Chemistry 125: Lecture 57 March 3, 2010 Normal Modes: Mixing and Independence in Infrared Spectroscopy This For copyright notice see final page of this file

Possibility of effective independence Coupled Oscillators illustrate: Complexity “Normal” mode analysis Phase of mixing

Coupled Oscillators Simple   2 = f/m

Coupled Oscillators Coupled to Frozen Partner   2 = (f+s)/m Simple   2 = f/m

Coupled Oscillators In-Phase Coupling   2 = 2f/2m = f/m SimpleCoupled to Frozen Partner   2 = (f+s)/m   2 = f/m

Coupled Oscillators   2 = 2(f+2s)/2m = (f+2s)/m Out-of-Phase Coupling SimpleCoupled to Frozen Partner In-Phase Coupling   2 = (f+s)/m   2 = f/m   2 = 2f/2m = f/m ip oop coupled isolated In such “Normal” Modes all atoms have same frequency

oop ip oop + ip Coupled Oscillators Superposition of Two Normal Modes of different frequency Vibration switches between oscillators as the two modes beat in- and out-of-phase Out-of-Phase Coupling In-Phase Coupling In such “Normal” Modes all atoms have same frequency   2 = 2(f+2s)/2m = (f+2s)/m   2 = 2f/2m = f/m

ip oop Very Different Oscillators are ~Independent Vibration remains localized when coupling is weak compared to  -mismatch ip oop coupled low  high  oop + ip

A General Molecule of N Atoms has 3N Independent Geometric Parameters. (e.g. as Cartesian Coordinates) or 3 to Fix Center of Mass 3 to Fix Orientation 3N-6 for Internal Vibrations (Normal Modes)

3N-6 Mixed-up Normal Modes sounds hopelessly complex. (though good for “fingerprint”) (Cf. Energy-match / Overlap) but mixing requires: Frequency Match & Coupling Mechanism ip oop coupled isolated

Butane C 4 H 10 3 x (4 + 10) = 42 degrees of freedom - 3 (translation) - 3 (rotation) = 36 vibrations C 4 : 3 stretch, 2 bend, 1 twist 10 C-H : 10 stretch, 20 bend or twist Mixed (according to frequency-match / coupling) into 36 normal modes.

C 8 Straight Chain Hydrocarbons Octane C 8 H 18 C-H stretch C-CH 3 umbrella + C-C stretch CH 2 rock CH 2 wag CH 2 scissors 26 atoms  72 normal modes (not all IR active) C-H stretch “Breathing” gives no net dipole change - no IR peak Half of C 4 H 10 ’s ten C-H stretch normal modes have no “handle” E(t) helps push 8 H in and out E(t) helps push 4 H up and down Timint has been disabled on this slide so you can step back and forth with the arrow keys to study vibrational modes.

C 8 Straight Chain Hydrocarbons Octane C 8 H 18 4-Octyne1-Octyne Why not in 4-octyne? CCH sp CCH CC (symmetric compound has no handle) Functional Group Identification Timing has been disabled on this slide so you can step back and forth with the arrow keys to study vibrational modes.

C 8 Straight Chain Hydrocarbons Octanetrans-4-Octenecis-4-Octene 2-Methyl-2-Hexene CC dipole change (weak) Functional Group Identification

Twist reduces  overlapFolding preserves  overlap 967 cm cm -1 hardereasier 828 cm -1 IR Active out-of-plane C-H bending (paired H atoms move in the same direction) Timing has been disabled on this slide so you can step back and forth with the arrow keys to study vibrational modes.

The Jewel in the Crown of Infrared Spectroscopy

1681 CH 3 C O NH 2 CH 3 -C=O(X) strong & independent 1727 CH 3 C O H 1715 CH 3 C O CH 3 CH 3 C O OCH CH 3 C O Cl n N  * C=O n O  * C-Cl n O  * C-OMe :: : C=O weakened by resonance C=O strengthened by resonance

1683?1618 CH 3 C O CH=CH CH 3 C O NH 2 CH 3 -C=O(X) strong & independent 1727 CH 3 C O H 1715 CH 3 C O CH 3 CH 3 C O OCH CH 3 C O Cl n N  * C=O n O  * C-Cl n O  * C-OMe + - C=O weakened by resonance C=O strengthened by resonance C=O C=C coupling out-of-phase mostly C=O Double ! in-phase mostly C=C But strong peak is at higher frequency than ketone C=O C=C ? ? ?

Sankaran & Lee, J. Phys. Chem. A 2002, 106, Difference (new spectrum - old) 1718 & 1623 grow 1696 shrinks hours irradiation at 308 nm IR Spectrum of Methyl Vinyl Ketone in Ar at 13K anti periplanar syn periplanar Mostly C=C is very weak because small C=O vibration fights its dipole change Mostly C=C is strong because small C=O vibration helps it Calculated Positions for s-trans Calculated Positions for (a different species) C=OC=C ? ? combination of two lower frequency transitions?

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