# 4.P: Problems (under construction)

$$\newcommand{\vecs}{\overset { \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$

## Problems

1. Chlorophyll a is a green pigment that is found in plants. Its molecular formula is C55H77O5N4Mg. How many degrees of freedom does this molecule possess? How many vibrational degrees of freedom does it have?
2. CCl4 was commonly used an as organic solvent until its severe carcinogenic properties were discovered. How many vibrational modes does CCl4 have? Are they IR and/or Raman active?
3. The same vibrational modes in H2O are IR and Raman active. WF6- has IR active modes that are not Raman active and vice versa. Explain why this is the case.
4. How many IR peaks do you expect from SO3? Estimate where these peaks are positioned in an IR spectrum.
5. Calculate the symmetries of the normal coordinates of planar BF3.

1. chlorophyll has 426 degrees of freedom, 420 vibrational modes
2. The point group is Td, Tvib = a1 + e + 2t2, a1 and e are Raman active, t2 is both IR and Raman active
3. For molecules that possess a center of inversion i, modes cannot be simultaneously IR and Raman active
4. Point group is D3h, one would expect three IR active peaks. Asymmetric stretch highest (1391 cm-1), two bending modes (both around 500 cm-1). The symmetric stretch is IR inactive
5. T3N = A1' + A2' + 3E' + 2 A2" + E" and Tvib= A1' + 2E' + A2"

• Kristin Kowolik, University of California, Davis

## Problems

1. Water molecule H2O was used as an example and was mentioned that water was rotated 180 degree around an axis bisecting the oxygen, then the molecule was superimposable on the original water molecule, how about CO2? Is it going to be like the water molecule since CO2 also has 2 atoms of oxygen.

Of course not, because every molecule has different molecular shape. To recognize the symmetry of any molecule the structure and the molecular shape of that molecule should be defined. The water molecule is bent but CO2 is not, and if CO2 is rotated 360 degree around the axis bisecting the C atom then it can be superimposed on the original molecule. We then see the symmetry for the CO2.

2. Why should all of the five symmetry elements be done on a molecule in order to find the point group the molecule belongs to, why is performing only one or two of the symmetry elements not enough for recognizing the point group?

One or two of the symmetry elements will not be able to tell us everything about the molecule's symmetry since those one or two properties do not tell us everything about the molecule. Also, while different molecules may have one or two symmetrical properties in common, the five properties will not be the same for all molecules.

3. What does the symbol Cn stand for and what does n represent? Why is it important to identify n?

C is the axis of rotation and n is the order of the axis.

4. How are the character tables helpful?

The character table tells us about all the operational elements performed on the molecule and indicates if we have forgotten to perform any of the symmetry elements. The tables serve as a checklist because all the operational elements should be done on the molecule in order to find the point group of the molecule.

5. Why is important to find symmetry in molecules?

Symmetry tells us about bounding for that molecular bonding.

4.P: Problems (under construction) is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.