Chemistry 2000 Slide Set 4: Molecular spectroscopy of diatomic - - PowerPoint PPT Presentation

Chemistry 2000 Slide Set 4: Molecular spectroscopy of diatomic molecules

Marc R. Roussel January 7, 2020

Marc R. Roussel Spectroscopy of diatomics January 7, 2020 1 / 20

Evidence for MO theory

Evidence for MO theory

How do we know that MO theory is correct? Equilibrium bond lengths: X-ray or neutron diffraction for solids Rotational (microwave) or vibrational (infrared) spectroscopy for gases Potential energy curve/surface: Vibrational (infrared) spectroscopy Orbital energy diagram: Photoelectron spectroscopy Electronic absorption (UV/visible) spectroscopy Fluorescence spectroscopy

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Effective potential

The effective potential

• 6
• 4
• 2

2 4 6 1 2 3 4 5 6 Veff R

The shape of the effective potential implies that a molecule below its dissociation energy vibrates, i.e. a diatomic molecule behaves like two balls connected by a spring.

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Effective potential

Quantization of vibrational energy

Vibrational energy is quantized, i.e. only certain vibrational energies are allowed:

E vibrational levels R

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Effective potential

The effective potential: interpretation

Req = bond length Veff R Nuclear-nuclear repulsion Long-range attraction due to electron-nucleus interaction Zero-point energy Dissociation energy Marc R. Roussel Spectroscopy of diatomics January 7, 2020 5 / 20

Infrared spectroscopy

Vibrational levels

E R

Stronger bond ← → narrower potential well ← → larger vibrational spacing

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Infrared spectroscopy

Infrared (vibrational) spectroscopy

Heteronuclear diatomics can absorb photons to undergo vibrational transitions. Homonuclear diatomics cannot make a vibrational transition by absorbing a single photon. (The basis for this rule will be seen later.) At room temperature, almost all molecules are in the ground vibrational state. By far the most likely process is the absorption of a photon to go from the ground state to the first excited vibrational state. Vibrational energy spacings correspond to the infrared region of the electromagnetic spectrum.

Marc R. Roussel Spectroscopy of diatomics January 7, 2020 7 / 20

Infrared spectroscopy

Infrared (vibrational) spectroscopy

E

E R

∆ h ν ∼

vib

infrared =

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Infrared spectroscopy

Summary of IR spectroscopy

IR spectroscopy gives us information about the strength of a chemical bond: Stronger bond ← → higher-energy (shorter wavelength) IR absorption The strength of the bond and spacing between vibrational levels are connected to the shape of the potential energy curve near the equilibrium bond length.

Marc R. Roussel Spectroscopy of diatomics January 7, 2020 9 / 20

Units

Units in spectroscopy

The energy of a photon is given by E = hν = hc λ SI units of E: Units of ν: Units of λ: Photon energies are sometimes given in electron-volts (eV): 1 eV = 1.602 176 634 × 10−19 J

Marc R. Roussel Spectroscopy of diatomics January 7, 2020 10 / 20

Units

Units in spectroscopy

Wavenumbers

If we define the wavenumber ˜ ν = 1/λ, E = hc˜ ν

˜ ν is often expressed in cm−1.

˜ ν is often casually referred to as a frequency, to which wavenumber is proportional: ν = c˜ ν

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Photoelectron spectroscopy

Photoelectron spectroscopy

How do we know that the orbital occupancies predicted by MO theory are correct? Photoelectron spectroscopy is similar in principle to the analysis of the photoelectric effect. An atom or molecule is ionized using a photon of energy hν. The maximum kinetic energy of the ejected electron is then Kmax = hν − Ii where Ii is the ionization energy of an electron in orbital i. Note: The notation for ionization energy differs from that used in Chem 1000. The ionization energy of an electron in a particular orbital is the negative of its orbital energy (εi). We measure K and calculate the orbital energy of occupied orbitals: −Ii = εi = Kmax − hν

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Photoelectron spectroscopy

Photoelectron spectroscopy (continued)

Removing a valence electron typically requires a photon in the ultraviolet range. Removing a core electron typically requires an x-ray photon.

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Photoelectron spectroscopy

Example: Photoelectron spectrum of Ne

0.1 0.2 0.3 0.4 0.5 0.6 0.7 10 20 30 40 50 60 10 20 30 40 50 60 Intensity I/eV K/eV hν = 60 eV 2s 2p

Orbital energy level diagram? Rotate clockwise!

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Photoelectron spectroscopy

A complication

For molecules, the ion formed also has vibrational levels. As a result, the photoelectron spectrum typically has vibrational substructure:

X2 e− E R X2

+

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Photoelectron spectroscopy

Instead of one ionization energy, the photoelectron spectrum gives us a band of several lines corresponding to the ionization of an electron from a particular orbital.

Evib(X2)

+

∆ Intensity Ii "ionization energy": X2 produced in its vibrational ground state

The photoelectron spectrum thus allows us to recover the vibrational spectrum of the ion formed.

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Photoelectron spectroscopy

We compare the vibrational spectrum of the molecule to that of the ion. The way in which the vibrational spectrum changed tells us how the potential energy curve changed, and thus how the bonding changed. This can be correlated to the MO diagram:

Removing an electron from an orbital not directly involved in bonding (e.g. the 1π orbital in HF) won’t change the vibrational spectrum much. Removing an electron from a bonding orbital will lead to a weaker bond in the ion, thus to lower vibrational frequencies for the associated normal mode(s) than in the parent molecule. Removing an electron from an antibonding orbital. . .

Marc R. Roussel Spectroscopy of diatomics January 7, 2020 17 / 20

Photoelectron spectroscopy

Example: UV photoelectron spectrum of N2

5 10 15 20 25 30 35 40 15 16 17 18 19 20 2150 cm-1 3σ 1860 cm-1 1π 2390 cm-1 2σ* Intensity I/eV

Note: The vibrational “frequency” of N2 is 2358 cm−1.

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Photoelectron spectroscopy

Additional hints for interpreting photoelectron spectra

Orbitals that are strongly bonding/antibonding will produce a number

• f lines.

(See the 1π orbital in the photoelectron spectrum of N2.) A strictly nonbonding orbital would produce exactly one line. Orbitals that are weakly bonding/antibonding tend to produce a small number of lines, often with the line at lower ionization energy being much more intense.

5 10 15 20 25 30 35 40 15 16 17 18 19 20 2150 cm-1 3σ 1860 cm-1 1π 2390 cm-1 2σ* Intensity I/eV

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Photoelectron spectroscopy

Example: UV photoelectron spectrum of CO

500 1000 1500 2000 15 16 17 18 19 20 21 1662 cm-1 2σ 1636 cm-1 1π Intensity I/eV

Note: The vibrational frequency of CO is 2170 cm−1.

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