Chemistry 302 - Review Sheet 2
Important Concepts and Relationships
Notice: These notes have not been reviewed by Professor Evans or GSI David Witker

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*Page references are from Miessler and Tarr, Inorganic Chemistry, 2nd ed.
*Terms marked with a green asterisk will not be on the second exam.
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Term Page #* Information Images/Links
Symmetry elements 73 Properties of symmetry of certain objects. Theses properties may include mirror planes, axes of rotation and inversion centers. Mirror plane and axis of rotation
c3sh
Symmetry operations 73 The actual reflection, rotation or inversion process across, around or through the symmetry element.
Group 88-91 A set of values and operations that have the following properties:
  1. CLOSURE: If a and b are in the group then a • b is also in the group.
  2. ASSOCIATIVITY: If a, b and c are in the group then (a • b) • c = a • (b • c).
  3. IDENTITY: There is an element e of the group such that for any element a of the group
    a • e = e • a = a.
  4. INVERSES: For any element a of the group there is an element a-1 such that
    • a • a-1 = e
      and
    • a-1 • a - e
A good source on group theory is The Dog School of Mathematics at http://dogschool.tripod.com/
The definitions at left are from that site.
Group multiplication table A table listing all of the operations in a group applied to one another. The table demonstrates the closure of groups by showing that the result of any two operations is the same as another single operation within the group.
Point group 79 The set of all symmetry operations for a molecule.
Mirror plane 76 A mirror plane is a plane across which an object can be reflected so that the reflection corresponds to the the original object at that point. The the operation of reflection across a mirror plane is referred to as a sigma. A sigmav is a mirror plane that passes through the primary rotation axis and an outer atom. A sigmad is a mirror plane that does not pass through an outer atom. An exception to this is in Td and Dnd, in which all mirror planes are referred to as sigmad. A sigmah is a mirror plane where the plane is perpendicular to the primary axis of rotation. Examples of sigmav, sigmad and sigmah are at right. sigmavc2sv
sigmadc2sd
sigmahc3sh
Rotation axis 75 A rotation axis is an axis about which an object can be rotated. The operation of rotation is referred to as a Cn operation, where n is the number of divisions withing 360o that result in a match to the original form. The axis with the highest value of n is referred to as the primary rotation axis or highest order rotation axis. Examples of a C2 and C4 are at right. C2C2
C4C4
Inversion center 76-77 A point through which an object can be inverted and have the inverted form match the original. The operation is denoted i. SF6 is an example of this, the yellow S is the inversion center. SF6Inversion center
Improper rotation axis 77 An axis about which a molecule can be rotated, and then reflected across a sigmah mirror plane to yield a match to the original molecule. This operation is denoted Sn, where 360/n is the required number of degrees of rotation about the axis. This operation is also called a rotation-reflection operation. An example using TaF8 is at right; when turned 22.5o (360/8) and then reflected across the horizontal mirror plane, the resultant form matches the original S8Improper rotation axis
Representation
Reducible representation*
Irreducible representation*
Class*
Character* 91 The sum of the numbers on the diagonal of a square matrix, running from upper left to lower right. C2: c2matrix
Character
= (-1)+(-1)+1 = -1
Character table* 92 The complete set of irreducible representations for a point group.
Basis (for a representation, reducible or irreducible)*
Dissymetric 96 The property of an object to not be superimposable on its mirror image. Also known as Chiral. An example using CHClFBr is at right. Dissymetric molecule
Dissymetric molecule
Dissymetric molecule
Asymmetric
Chirality
Hetero and homo-chiral
Criteria for evidence of a polar vector (dipole moment)
IR- and Raman active vibrational modes*
LCAO 109 Linear Combination of Atomic Orbitals. This is done simply by adding the two atomic orbital wavefunctions together. Linear Combination of Atomic Orbitals
Molecular overlap
Overlap criterion
Symmetry and energy constraints on overlap
Homonuclear diatomics
Heteronuclear diatomics
Bond Energy (De and Do)
Highest occupied molecular orbital (HOMO) 126 The molecular orbital of highest energy that contains an electron. Please click here to go to a more in-depth explanation of HOMO and LUMO
Lowest unoccupied molecular orbital (LUMO) 126 The molecular orbital of lowest energy that has a space available for an electron.
Bonding molecular orbital
Antibonding molecular orbital
Non-bonding molecular orbital
Frontier orbitals 126 The HOMO and LUMO orbitals. These are known as such because they are at the outside of the molecule, and are the orbitals that determine the molecule's intereaction with other species.


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