Mirror plane ()

• Center of symmetry or center of inversion (i)

• Improper (rotation) axis (Sn)

Page 12: Chapter 4. Molecular Symmetry 근정전. Chapter 4. Molecular Symmetry 청와대 본관

Four kinds of Symmetry Elements and Symmetry Operations Required in Specifying Molecular Symmetry (1)

• Proper (rotation) axis (Cn) : n-fold symmetr

y axis. A Cn axis generates n operations.

• Rotation about Cn axis by 2/n

*1: E : Identity (x1) *2: Right-handed rotation

Page 13: Chapter 4. Molecular Symmetry 근정전. Chapter 4. Molecular Symmetry 청와대 본관

Four kinds of Symmetry Elements and Symmetry Operations Required in Specifying Molecular Symmetry (1)

• Proper (rotation) axis (Cn) : n-fold symmet

ry axis. A Cn axis generates n operations.

• Rotation about Cn axis by 2/n

* Principal rotational axis: highest-fold rotational axis* If more than one pricnipal axes exist, any onecan be the principal axis.

Page 14: Chapter 4. Molecular Symmetry 근정전. Chapter 4. Molecular Symmetry 청와대 본관

Four kinds of Symmetry Elements and Symmetry Operations Required in Specifying Molecular Symmetry (2)

• Mirror plane ()• Reflection about the plane.

Page 15: Chapter 4. Molecular Symmetry 근정전. Chapter 4. Molecular Symmetry 청와대 본관

Four kinds of Symmetry Elements and Symmetry Operations Required in Specifying Molecular Symmetry (2)

6

How many mirror planes?

• Mirror plane ()• Reflection about the plane.

Page 16: Chapter 4. Molecular Symmetry 근정전. Chapter 4. Molecular Symmetry 청와대 본관

Four kinds of Symmetry Elements and Symmetry Operations Required in Specifying Molecular Symmetry (2)

How many mirror planes in linear molecules?

C=O N=N

• Mirror plane ()• Reflection about the plane.

Page 17: Chapter 4. Molecular Symmetry 근정전. Chapter 4. Molecular Symmetry 청와대 본관

Four kinds of Symmetry Elements and Symmetry Operations Required in Specifying Molecular Symmetry (2)

• Mirror plane ()• Reflection about the plane.

* h : mirror planes perpendicular to the principal axis.

*v : mirror planes containing the principal axis Unless it is d.*d : mirror planes bisecting x, y, or z axis or bisecting C2 axes perpendicular to the principal axis.

Page 18: Chapter 4. Molecular Symmetry 근정전. Chapter 4. Molecular Symmetry 청와대 본관

How to define molecular axes (x, y, z)?

1. The principal axis is the z axis.

2. If there are more than one possible principal axis, then the one that connects the most atoms is the z axis.

3. If the molecule is planar, then the z axis is the principal axis in that plane. The x axis

is perpendicular to that plane.

4. If a molecule is planar and the z axis is perpendicular to that plane, then the x axis is

the one that connects the most number of atoms.

Page 19: Chapter 4. Molecular Symmetry 근정전. Chapter 4. Molecular Symmetry 청와대 본관

Four kinds of Symmetry Elements and Symmetry Operations Required in Specifying Molecular Symmetry (3)

• Center of symmetry or center of inversion (i)• Inversion of all objects through the center.

i is Pt atom.

i is a point in space.

Page 20: Chapter 4. Molecular Symmetry 근정전. Chapter 4. Molecular Symmetry 청와대 본관

Four kinds of Symmetry Elements and Symmetry Operations Required in Specifying Molecular Symmetry (4)

• Improper (rotation) axis (Sn)• Rotation about an axis by 2/n followed by a reflection through

a plane perpendicular to that axis or vice versa.

S6

Page 21: Chapter 4. Molecular Symmetry 근정전. Chapter 4. Molecular Symmetry 청와대 본관

Four kinds of Symmetry Elements and Symmetry Operations Required in Specifying Molecular Symmetry (4)

• Improper (rotation) axis (Sn)• Rotation about an axis by 2/n followed by a reflection through

a plane perpendicular to that axis or vice versa.

Page 22: Chapter 4. Molecular Symmetry 근정전. Chapter 4. Molecular Symmetry 청와대 본관

Four kinds of Symmetry Elements and Symmetry Operations Required in Specifying Molecular Symmetry (4)

• Improper (rotation) axis (Sn)• Rotation about an axis by 2/n followed by a reflection through

a plane perpendicular to that axis or vice versa.Sn generates n operations for even n and 2n operations for odd n.

Page 23: Chapter 4. Molecular Symmetry 근정전. Chapter 4. Molecular Symmetry 청와대 본관

Four kinds of Symmetry Elements and Symmetry Operations Required in Specifying Molecular Symmetry (4)

• Improper (rotation) axis (Sn)• Rotation about an axis by 2/n followed by a reflection through

a plane perpendicular to that axis or vice versa.Sn generates n operations for even n and 2n operations for odd n.

Page 24: Chapter 4. Molecular Symmetry 근정전. Chapter 4. Molecular Symmetry 청와대 본관

Point Groups

Equivalent atoms

EquivalentF1, F2, F3

EquivalentFa, Fb

Not equivalentEquivalent symmetry operations

EquivalentC2

’, C2

EquivalentC2

’’, C2’’’

Symmetry classes

3 C2 classes – C2, C2’, C2” - and others symmetry classes

C2’

C2’’

Page 25: Chapter 4. Molecular Symmetry 근정전. Chapter 4. Molecular Symmetry 청와대 본관

Point Groups