Rotational Spectra Simplest Case: Diatomic or Linear Polyatomic molecule Rigid Rotor Model: Two nuclei joined by a weightless rod J = Rotational quantum number (J = 0, 1, 2, …) I = Moment of inertia = mr2 = reduced mass = m1m2 / (m1 + m2) r = internuclear distance m2 m1 r

Rigid Rotor Model In wavenumbers (cm-1): Separation between adjacent levels: F(J) – F(J-1) = 2BJ

Rotational Energy Levels Selection Rules: Molecule must have a permanent dipole. DJ = 1 J. Michael Hollas, Modern Spectroscopy, John Wiley & Sons, New York, 1992.

Rotational Spectra J” → J’ F(J’)-F(J”) 3 → 4 2(1.91)(4) 15.3 cm-1 4 → 5 2(1.91)(5) 19.1 cm-1 5 → 6 2(1.91)(6) 22.9 cm-1 6 → 7 2(1.91)(7) 26.7 cm-1 7 → 8 2(1.91)(8) 30.6 cm-1 8 → 9 2(1.91)(9) 34.4 cm-1 9 → 10 2(1.91)(10) 38.2 cm-1 J. Michael Hollas, Modern Spectroscopy, John Wiley & Sons, New York, 1992.

Intensity of Transitions cm-1 J. Michael Hollas, Modern Spectroscopy, John Wiley & Sons, New York, 1992.

Are you getting the concept? Calculate the most intense line in the CO rotational spectrum at room temperature and at 300 °C. The rigid rotor rotational constant is 1.91 cm-1. Recall: k = 1.38 x 10-23 J/K h = 6.626 x 10-34 Js c = 3.00 x 108 m/s

Account for the dynamic nature of the chemical bond: The Non-Rigid Rotor Account for the dynamic nature of the chemical bond: DJ = 0, 1 D is the centrifugal distortion constant (D is large when a bond is easily stretched) Typically, D < 10-4*B and B = 0.1 – 10 cm-1

More Complicated Molecules Still must have a permanent dipole DJ = 0, 1 K is a second rotational quantum number accounting for rotation around a secondary axis A.

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.

Infrared Spectroscopy Near Infrared: 770 to 2500 nm 12,900 to 4000 cm-1 Mid Infrared: 2500 to 50,000 nm (2.5 to 50 mm) 4000 to 200 cm-1 Far Infrared: 50 to 1000 mm 200 to 10 cm-1

Ingle and Crouch, Spectrochemical Analysis Infrared Spectroscopy: Vibrational Modes Ingle and Crouch, Spectrochemical Analysis

Group Frequencies Estimate band location: Pretsch/Buhlmann/Affolter/ Badertscher, Structure Determination of Organic Compounds

Are you getting the concept? Estimate the stretching vibrational frequency for a carbonyl group with a force constant, k, of 12 N/cm. If a C=S bond had the same force constant, where would its stretching band appear in the infrared absorption spectrum? Recall: 1 amu = 1.6605 x 10-27 kg 1N = 1 kg*m*s-2 Atomic masses C → 12.000 amu O → 15.995 amu S → 31.972 amu

Infrared Spectroscopy Near Infrared: 770 to 2500 nm 12,900 to 4000 cm-1 * Overtones * Combination tones * Useful for quantitative measurements Mid Infrared: 2500 to 50,000 nm (2.5 to 50 um) 4000 to 200 cm-1 * Fundamental vibrations * Fingerprint region 1300 to 400 cm-1 (characteristic for molecule as a whole) Far Infrared: 2.5 to 1000 um 200 to 10 cm-1 * Fundamental vibrations of bonds with heavy atoms (useful, e.g., for organometallics)

Example of an Overtone Wagging vibration at 920 cm-1. Overtone at approximately 2 x 920 cm-1 = 1840 cm-1.

Fermi Resonance N.B. Colthup et al., Introduction to Infrared and Raman Spectroscopy, Academic Press, Boston, 1990.

Example of a Fermi Resonance Stretching vibration of C-C=(O) at 875 cm-1. Overtone at approximately 2 x 875 cm-1 = 1750 cm-1 coincides with C=O stretch

Light Source: Globar Silicon Carbide Rod (5mm diameter, 50 mm long) Heated electrically to 1300 – 1500 K Positive temperature coefficient of resistance Electrical contact must be water cooled to prevent arcing Ingle and Crouch, Spectrochemical Analysis

Ingle and Crouch, Spectrochemical Analysis Sample Preparation for IR Spectroscopy Ingle and Crouch, Spectrochemical Analysis

Liquid Samples: Cell Thickness Ingle and Crouch, Spectrochemical Analysis

Ingle and Crouch, Spectrochemical Analysis Window and Cell Materials Ingle and Crouch, Spectrochemical Analysis

Solvents Pretsch/Buhlmann/Affolter/Badertscher, Structure Determination of Organic Compounds

Suspension Media for Solid Samples Pretsch/Buhlmann/Affolter/Badertscher, Structure Determination of Organic Compounds

Interferences Pretsch/Buhlmann/Affolter/ Badertscher, Structure Determination of Organic Compounds