Vibrational Spectroscopy I CHEM 515 Spectroscopy Vibrational Spectroscopy I

Rotational, Vibrational and Electronic Levels

Molecular Vibrations of CO2

Harmonic Oscillator Approximation Selection rule Δv = ± 1

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

Types of Potential Function Curves 1330 cm-1 667 cm-1 V V R R Dissociatve Non-dissociatve

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.

Anharmonicity Deviations due to anharmonicity become more clear at higher energy levels (v), and larger x = r – re values that correspond to dissociation.

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, …

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.

Vibrational Spectrum of HCl Vibrational spectrum of HCl is based on the harmonic oscillator model with ωe = 2989 cm-1. v ν (cm-1)

Vibrational Spectrum of HCl

Vibrational Spectrum of HCl

Vibrational Spectrum of HCl

Morse Potential

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.

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

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.

Dissociation Energy from Spectroscopic Data

Birge-Sponer Diagram

Birge-Sponer Diagram

Vibration-Rotation Spectra Energy increases

Vibration-Rotation Spectra Infrared spectrum ΔJ = ±1 Raman spectrum ΔJ = 0 , ±2

Vibration-Rotation Infrared Spectrum of HCl νvib is different for H35Cl and H37Cl molecules due to the slight difference in their reduced masses. au

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.

Vibration-Rotation Infrared Spectrum of HCl Band center H35Cl Band center H37Cl

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.

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.

Vibration-Rotation Infrared Spectrum of HCl Approximation of B values

Vib-Rot Infrared Spectrum of Nitric Oxide R-branch P-branch Q-branch Exceptions to the infrared ΔJ ≠ 0 selection rule are found for some diatomic molecules such as NO.

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

Raman Stokes and Anti-Stokes Transitions v v v

Rot-Vib Raman Spectrum of Carbon Oxide Selection rule for Raman transitions in diatomic molecules is ΔJ = 0, ±2.

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.