Molecular Spectroscopy

Attila Cangi

COSMOS (summer 2008) lecture:

Etymology: Spectro-scopy

First of all, what is a spectrum?

In science it means range or spread of a certain quantity.

In our context: Range of frequencies or wavelengths.

What is spectroscopy?

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(lat.) specere: to look at, to view (gr.) skopein: examine

Example: The Electromagnetic Spectrum

Planck’s relation: Relation between energy,frequency, and wavelength.

What is spectroscopy?

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E = h! = hc

"

Planck’s constanth :Max Planck (1918)

Separation of light by a glass prism.

Invention of the spectroscope (1859)

What is spectroscopy?

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Isaac Newton

G. R. Kirchhoff and W. E. Bunsen

Light of different wavelengths travels at different speeds

through a medium (here glass).

A rainbow on the sky appears because of that reason.

With a spectroscope the light falling on a prism can be analyzed

more accurately.

Bunsen-Kirchhoff spectroscope

Spectroscopy is the study of experimentally obtained spectra.

We distinguish emission and absorption spectra.

Now, we know the answer!

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Stimulated emission. Stimulated absorption. Spontaneous emission.

Example: Spectrum of the Sun

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Example: Spectrum of the Sun

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Joseph von Fraunhofer observes the spectrum of the Sun.

Atoms in the atmosphere of the sun absorb energy of specific

wavelengths.-> Sharp, dark absorption lines.

We can identify, which atoms are responsible for the absorption

lines by comparison.

Spectroscopy is a useful tool to identify and analyze atoms, molecules, and functional groups in molecules.

Let’s review some basic concepts about molecules before we go into more detail.

What is spectroscopy?

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Spectroscopy

Absorption/Emission Raman (scattering)

Apply Born-Oppenheimer approximation.

Hence, electrons find their lowest energy state for each nuclear configuration.

Imagine electrons connecting the nuclei by springs.

Molecular Vibrations

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me ! mnuc " Te =p2

2me# p2

2mnuc= Tnuc

Harmonic approximation:

In quantum mechanics:

Molecular Vibrations

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F = !kx

V =12kx2

Spring model

Quantum harmonic oscillator

In contrast to the classical harmonic

oscillator, the energy levels in a quantum

oscillator are quantized.

E(n) = (n +12)!!

Anharmonic approximation:

Molecular Vibrations

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Real molecules are not idealized systems.When the spring is compressed or

expanded beyond certain limit Hooke’s law does not apply. (E.g., in case of dissociation)We have to consider anharmonic terms.

E(n) = (n + 1/2)!!

+ (n + 1/2)2!xe

+ (n + 1/2)3!ye + . . .

xe, ye : Anharmonicity constants.

Polyatomic molecules have many different ways to vibrate, i.e., many vibrational modes.

Example: Benzene

Molecular Vibrations

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m = 3N ! 6= 3N ! 5

N is the number of atoms.(if molecule is linear.)

Molecular rotationsRigid-Rotor approximation:

Rotational energy levels:

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Consider bonds between nuclei as rigid rods, and hence, the entire

molecule as a rigid rotor.

E(J) =h2

8!2IJ(J + 1)

Moment of inertia

Rotational quantum numberJ :I :

Molecular rotationsNon-rigid rotors:

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If the speed of rotation is getting high the rigid-rotor

approximation is no longer valid, why?

Because the spring-like bonds expand due to centrifugal forces.

This effect is called centrifigual distortion.

What have we discussed so far?Our notion of molecular structure:

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The internal energy can be divided into several degrees of

freedom; the electronic, vibrational, and rotational.

Transistions for these different degrees of freedom have

different energies.

The order is:Electronic > Vibrational >

Rotational

E = Ee + Evib + Erot

Obtaining SpectraAbsorption spectroscopy

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Obtaining SpectraAbsorption spectroscopy: Beer-Lambert law

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The Beer-Lambert law tells us the concentration of the substance in the sample cell.

A = log10(I0/I)

A = ! c l

Absorbance (degree of absorption)A :

c :! : Absorption coefficient

Concentration of substance

Obtaining SpectraRaman spectroscopy:

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Neither emission, nor absorption, but scattering of radiation by the sample.

Small portion of the scattered light is of slightly increased or decreased wavelength. -> Raman scattering.

Lasers are used as a source of radiation.

Example 1Molecular structure from rotational spectrum

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From the spectrum we obtain the rotational constant B, which is related to the moment of inertia:

From the moment of inertia we obtain the bond length:

reduced mass.

I =h

8!2B

I = µ r2

µ :

Part of the rotational spectrum of hepta-2,4,6-triynenitrile.

Example 2Group vibrations: Identify functional groups

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Each functional group has a specific vibrational frequency.

By recording the vibrational spectrum we can identify certain functional groups in a particular

sample.

Imagine an organic synthesis.If at a certain stage a particular functional group is produced (e.g.,

CO-group), with vibrational spectroscopy we can determine whether this particular group is present. Hence, we know whether a certain chemical reaction has

occurred.

Example 3Beer-Lambert law:

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If the molar absorption coefficient at a particular

wavelength is known, we can determine the concentration of a sample by recording its electronic spectrum, i.e., by measuring the

its absorbance.

Electronic spectra also indicate the presence of groups within a molecule, since certain groups

have a particular signature in the recorded spectrum.

Near-UV absorption spectrum of penta-1,3-diene in solution in heptane

What have we learned?Spectroscopy is a useful tool to identify and analyze the structure of molecules.

Rotational spectroscopy: Bond lengths.

Vibrational spectroscopy: Identify atoms, molecules, or functional groups.

Beer-Lambert law: Determine concentration ofa substance.

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