CHEM 515Spectroscopy

Vibrational Spectroscopy I

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Rotational, Vibrational and Electronic Levels

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Molecular Vibrations of CO2

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Harmonic Oscillator Approximation

Selection rule

Δv = ± 1

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Harmonic Oscillator Approximation

• At lower energies, the harmonic oscillator model determines the quantum levels quite well. Deviations become more significant at higher energy levels.

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Types of Potential Function Curves

V V

R R

Dissociatve

Non-dissociatve

1330 cm-1 667 cm-1

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Force Constant

• The force constant is a measure of the strength of the spring (or chemical bond) connecting two particles.The force constants is proportional to the bond order.

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Anharmonicity

• Deviations due to anharmonicity become more clear at – higher energy

levels (v), and

– larger x = r – re values that correspond to dissociation.

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Anharmonicity

• Electrical anharmonicity: (electrical properties, dipole moment and polarizability).

• Mechanical anharmonicity: (nature of molecular vibration).

Selection rule because of the effect of anharmonicity:

Δv = ± 1, ± 2, ± 3, …

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Types of Vibrational Transitions

• The intensity of Δv= ±1 transitions is stronger than that for Δv= ±2, ±3, … transitions.

• Both electrical and mechanical anharmonicity contribute to the intensities of Δv= ±2, ±3, … transitions.

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Vibrational Spectrum of HCl

ν (cm-1)

v

Vibrational spectrum of HCl is based on the harmonic oscillator model with ωe = 2989 cm-

1.

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Vibrational Spectrum of HCl

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Vibrational Spectrum of HCl

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Vibrational Spectrum of HCl

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Morse Potential

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Morse Potential

• It is a better approximation for the vibrational structure of the molecule than the quantum harmonic oscillator because it explicitly includes the effects of bond breaking, such as the existence of unbound states.

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Morse Potential

• It also accounts for the anharmonicity of real bonds and the non-zero transition probability for overtones and combinations.

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Morse Potential

• Morse function is not well behaved where r 0 or x – re . Although V(x) becomes large but is doesn’t go to infinity.

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Dissociation Energy from Spectroscopic Data

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Birge-Sponer Diagram

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Birge-Sponer Diagram

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Vibration-Rotation Spectra

Energy increases

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Vibration-Rotation Spectra

Infrared spectrumΔJ = ±1

Raman spectrumΔJ = 0 , ±2

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Vibration-Rotation Infrared Spectrum of HCl

• νvib is different for H35Cl and H37Cl molecules due to the slight difference in their reduced masses.

au

au

972.036

35ClH35

974.038

35ClH37

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Vibration-Rotation Infrared Spectrum of HCl

• The lines due to H35Cl transitions are more intense because the isotopic abundance ration of H35Cl to H37Cl molecules is 3:1.

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Vibration-Rotation Infrared Spectrum of HCl

B2B2B2B2 B2 B2 B2 B2B4

Band centerH35Cl

Band centerH37Cl

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Vibration-Rotation Infrared Spectrum of HCl

• The rotational constant B slightly decreases as going to higher vibrational levels. This results in decrease of the gaps between transition lines as one goes to higher frequencies.

B2B2B2B2 B2 B2 B2 B2B4

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Vibration-Rotation Infrared Spectrum of HCl

• The rotational constant B slightly decreases as going to higher vibrational levels. This results in decrease of the gaps between transition lines as one goes to higher frequencies.

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Vibration-Rotation Infrared Spectrum of HCl

B2B2B2B2 B2 B2 B2 B2B4Approximation of B

values

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Vib-Rot Infrared Spectrum of Nitric Oxide

• Exceptions to the infrared ΔJ ≠ 0 selection rule are found for some diatomic molecules such as NO.

Q-branch

P-branch

R-branch

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Vib-Rot Infrared Spectrum of the DCl Molecule

• νvib(HCl) > νvib(DCl) because of the differences in force constants and reduced massed between the two molecules.

• B0 = 5.392263 cm-1

B1 = 5.279890 cm-1

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Raman Stokes and Anti-Stokes Transitions

v

v

v

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Rot-Vib Raman Spectrum of Carbon Oxide

• Selection rule for Raman transitions in diatomic molecules is ΔJ = 0, ±2.

B4B4

B12

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Gross Selection Rule of Infrared Vibrational Spectroscopy

• The gross selection rule for infrared vibrational spectroscopy states that electric dipole moment of the molecule must change when the atoms are displaced.

• The molecule need NOT to have permanent dipole moment in order to be infrared active.