How to assign symmetry to water molecule using D4h symmetry?

In summary, when an H2O molecule attacks Ni(CN)4 ^(2-) in square planar geometry with D4h symmetry, it would result in a complex with A2u symmetry. This is because the HOMO of the p orbital of H2O would have a p orbital and link to an irreducible representation in the D4h character table. However, when considering the operations of the complex, the numbers obtained do not correspond to any irreducible representations. This could be due to the water molecule lowering the symmetry of the complex to at least C2v, resulting in the p orbital having the same symmetry as in water alone.
  • #1
fangrz
38
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Could you explain why an H2O that attacks Ni(CN)4 ^(2-) (in square planar) (which has D4h symmetry) at one of the axial sites would have A2u symmetry? I know that the "HOMO" for the p orbital of the H2O would be a p orbital. I also tried to link that electron pair to an irreducible representation in the D4h character table.

Going across the row:

E 2C4 (z) C2 2C'2 2C''2 i 2S4 σh 2σv 2σd

I got the following numbers: +1, +1, +1, 0, 0, 0, 0, 0, +1, +1...which doesn't correspond with any of the irreducible representations. (When the H2O flips because of a C2' or C2'' rotation (and others...), it gives 0s. Was there something wrong in my approach? I used the metal center as the center for all operations.
 
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  • #2
The water molecule would lower the symmetry of the complex to at least C2v. Then the p orbital has simply the symmetry it has in water alone.
 

FAQ: How to assign symmetry to water molecule using D4h symmetry?

How do you determine the symmetry of a water molecule?

To determine the symmetry of a water molecule, one must consider the molecular structure and the arrangement of its atoms. In the case of water, it has a bent structure with two hydrogen atoms bonded to a central oxygen atom. This structure falls under the D4h symmetry group due to its four C2 axes and four mirror planes.

What is D4h symmetry?

D4h symmetry is a point group symmetry that describes objects with four-fold rotational symmetry and four mirror planes of symmetry. It is also known as the dihedral group of order 8 and is commonly found in molecules with tetrahedral or square planar structures.

How do you assign D4h symmetry to a water molecule?

To assign D4h symmetry to a water molecule, one must first identify its molecular structure and determine its symmetry elements. In the case of water, it has four C2 axes and four mirror planes. These symmetry elements correspond to the D4h point group, thus assigning D4h symmetry to the molecule.

What are the benefits of knowing the symmetry of a water molecule?

Knowing the symmetry of a water molecule allows scientists to predict its physical and chemical properties. It also helps in understanding the molecule's behavior and interactions with other molecules. Additionally, symmetry plays a crucial role in spectroscopy and crystallography studies.

Can a water molecule have other types of symmetry?

Yes, a water molecule can have other types of symmetry, depending on its molecular structure and arrangement of atoms. For example, a water molecule in a linear structure would have C∞v symmetry, while a water molecule in a trigonal planar structure would have C3v symmetry. However, the most common and stable form of a water molecule is in the bent structure, which has D4h symmetry.

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