# Solution to Inorganic Problem 3.25: Explaining D6h Symmetry of C6O6 2- Anion

• telethrow
In summary, the problem involves explaining why the anion C6O6 2- has the D6h symmetry based on the given IR and Raman absorptions. To solve this, the character table method is used to find the atom basis representation and break it down into irreducible representations using the D6h character table. Then, the direct product is taken with the vector representation in D6h symmetry to determine the symmetries of the vibrational modes. IR active modes transform like the coordinates, while Raman active modes transform like the quadratic combinations of the coordinates. This process may be tedious, but it is not difficult.
telethrow

## Homework Statement

I am trying to explain why an anion C6O6 2- would have the symmetry D6h. The problem gives you all of the IR and Raman absorptions and asks to explain why D6h is the proper symmetry for C6O6 2- anion.

For you reference the problem is 3.25 in "Inorganic Chemistry" written by Huhney(sorry if i spelled your name wrong)

## The Attempt at a Solution

Do you use character tables to figure this out? Or do I really have to go through the whole process of finding the irreducible set from the reducible set?

telethrow said:
Do you use character tables to figure this out? Or do I really have to go through the whole process of finding the irreducible set from the reducible set?
Yes and Yes.
The process is tedious, but not particularly difficult. First, figure out the characters of the representation in the atom basis. Break this down into irreducible representations using the D6h character table. Then, in order to figure out the symmetries of the vibrational modes of the molecule, you need to take the direct product of the atom basis representation with the vector representation in D6h symmetry. (The nice thing about using characters is that you can just multiply them directly). Finally, this will give you a collection of irreducible representations that correspond to the vibrational mode symmetries. The IR active modes are the ones that transform like the coordinates (because of the form of the dipole moment operator), and the Raman active modes transform like the quadratic combinations of the coordinates (because of the form of the polarizibility operator).

## 1. What is the D6h symmetry of the C6O6 2- anion?

The D6h symmetry of the C6O6 2- anion refers to the arrangement of its atoms and electrons in a six-fold rotational and reflection symmetry, with a hexagonal shape and six planes of symmetry.

## 2. How is the D6h symmetry of the C6O6 2- anion determined?

The D6h symmetry of the C6O6 2- anion is determined by analyzing its molecular structure and using symmetry operations, such as rotations, reflections, and inversions, to identify its symmetry elements and planes of symmetry.

## 3. What is the significance of the D6h symmetry of the C6O6 2- anion?

The D6h symmetry of the C6O6 2- anion is significant because it allows for efficient energy transfer and stability within the molecule, making it a key component in various chemical reactions and processes.

## 4. How does the D6h symmetry of the C6O6 2- anion relate to its properties?

The D6h symmetry of the C6O6 2- anion plays a crucial role in determining its physical and chemical properties, such as its electronic structure, reactivity, and spectroscopic behavior, as it affects the distribution and interactions of its electrons and atoms.

## 5. Can the D6h symmetry of the C6O6 2- anion be observed experimentally?

Yes, the D6h symmetry of the C6O6 2- anion can be observed experimentally through various techniques, such as X-ray crystallography, nuclear magnetic resonance spectroscopy, and infrared spectroscopy, which allow for the visualization and analysis of its molecular structure and symmetry elements.

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