Types of Molecular Vibrations

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1 Important concepts in IR spectroscopy Vibrations that result in change of dipole moment give rise to IR absorptions. The oscillating electric field of the radiation couples with the molecular vibration to cause an alternating electric field produced by the changing dipole. Absorption bands in vibration spectra appear as broad bands (not a single energy) if the rotational states of the molecules are not resolved as it is usually the case in liquid or solid phases. An IR spectrum is characteristic of an entire molecule and is as unique as a fingerprint (molecular fingerprint). Many localized vibrations help to identify functional groups. Band intensities are expressed as either transmission (T) or absorption (A) A = log 0 (/T) In addition to fundamental transitions, IR spectra can contain overtone bands, due to excitation into higher vibrational states, and combination bands, due to coupling of two or several group vibrations. Group vibrations can couple if their frequencies are similar and they share a common atom. A special case of coupling occurs when a fundamental vibration couples with an overtone or combination vibration. This phenomenon is known as Fermi resonance. Types of Molecular Vibrations Stretching or bonding vibrations (ν) alter the bond lengths; Bending or deformation vibrations alter the bond angles, while the bond lengths remain unchanged; They can be subdivided into in-plane (δ) and out-of-plane modes (γ); These modes are often referred to as twisting, wagging, and rocking vibration of a fragment; Torsional vibrations involve an alternation of the torsion angle; A further division into symmetric (s), antisymmetric (as), and degenerated (e) vibrations is possible. in-plane out-of-plane in-plane IR and molecular symmetry Every atom has a translational freedom of 3 because it can move in one of the three orthogonal directions (i.e. in the x, y, or z direction). There are a total of 3N possible motions for a molecule containing N atoms and each set of possible atomic motions is known as a mode. Linear molecules, such as CO 2, have 3N-5 vibrational modes because 3 of all the modes result in a translation and 2 in a rotation. 285 cm cm - ν (s) C=O IR inactive, Raman active ν (as) C=O IR active, Raman active 666 cm - δ (s) O=C=O IR active, degenerated

2 Bent molecules, such as H 2 O, have 3N-6 vibrational modes because 3 of all the modes result in a translation and 3 in a rotation cm cm - ν (s) O-H IR active ν (as) O-H IR active 595 cm - δ (s) H-O-H IR active, degenerated All IR absorptions result not only in a vibrational excitation but also in transitions between different rotational states. Those rotational transitions can be resolved in gas phase IR spectroscopy. Rotational spectroscopy specifically measures transitions between rotational states and involves microwave radiation. It is an important method in gas phase chemistry , notes 6, Macdonald Vibrational Spectroscopy and Symmetry Example, the vibrational modes of water. z The E operation leaves everything where it is so all nine O y vectors stay in the same place and the character is 9. The C 2 operation moves both H atoms so we can ignore the H H x vectors on those atoms, but we have to look at the vectors on the oxygen atom, because it is still in the same place. The C 2 vector in the z direction does not change (+) but the vectors in the x, and y directions are reversed (- and -) so the character for C 2 is -. The σ v (xz) operation leaves each atom where it was so we have to look at the vectors on each atom. The vectors in the z and x directions do not move (+3 and +3) but the vectors in σ v (xz) the y direction are reversed (-3) so the character is 3. The σ v (yz) operation moves both H atoms so we can ignore the vectors on those atoms, but we have to look at the vectors on the oxygen atom, because it is still in the same place. The vectors in the z and y directions do not move (+ and +) but the vectors in the x direction is reversed (-) so the character is. σ v (yz) C 2V E C 2 σ v (xz) σ v (yz) 9-3 Γ tot Vibrational Spectroscopy and Symmetry C 2V Γ tot E 9 C 2 - σ v (xz) 3 σ v (yz) C 2V E C 2 σ v (xz) σ v (yz) A A B - - B z R z x, R y y, R x x 2,y 2,z 2 xy xz yz From the Γ tot and the character table, we can figure out the number and types of modes using the same equation that we used for bonding: n = X [ (# of operations in class ) (character of RR) ( character of X) ] order This gives: n [ ()( )() ()( )() ()( )() ()()() ] A = n [ ()( )() ()( )( ) ()( )() ()()( ) ] B = n [ ()( )() ()( )() ()( )( ) ()()( ) ] n [ ()( )() ()( )( ) ()( )( ) ()()() ] A 2 = B 2 = Which gives: 3 A s, A 2, 3 B s and 2 B 2 s or a total of 9 modes, which is what we needed to find because water has three atoms so 3N = 3(3) =9.

3 An IR active vibrational mode must result in a change of dipole moment of the absorbing group; The requirement for a Raman active vibrational mode is a change in polarizability of the absorbing group; Almost every chemical bond between different elements has a dipole moment but dipole moments of a functional group or molecule might cancel out due to symmetry! Stretching and Bending vibrations of CH ν(as) 2926 cm - ν(s) 2853 cm - δ(in-plane) 65 cm - δ(out-of-plane) cm - - Out-of plane bend or twist cm In-plane bend or rocking cm - a CH 3 b H 3 2 H c 8 H d H e i k f 5 CH 3 7 H h g O OH6 2-methoxyphenol (Guaiacol) trans-methylstyrene

4 C-H Stretch CH 3 (as) 2962 CH 3 (s) 2872 CH 2 (as) 292 CH 2 (s) 2853 IR of Normal Alkanes C-H Bend CH 2 (s) 67 CH 3 (as) 50 CH 3 (s) 378 C-H twist CH (weak) νc-c (weak) δc-c bend below 500 C-H Rock CH 2 72 dodecane IR of Alkenes ν C=C Stretch in simple alkenes ν C=C in conjugated alkenes near 650 and 600 (why lower?) C-H stretch C-H bend (aliphatic & alkene in-plane) C-H bend (out-of-plane) ν C=C 60 (s) w =C-Hstretch ν C=C 598(as) s isoprene IR of Alkynes C-H stretch C-H stretch 330 C C stretch 29 C-H bend overtone 250 C-H bend 630 -hexyne

5 Aromatics Prominent (strong) absorptions: ν C-H stretch cm - δ in-plane C-H bend cm - δ out of plane C-H bend cm - (characteristic for substitution pattern) ν C=C ring stretches and cm - δ out of plane C=C bend cm - Overtone and Combination bands cm - combination bands ν C=C ring δ out of plane C-H bend Aromatic overtone and combination bands

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