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Vibrational Transitions

Vibrational Transitions. Simplest Case: Diatomic Molecule. Harmonic Oscillator Model: Two atoms connected by a spring. in Joules. in cm -1. v = vibrational quantum number (v = 0, 1, 2, …) n = classical vibrational frequency. k = force constant (related to the bond order).

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Vibrational Transitions

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  1. Vibrational Transitions Simplest Case:Diatomic Molecule Harmonic Oscillator Model:Two atoms connected by a spring. in Joules in cm-1 v = vibrational quantum number (v = 0, 1, 2, …) n = classical vibrational frequency k = force constant (related to the bond order).

  2. Vibrational Energy Levels • Selection Rules: • Must have a change in dipole moment (for IR). • 2) Dv = 1 J. Michael Hollas, Modern Spectroscopy, John Wiley & Sons, New York, 1992.

  3. Anharmonicity Selection Rules: Dv = 1, 2, 3, … Dv = 2, 3, … are called overtones. Overtones are often weak because anharmonicity at low v is small. Ingle and Crouch, Spectrochemical Analysis

  4. Rotation – Vibration Transitions The rotational selection rule during a vibrational transition is: DJ = 1 Unless the molecule has an odd number of electrons (e.g. NO). Then, DJ = 0, 1 Bv signifies the dependence of B on vibrational level

  5. Rotation – Vibration Transitions If DJ = -1 P – Branch If DJ = 0 Q – Branch If DJ = +1 R – Branch Ingle and Crouch, Spectrochemical Analysis

  6. Rotation – Vibrational Spectra Why are the intensities different? J. Michael Hollas, Modern Spectroscopy, John Wiley & Sons, New York, 1992.

  7. Are you getting the concept? In an infrared absorption spectrum collected from a mixture of HCl and DCl, there are eight vibrational bands (with rotational structure) centered at the values listed below. Identify the cause (species and transition) for each band. Atomic masses H → 1.0079 amu D → 2.0136 amu 35Cl → 34.9689 amu 37Cl → 36.9659 amu

  8. Raman Spectra Selection Rule: DJ = 0, 2 J. Michael Hollas, Modern Spectroscopy, John Wiley & Sons, New York, 1992.

  9. Polyatomics If linear  (3N – 5) vibrational modes (N is the # of atoms) If non-linear  (3N – 6) vibrational modes Only those that have a change in dipole moment are seen in IR. http://jchemed.chem.wisc.edu/JCEWWW/Articles/WWW0001/index.html

  10. Linear Polyatomic How many vibrational bands do we expect to see? J. Michael Hollas, Modern Spectroscopy, John Wiley & Sons, New York, 1992.

  11. Nonlinear Polyatomic (Ethylene) J. Michael Hollas, Modern Spectroscopy, John Wiley & Sons, New York, 1992.

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