Test 1 Flashcards
Symmetry operation
A movement along a symmetry element where we cant tell if something moved or not- its in the same spot.
What are symmetry elements?
An imaginary geometrical identity like a line, plane, or point at which symmetry operation can be performed
Point group
Collection of Symmetry operations possible for an isolated object. Symmetry elements of these operations have a center point
Space group
Group of Symmetry operations valid for a continuous array. Can be point symmetry operations, translations, or combos
Explain the identity operation E
Identity. Operation that moves object or all parts of an object to starting position
Explain the symmetry operation Cn
Is a proper rotation. It is an operation that is themovement around an axis by 360/n where n is the order (and an integer)
Principle axis
The highest order rotational axis an object possesses
Explain the symmetry operation Sigma
Reflection. Occurs when a point normal to a mirror plane is found at an equivalent, opposite point
Explain the operation i
Inversion. Inversion occurs if for any point there is an equivalent point through the center and on the opposite side of the object
What is another word for an object that has inversion?
Centrosymmetric
Explain the symmetry operation S
Improper rotation. It consists of a proper rotation followed by a reflection across a mirror plane perpendicular to the principle axis
Define chirality
An object is chiral if it only has identity operation or only proper rotation. Groups that are chiral are: Cn, Dn, T, O, I
When can a molecule have a dipole?
There can be a dipole if a symmetry operation must go through a certain point/vector. Dipoles can exist in C1, CS(if in mirror plane), Cn (if dipole is on axis), and Cnv ( if dipole is in axis)
No dipole if it has inversion, rotational axis |_ to mirror plane, or more than one rotational axis
What is an irreducible representation?
They are the simplest, fundamental representations (of symmetry?) for a group
What is a reducible representation?
Is a combination of irreducible representations
How do we know the dimensions of an irreducible representations?
The character under identity operations tells us how big a matrix is
What is the order of a point group?
It is the total number of symmetry operations in a group. We find if by adding all the numbers at the top of a character table
What is a basis function?
The functions on the very right of a character table that calculate how an object is affected by a symmetry operation
What is the reduction formula and what do the terms stand for?
N= 1/h sum( gi Xi Xr)
The number of times a irreducible representations appears in the reducible representation= 1/ order of group sum( number of operations for class x characters is reducible representation x characters in irreducible representation)
What is a shortcut i can use when applying the reduction formula?
I can multiply the number of symmetry operations by the # of characters from gamma reducible
What is a direct product?
It is two irreducible representations multiplied together to get a gamma reducible. From there we can use the reduction formula
List the steps to find whether a vibration mode will show up on IR or Raman spectra.
Find point group
Assign vectors
Find vectors that don’t move to produce gamma reducible(remember you can have inversion if i assigned 3 vectors)
Apply reduction formula
If 3 vectors were put on each atom, take out rotational/tranlational movements
Determine which modes would show up on the specta
Which vibrational modes show up in IR?
Irreducible representations with Rx, Ry, Rz or only x, y, and z
What vibrational modes show up in Raman spectra?
Quadratic functions
Can a single vibrational mode show up on both spectra?
No.
What does E for gamma reducible tell us?
It tells us the number of vectors we have
When do we take out translational and rotational modes?
When we assigned 3 vectors for each atom
What is a unit cell?
It is the simplest 3D crystal from which a crystal can be made fron successive translations
