CHEM 370 | Week 8

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<h1 style = "text-align: left; font-weight: bold; margin-left: 175px;">Week 8: Spectroscopy Theory</h1>
<h5 style = "text-align: left; font-weight: bold; margin-left: 175px;">Harvey Ch 10</h5>
<img src="img/chapter-10/energy-levels-abs-ems.png" style = "margin-left: auto; margin-right: auto; display: block; height: 300px;">

.image-credit[David Harvey / [Analytical Chemistry 2.1](https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Book%3A_Analytical_Chemistry_2.1_%28Harvey%29) / [CC BY-SA 4.0](https://creativecommons.org/licenses/by-sa/3.0/at/deed.en)]

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# Types of Spectroscopy

*We could also divide these into **vibrational** and **electronic** spectroscopy.*

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# Why do Chemicals Absorb (UV-visible) Light?

Short answer:

1. There must be a mechanism by which the analyte interacts with the magnetic or electric field of the radiation (valence electrons).
1. Energy of absorbed photon ($E$) must exactly equal the difference in energy between two of the analyte’s quantized energy states ($\Delta E$).

Here are the **selection rules**:

1. *Energy selection rule:* Energy of absorbed photon must match the difference in energy between quantized states of atom or molecule.
2. *Spin selection rule:* Electronic transition cannot change the net spin multiplicity of the molecule. (i.e. forbidden if there is a change in paired/unpaired electons)
3. *LaPorte selection rule:* Transitions between orbitals of the same symmetry (parity) are forbidden.
4. *Frank-Condon rule:* Symmetry of ground state and excited state must overlap.

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# Transitions that Lead to Absorption

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# UV-vis: Electronic Transitions

*IR spectroscopy involves vibrational and rotational energy states.*

> **Chromophore:** A bond or functional group that gives rise to absorption.

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# UV-vis: Electronic Transitions

.image-credit[[chem.ucla.edu](https://www.chem.ucla.edu/~bacher/UV-vis/uv_vis_tetracyclone.html.html)]
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# UV-vis: Electronic Transitions

.image-credit[[chemistry.msu.edu](https://www2.chemistry.msu.edu/faculty/reusch/virttxtjml/spectrpy/uv-vis/spectrum.htm)]

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# Molecular Structure Lead to Color

- As unsaturation increases, a molecule is more likely to absorb UV-vis radiation. (more $\pi \rightarrow \pi^{*}$ transitions)

.image-credit[[chemistry.msu.edu](https://www2.chemistry.msu.edu/faculty/reusch/virttxtjml/spectrpy/uv-vis/spectrum.htm)]

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# Molecular Structure Lead to Color

- Lone pairs and and double bonds (from heteroatoms) act as chromophores. (more $n \rightarrow \pi^{\*}$ and $\pi \rightarrow \pi^{\*}$ transitions)

.image-credit[[chemistry.msu.edu](https://www2.chemistry.msu.edu/faculty/reusch/virttxtjml/spectrpy/uv-vis/spectrum.htm)]

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# Molecular Structure Lead to Color

- As conjugation increases, absorption bands are red-shifted, called **bathochromic shift**. (bigger "box": $E\_n = \frac{h^2n^2}{8ma^2}$)

.image-credit[[chemistry.msu.edu](https://www2.chemistry.msu.edu/faculty/reusch/virttxtjml/spectrpy/uv-vis/spectrum.htm)]

???

h = Planck's constant
n = + whole number for quantum state
m = mass
a = length of "box"

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# Molecular Structure Lead to Color

- Although $\sigma$-bonds do absorb light, it is typically < 200nm and therefore not detectable in traditional UV-vis.

.image-credit[[Mainz Spectral Atlas](http://satellite.mpic.de/spectral_atlas/cross_sections/Alkanes+alkyl%20radicals/Alkanes/C2H6.spc)]

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# Vibronic Transitions

Molecular UV-vis actually measures superimposed electronic and vibrational (vibronic) transitions.  Thus the broad features.

.image-credit[[NIST Chemistry WebBook](https://webbook.nist.gov/cgi/inchi?ID=C486259&Mask=400#UV-Vis-Spec)]

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# Vibronic Transitions

Molecular UV-vis actually measures superimposed electronic and vibrational (vibronic) transitions.  Thus the broad features.

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# IR: Vibrational Spectroscopy

- Remember that molecules are constantly stretching, bending, twisting, rocking, scissoring, wagging 
- This occurs at a defined (quantized) frequency (energy).

???

[Nice GIF on Wikipedia](https://en.wikipedia.org/wiki/Infrared_spectroscopy#Number_of_vibrational_modes)

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# IR: Vibrational Spectroscopy

- Smaller $\Delta E$ than electronic transitions (UV-vis)
- Narrower features than UV-vis (no electronic excitation)
- **Fundamental:** $\Delta \nu = 1$
- **Overtones:** $\Delta \nu = 2, 3, ...$

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# IR: Selection Rules

- A **linear molecule** has (max) $3N-5$ vibrational modes.
- A **non-linear molecule** has (max) $3N-6$ vibrational modes.
- Not all modes lead to absorption.
- Must have net dipole moment.

## Example: Carbon Dioxide

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# IR: Selection Rules

- A **linear molecule** has (max) $3N-5$ vibrational modes.
- A **non-linear molecule** has (max) $3N-6$ vibrational modes.
- Not all modes lead to absorption.
- Must have net dipole moment.

## Example: Carbon Dioxide

.image-credit[[NIST Chemistry WebBook](https://webbook.nist.gov/cgi/inchi?ID=C486259&Mask=400#UV-Vis-Spec)]

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# IR: Selection Rules

- A **linear molecule** has (max) $3N-5$ vibrational modes.
- A **non-linear molecule** has (max) $3N-6$ vibrational modes.
- Not all modes lead to absorption.
- Must have net dipole moment.

## Example: Nitrogen

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# IR: Selection Rules

- A **linear molecule** has (max) $3N-5$ vibrational modes.
- A **non-linear molecule** has (max) $3N-6$ vibrational modes.
- Not all modes lead to absorption.
- Must have net dipole moment.

## Example: Water
<img src="https://upload.wikimedia.org/wikipedia/commons/b/b7/H2O_2D_labelled.svg" style = "margin-left: auto; margin-right: auto; display: block; width: 400px;">

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# Bond Types and Substituents Determine IR "Color"

Chemical bonds may be considered springs (harmonic oscillator) with a mass on each end:

$$f = \frac{1}{2\pi}\sqrt{\frac{k}{m}}$$

For chemical bonds this becomes:

$$\overline{\nu} = \frac{1}{2 \pi c}\sqrt{\frac{k}{\mu}}$$

where $\mu$ is the *reduced mass*:

$$\mu = \frac{m\_A m\_B}{m\_A + m\_B}$$

.image-credit[Svjo via [Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Mass-spring-system.png) / [CC BY-SA 3.0](https://creativecommons.org/licenses/by-sa/3.0/at/deed.en)]

???

- k is a spring constant, unique to each bond type
- $\mu$ is the mass attached to the spring

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.image-credit[[NIST Chemistry WebBook](https://webbook.nist.gov/cgi/inchi?ID=C486259&Mask=400#UV-Vis-Spec)]

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# What happens after absorption?

$$\Delta E \ E\_2 - E\_1$$

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# What happens after absorption?