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Unformatted text preview: Welcome to:!
Chemistry 120A!
Lecture 4!
Symmetry, !
Symmetry Elements and
Operations!
Prof. Joshua Figueroa ! How do we Systematically Describe the Bonding in !
Complex Molecules?! Chromium Hexacarbonyl!
Cr(CO)6!
jmol ! What do we mean by symmetry and where do we ﬁnd it?!
Some Examples of Natural and HumanMade Symmetry! What Properties of These Objects Deﬁne Their Symmetry?! Mirror Plane Six
fold Rota4on Axis And inversion center Four
fold Rota4on Axis And inversion center Mirror Plane What Properties of These Objects Deﬁne Their Symmetry?! Mirror Plane Six
fold Rota4on Axis And inversion center Mirror Plane Four
fold Rota4on Axis And inversion center These Features are Called Symmetry Elements! Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! Order of Rotation (n) = A rotation by 360˚/n!
Renders the object unchanged !
We say “an object therefore has nfold rotational!
symmetry”!
What is the order of rotation for these objects?! Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i! Order of Rotation (n) = A rotation by 360˚/n!
Renders the object unchanged !
We say “an object therefore has nfold rotational!
symmetry”!
What is the order of rotation for these objects?! Improper Rotation Axes, Sn!
The Identity, E! 4
fold 5
fold 16
fold Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! Order of Rotation (n) = A rotation by 360˚/n!
Renders the object unchanged !
We say “and object therefore has nfold rotational!
symmetry”!
What is the order of rotation for these molecules?! Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i! Order of Rotation (n) = A rotation by 360˚/n!
Renders the object unchanged !
We say “and object therefore has nfold rotational!
symmetry”!
What is the order of rotation for these molecules?! Improper Rotation Axes, Sn! 6 The Identity, E! 3 5 6 Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! Order of Rotation (n) = A rotation by 360˚/n!
Renders the object unchanged !
Objects or molecules can have more than !
one rotational axis! How many different Cn axis are in this !
Snowﬂake?! Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! The answer is three: C6, C3 and C2 Is there a C4? Order of Rotation (n) = A rotation by 360˚/n!
Renders the object unchanged !
Objects or molecules can have more than !
one rotational axis! How many different Cn axis are in this !
Snowﬂake?! Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! Order of Rotation (n) = A rotation by 360˚/n!
Renders the object unchanged !
Objects or molecules can have more than !
one rotational axis! How many different Cn axis are in this !
Octahedron? What are they?! Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! C4 Order of Rotation (n) = A rotation by 360˚/n!
Renders the object unchanged !
Objects or molecules can have more than !
one rotational axis! How many different Cn axis are in this !
Octahedron? What are they?!
C4 Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn! Order of Rotation (n) = A rotation by 360˚/n!
Renders the object unchanged !
Objects or molecules can have more than !
one rotational axis! How many different Cn axis are in this !
Octahedron? What are they?! The Identity, E! 2 C4( there is one more) C4 Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! Order of Rotation (n) = A rotation by 360˚/n!
Renders the object unchanged !
Objects or molecules can have more than !
one rotational axis! How many different Cn axis are in this !
Octahedron? What are they?! C2 C2 Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! C2 Along Axes Order of Rotation (n) = A rotation by 360˚/n!
Renders the object unchanged !
Objects or molecules can have more than !
one rotational axis! How many different Cn axis are in this !
Octahedron? What are they?! C2 C2 C2 Symmetry Elements!
Order of Rotation (n) = A rotation by 360˚/n!
Renders the object unchanged ! Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! Objects or molecules can have more than !
one rotational axis! How many different Cn axis are in this !
Octahedron? What are they?! C2 C2 Between Axes C2 And there are four more C2’s Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! Order of Rotation (n) = A rotation by 360˚/n!
Renders the object unchanged !
Objects or molecules can have more than !
one rotational axis! How many different Cn axis are in this !
Octahedron? What are they?! What else? Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! Order of Rotation (n) = A rotation by 360˚/n!
Renders the object unchanged !
Objects or molecules can have more than !
one rotational axis! How many different Cn axis are in this !
Octahedron? What are they?! C3 C3 How many C3’s are there? Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! Order of Rotation (n) = A rotation by 360˚/n!
Renders the object unchanged !
Objects or molecules can have more than !
one rotational axis! How many different Cn axis are in this !
Octahedron? What are they?! C3 C3 How many C3’s are there? (There are three others) Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! An object remains unchanged when reﬂected !
Through a plane (aka Mirror Plane)!
Objects or molecules can have more than !
One Plane of Reﬂection! Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! An object remains unchanged when reﬂected !
Through a plane (aka Mirror Plane)!
Objects or molecules can have more than !
One Plane of Reﬂection! Consider this object Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ An object remains unchanged when reﬂected !
Through a plane (aka Mirror Plane)!
Objects or molecules can have more than !
One Plane of Reﬂection! The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! Consider this object σ Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ An object remains unchanged when reﬂected !
Through a plane (aka Mirror Plane)!
Objects or molecules can have more than !
One Plane of Reﬂection! The Inversion Center, i!
Consider this object Improper Rotation Axes, Sn!
The Identity, E! Are there any mirror Planes? Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ An object remains unchanged when reﬂected !
Through a plane (aka Mirror Plane)!
Objects or molecules can have more than !
One Plane of Reﬂection! The Inversion Center, i!
Consider this object Improper Rotation Axes, Sn!
The Identity, E! Are there any mirror Planes? How many, where? Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ An object remains unchanged when reﬂected !
Through a plane (aka Mirror Plane)!
Objects or molecules can have more than !
One Plane of Reﬂection! The Inversion Center, i!
Consider this object Improper Rotation Axes, Sn!
The Identity, E! Are there any mirror Planes? How many, where? Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ An object remains unchanged when reﬂected !
Through a plane (aka Mirror Plane)!
Objects or molecules can have more than !
One Plane of Reﬂection! The Inversion Center, i!
Consider this object Improper Rotation Axes, Sn!
The Identity, E! Are there any mirror Planes? How many, where? Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ An object remains unchanged when reﬂected !
Through a plane (aka Mirror Plane)!
Objects or molecules can have more than !
One Plane of Reﬂection! The Inversion Center, i!
Consider this object Improper Rotation Axes, Sn!
The Identity, E! Are there any mirror Planes? How many, where? Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ An object remains unchanged when reﬂected !
Through a plane (aka Mirror Plane)!
Objects or molecules can have more than !
One Plane of Reﬂection! The Inversion Center, i!
How many Mirror Planes in H2O? Improper Rotation Axes, Sn! Z The Identity, E!
y O
H X H Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ An object remains unchanged when reﬂected !
Through a plane (aka Mirror Plane)!
Objects or molecules can have more than !
One Plane of Reﬂection! The Inversion Center, i!
How many Mirror Planes in H2O? Improper Rotation Axes, Sn! Z The Identity, E!
y These are σv planes: They are coincident (or parallel to primary rotaDon axis) O X Plane of Molecule H H Plane perpendicular to molecule Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ An object remains unchanged when reﬂected !
Through a plane (aka Mirror Plane)!
Objects or molecules can have more than !
One Plane of Reﬂection! The Inversion Center, i!
How many Mirror Planes in H2O? Improper Rotation Axes, Sn! σv' Z The Identity, E!
y σv These are σv planes: They are coincident (or parallel) to primary rotaDon axis By convenDon, σv is in plane of molecule (yz plane) O X Plane of Molecule H H Plane perpendicular to molecule Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i! An object remains unchanged when reﬂected !
Through a plane (aka Mirror Plane)!
Objects or molecules can have more than !
One Plane of Reﬂection! How many Mirror Planes in BF3? Z Improper Rotation Axes, Sn!
The Identity, E! y F
F X B F Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i! An object remains unchanged when reﬂected !
Through a plane (aka Mirror Plane)!
Objects or molecules can have more than !
One Plane of Reﬂection! How many Mirror Planes in BF3? Z Improper Rotation Axes, Sn!
The Identity, E! σv planes: They are coincident (or parallel) to primary rotaDon axis y F
F σh planes: They are perpendicular to primary rotaDon axis X B F Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ An object remains unchanged when reﬂected !
Through a plane (aka Mirror Plane)!
Objects or molecules can have more than !
One Plane of Reﬂection! The Inversion Center, i! How many Mirror Planes in BF3? Z Improper Rotation Axes, Sn!
The Identity, E! A F σv planes: They are coincident (or parallel) to primary rotaDon axis σh planes: They are perpendicular to primary rotaDon axis B F Which is which? How Many of each? y
X B F Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ An object remains unchanged when reﬂected !
Through a plane (aka Mirror Plane)!
Objects or molecules can have more than !
One Plane of Reﬂection! The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! σv planes: They are coincident (or parallel) to primary rotaDon axis There are 3 Equivalent σv planes In BF3 σh planes: They are perpendicular to primary rotaDon axis How many Mirror Planes in BF3? Z σv y F X B F F Which is which? How Many of each? σh Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ An object remains unchanged when reﬂected !
Through a plane (aka Mirror Plane)!
Objects or molecules can have more than !
One Plane of Reﬂection! The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! σv planes: They are coincident (or parallel) to primary rotaDon axis There are 3 Equivalent σv planes In BF3 σh planes: They are perpendicular to primary rotaDon axis How many Mirror Planes in BF3? Z σv y F X B F F Which is which? How Many of each? σh Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! σv planes: They are coincident (or parallel) to primary rotaDon axis There are 3 Equivalent σv planes In BF3 σh planes: They are perpendicular to primary rotaDon axis An object remains unchanged when reﬂected !
Through a plane (aka Mirror Plane)!
Objects or molecules can have more than !
One Plane of Reﬂection! How many Mirror Planes in BF3? Z σv y F X B F F Which is which? How Many of each? σh Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i! An object remains unchanged when reﬂected !
Through a plane (aka Mirror Plane)!
Objects or molecules can have more than !
One Plane of Reﬂection! How many Mirror Planes in BF3? Z Improper Rotation Axes, Sn! σv The Identity, E! σv planes: They are coincident (or parallel) to primary rotaDon axis There are 3 Equivalent σv planes In BF3 σh planes: They are perpendicular to primary rotaDon axis F y
X B F F Which is which? How Many of each? σh Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! N
H H
H Do these Molecules have a Mirror Plane? How Many, What kind? 1
Ammonia, NH3 2
Sulfur tetraﬂuoride, SF4 3
Carbon monoxide, CO 4
Dioxygen, O2 5
Diborane, B2H6 Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! N
H H
H Do these Molecules have a Mirror Plane? How Many, What kind? 1
Ammonia, NH3 2
Sulfur tetraﬂuoride, SF4 3
Carbon monoxide, CO 4
Dioxygen, O2 5
Diborane, B2H6 Three σv’s Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! F S
F F F Do these Molecules have a Mirror Plane? How Many, What kind? 1
Ammonia, NH3 2
Sulfur tetraﬂuoride, SF4 3
Carbon monoxide, CO 4
Dioxygen, O2 5
Diborane, B2H6 Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! F S
F F Do these Molecules have a Mirror Plane? How Many, What kind? 1
Ammonia, NH3 2
Sulfur tetraﬂuoride, SF4 3
Carbon monoxide, CO 4
Dioxygen, O2 5
Diborane, B2H6 F Two σv’s Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! F S
F F Do these Molecules have a Mirror Plane? How Many, What kind? 1
Ammonia, NH3 2
Sulfur tetraﬂuoride, SF4 3
Carbon monoxide, CO 4
Dioxygen, O2 5
Diborane, B2H6 F Two σv’s Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! C O Do these Molecules have a Mirror Plane? How Many, What kind? 1
Ammonia, NH3 2
Sulfur tetraﬂuoride, SF4 3
Carbon monoxide, CO 4
Dioxygen, O2 5
Diborane, B2H6 Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! C O Do these Molecules have a Mirror Plane? How Many, What kind? 1
Ammonia, NH3 2
Sulfur tetraﬂuoride, SF4 3
Carbon monoxide, CO 4
Dioxygen, O2 5
Diborane, B2H6 Inﬁnite σv’s Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! C O Do these Molecules have a Mirror Plane? How Many, What kind? 1
Ammonia, NH3 2
Sulfur tetraﬂuoride, SF4 3
Carbon monoxide, CO 4
Dioxygen, O2 5
Diborane, B2H6 Inﬁnite σv’s Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! O O Do these Molecules have a Mirror Plane? How Many, What kind? 1
Ammonia, NH3 2
Sulfur tetraﬂuoride, SF4 3
Carbon monoxide, CO 4
Dioxygen, O2 5
Diborane, B2H6 Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! O O Do these Molecules have a Mirror Plane? How Many, What kind? 1
Ammonia, NH3 2
Sulfur tetraﬂuoride, SF4 3
Carbon monoxide, CO 4
Dioxygen, O2 5
Diborane, B2H6 Inﬁnite σv’s One σh Symmetry Elements! Do these Molecules have a Mirror Plane? How Many, What kind? Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! H
H
H B B
H H
H 1
Ammonia, NH3 2
Sulfur tetraﬂuoride, SF4 3
Carbon monoxide, CO 4
Dioxygen, O2 5
Diborane, B2H6 Symmetry Elements! Do these Molecules have a Mirror Plane? How Many, What kind? Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! 1
Ammonia, NH3 2
Sulfur tetraﬂuoride, SF4 3
Carbon monoxide, CO 4
Dioxygen, O2 5
Diborane, B2H6 H
H
H B B
H H
H Three Perpendicular C2 Axes Therefore, just three σ Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! A Reﬂec;on (or Inversion) through the Mid
Point (Center) of the Molecule or Object Note Emphasis on POINT Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! A Reﬂec;on (or Inversion) through the Mid
Point (Center) of the Molecule or Object Note Emphasis on POINT Is there an Inversion Center? 1
Ethylene, C2H4 2
Methane, CH4 3 – Water, H2O 4
Diborane, B2H6 Symmetry Elements!
A Reﬂec;on (or Inversion) through the Mid
Point (Center) of the Molecule or Object Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! H Is there an Inversion Center? 1
Ethylene, C2H4 2
Methane, CH4 3 – Water, H2O 4
Diborane, B2H6 H
C H Note Emphasis on POINT C
H A – Yes B
No Symmetry Elements!
A Reﬂec;on (or Inversion) through the Mid
Point (Center) of the Molecule or Object Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! H Is there an Inversion Center? 1
Ethylene, C2H4 2
Methane, CH4 3 – Water, H2O 4
Diborane, B2H6 H
C H Note Emphasis on POINT C
H A – Yes B
No Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! A Reﬂec;on (or Inversion) through the Mid
Point (Center) of the Molecule or Object Note Emphasis on POINT Is there an Inversion Center? 1
Ethylene, C2H4 2
Methane, CH4 3 – Water, H2O 4
Diborane, B2H6 H
C
H H
H A – Yes B
No Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! A Reﬂec;on (or Inversion) through the Mid
Point (Center) of the Molecule or Object Note Emphasis on POINT Is there an Inversion Center? 1
Ethylene, C2H4 2
Methane, CH4 3 – Water, H2O 4
Diborane, B2H6 H
C
H H
H A – Yes B
No Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! O
H H A Reﬂec;on (or Inversion) through the Mid
Point (Center) of the Molecule or Object Note Emphasis on POINT Is there an Inversion Center? 1
Ethylene, C2H4 2
Methane, CH4 3 – Water, H2O 4
Diborane, B2H6 A – Yes B
No Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! O
H H A Reﬂec;on (or Inversion) through the Mid
Point (Center) of the Molecule or Object Note Emphasis on POINT Is there an Inversion Center? 1
Ethylene, C2H4 2
Methane, CH4 3 – Water, H2O 4
Diborane, B2H6 A – Yes B
No Symmetry Elements!
A Reﬂec;on (or Inversion) through the Mid
Point (Center) of the Molecule or Object Axis of Rotation, Cn! Note Emphasis on POINT Planes of Reﬂection, σ Is there an Inversion Center? The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! 1
Ethylene, C2H4 2
Methane, CH4 3 – Water, H2O 4
Diborane, B2H6 H
H
H B B
H H
H A – Yes B
No Symmetry Elements!
A Reﬂec;on (or Inversion) through the Mid
Point (Center) of the Molecule or Object Axis of Rotation, Cn! Note Emphasis on POINT Planes of Reﬂection, σ Is there an Inversion Center? The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! 1
Ethylene, C2H4 2
Methane, CH4 3 – Water, H2O 4
Diborane, B2H6 H
H
H B B
H H
H A – Yes B
No Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! An Improper Rota;on Axis is a Rota;on By 360˚/n followed by a reﬂec;on through Plane perpendicular to the axis (σh) This is an Sn axis (Cn + σh) = Sn Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! An Improper Rota;on Axis is a Rota;on By 360˚/n followed by a reﬂec;on through Plane perpendicular to the axis (σh) This is an Sn axis (Cn + σh) = Sn Consider Methane, CH4 Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! What is the order of Sn? An Improper Rota;on Axis is a Rota;on By 360˚/n followed by a reﬂec;on through Plane perpendicular to the axis (σh) This is an Sn axis (Cn + σh) = Sn Consider Elemental Sulfur, S8 Symmetry Elements!
Axis of Rotation, Cn!
Planes of Reﬂection, σ The Inversion Center, i!
Improper Rotation Axes, Sn!
The Identity, E! What is the order of Sn? S8 An Improper Rota;on Axis is a Rota;on By 360˚/n followed by a reﬂec;on through Plane perpendicular to the axis (σh) This is an Sn axis (Cn + σh) = Sn Consider Elemental Sulfur, S8 C8 ...
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This note was uploaded on 08/15/2011 for the course CHEM 114B taught by Professor Wang during the Spring '09 term at UCSD.
 Spring '09
 WANG
 Mole

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