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 
Symmetry operations  73  The actual reflection, rotation or inversion process across, around or through the symmetry element.  
Group  8891  A set of values and operations that have the following properties:

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 . A _{v} is a mirror plane that passes through the primary rotation axis and an outer atom. A _{d} is a mirror plane that does not pass through an outer atom. An exception to this is in T_{d} and D_{nd}, in which all mirror planes are referred to as _{d}. A _{h} is a mirror plane where the plane is perpendicular to the primary axis of rotation. Examples of _{v}, _{d} and _{h} are at right.  _{v} _{d} _{h} 
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 C_{n} operation, where n is the number of divisions withing 360^{o} 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 C_{2} and C_{4} are at right.  C_{2} C_{4} 
Inversion center  7677  A point through which an object can be inverted and have the inverted form match the original. The operation is denoted i. SF_{6} is an example of this, the yellow S is the inversion center.  SF_{6} 
Improper rotation axis  77  An axis about which a molecule can be rotated, and then reflected across a _{h} mirror plane to yield a match to the original molecule. This operation is denoted S_{n}, where 360/n is the required number of degrees of rotation about the axis. This operation is also called a rotationreflection operation. An example using TaF_{8} is at right; when turned 22.5^{o} (360/8) and then reflected across the horizontal mirror plane, the resultant form matches the original  S_{8} 
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.  C_{2}: 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.  
Asymmetric  
Chirality  
Hetero and homochiral  
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.  
Molecular overlap  
Overlap criterion  
Symmetry and energy constraints on overlap  
Homonuclear diatomics  
Heteronuclear diatomics  
Bond Energy (D_{e} and D_{o})  
Highest occupied molecular orbital (HOMO)  126  The molecular orbital of highest energy that contains an electron.  Please click here to go to a more indepth 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  
Nonbonding 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. 
This page was made by Erik Epp.