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).

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.

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

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

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

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

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. Band Location Species/Transition 2096 cm-1 2101 cm-1 2903 cm-1 2906 cm-1 4133 cm-1 4139 cm-1 5681 cm-1 5685 cm-1 Atomic masses H → 1.0079 amu D → 2.0136 amu 35Cl → 34.9689 amu 37Cl → 36.9659 amu

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

Only those that have a change in dipole moment are seen in IR. 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

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

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