what is the point group and character table for: cis-Fe(CO)4Cl2?
I got D2d as the point group
and
4,0,0,0,0 as the character table
(although I don't think that is correct)
THANKS
It's actually a C2V group
To determine the point group and character table for the molecule cis-Fe(CO)4Cl2, we need to follow a systematic approach. Here's how you can do it:
Step 1: Identify the Symmetry Elements
To determine the point group, we first need to identify the symmetry elements present in the molecule. Symmetry elements include rotation axes, reflection planes, inversion centers, and improper rotation axes. Look for these elements in the molecule and note their presence.
In cis-Fe(CO)4Cl2, we have the following symmetry elements:
- A C4 rotation axis passing through the Fe atom
- A C2 rotation axis perpendicular to the plane of the molecule passing through the Fe and Cl atoms
- A mirror plane containing the Fe and Cl atoms
Step 2: Assign Symmetry Operations
After identifying the symmetry elements, we need to assign symmetry operations to each element. Symmetry operations include E (identity), Cn (rotation by 2π/n), σ (reflection), and i (inversion).
In cis-Fe(CO)4Cl2, we have the following symmetry operations:
- E (identity operation)
- C4 rotation
- C2 rotation
- Reflection through the mirror plane
Step 3: Build the Character Table
Now that we have identified the symmetry elements and assigned symmetry operations, we can construct the character table for the point group.
The D2d point group has the following character table:
E 2C4(C2) 2C2 2σd 2σc i 2S4 2S2
A1 1 1 1 1 1 1 1
A2 1 1 -1 -1 1 1 -1
B1 1 -1 1 -1 -1 1 -1
B2 1 -1 -1 1 -1 1 1
Each row represents an irreducible representation (irrep) of the point group, and each column represents a symmetry operation. The character for each irrep is calculated by applying the corresponding symmetry operation to each element of the irrep and summing the results.
Note: The numbers in the character table represent how many basis functions (atomic or molecular orbitals) transform under each irrep.
To determine which irrep corresponds to each symmetry operation in cis-Fe(CO)4Cl2, you need to apply the operations to the basis set of the molecule (atomic or molecular orbitals). This process involves solving a set of group theory equations using symmetry-adapted linear combinations (SALCs) of the basis functions.
Unfortunately, I cannot provide you with the character table without detailed molecular orbital information. However, please note that the character table you provided (4, 0, 0, 0, 0) does not seem to be correct.
To obtain an accurate character table for cis-Fe(CO)4Cl2, you may need to consult specialized software or textbooks on group theory.