6.2 Polyatomic Molecules

Transcription

1 6.2 Polyatomic Molecules Group Vibrations An N-atom molecule has 3N - 5 normal modes of vibrations if it is linear and 3N 6 if it is non-linear. Lissajous motion A polyatomic molecule undergoes a complicated motion, called Lissajous motion which includes bond-stretching and angle-bending. The Lissajous motion can be broken down into a combination of normal modes. normal mode of vibration All the nuclei undergo harmonic motion, have the same frequency of oscillation, and move in phase but generally have different amplitudes. The normal vibrations may be obtained from a knowledge of bond lengths and angles and of the bond-stretching and bondbending force constants, which are a measure of the strengths of the various springs in ball-and-spring model. wbt 1

2 Expt. Calc. Some normal vibrations of 5-methylindole S 1, 625 (612) cm -1 S 1, 471 (497) cm -1 D 0, 780 (782) cm -1 D 0, 550 (565) cm -1 42, γ(ch), pyrrole 45, γ(ccc) S 1, 435 (433) cm -1 S 1, 394 (383) cm -1 D 0, 392 (407) cm -1 D 0, 439 (456) cm -1 32, β(ccc), [6a] 33, skeleton scissoring S 1, 703 (707) cm -1 S 1, 737 (738) cm -1 D 0, 674 (653) cm -1 D 0, 885 (877) cm -1 30, β(ccc), [6b] 29, breathing, [1] wbt 2

3 Quantum mechanical treatment in harmonic oscillator (HO) approximation shows that the vibrational term values G(v i ) associated with each normal vibration i, are given by G(v i ) = ω i (v i + ½) Eq. (6.41) In general, for vibrations with a degree of degeneracy d i, Eq. (6.41) becomes G(v i ) = ω i (v i + d i /2) Eq. (6.41) Selection rule: Δv i = ±1 for IR and Raman vib. transitions Δv i = ±2, ±3, for overtone transitions. wbt 3

4 (a,b) Fundamental and overtone, and (c) combination tone transitions involving vibrations v i and v j. wbt 4

5 2-chlorofluorobenzene o-c 6 H 4 FCl, N = 12, 30 normal modes C s symmetry For 2-chlorofluorobenzene, all 30 normal vibrations involve a change of dipole moment and of amplitude of the induced dipole. Thus, all Δv i = 1 transitions are allowed in the IR and Raman spectra. However, their intensities depend on the magnitudes of the change. wbt 5

6 In general, normal vibrations tend to be localized in a particular group of atoms. It follows that the force constants of two dissimilar chains of atoms may be quite different from each other. For example, in HC C CH=CH 2 the force constants of the C C, C=C, and C C bonds are quite dissimilar. Not all parts of a molecule are characterized by group vibrations. Many normal modes involve strong coupling between stretching or bending motions of atoms in straight chain, a branched chain, or a ring. Such vibrations are called skeletal vibrations and tend to be specific for a particular molecule. They mostly occur from 1300 cm -1 to low wavenumber which is called finger print region. The cm -1 region where many transferable group vibrations occur, is known as the functional group region. wbt 6

7 (a) rocking, (b) twisting, (c) scissoring, (d) wagging, (e) torsion, (f) breathing, (g) inversion or umbrella wbt 7

8 Hydrogen bonding between phenol and diethylether The O H stretching vibration in hexane solvent has a wavenumber of 3622 cm -1 and is reduced to 3344 cm -1 in diethylether resulting from the H-bonding. wbt 8

9 The Raman band intensity is related to the change of the amplitude of the induced dipole moment (polarization) resulting from molecular vibrations. The group vibration intensities are more accurately transferable from one molecule to another, and from one solvent to another, in the Raman than in the IR spectrum. Although a laser Raman spectrometer is more expensive than a typical IR spectrometer used for qualitative analysis it does have the advantage that low and high wavenumber vibrations can be observed. wbt 9

10 The IR vibrational spectrum of crotonaldehyde. (a) 10%, (b) 1% in CCl 4, (c) thin liquid film. v 3 v 17 v 15 v 16 v 3, 2944 cm -1, CH 3 antisymmetric stretch v 15, 931 cm -1, C-CH 3 stretch v 16, 542 cm -1, CH 3 C=C bend v 17, 459 cm -1, C=C C bend wbt 10

11 The laser Raman vibrational spectrum of liquid crotonaldehyde. v 3 v 17 v 16 v 15 v 3, 2949 cm -1, CH 3 antisymmetric stretch v 15, 931 cm -1, C-CH 3 stretch v 16, 545 cm -1, CH 3 C=C bend v 17, 464 cm -1, C=C C bend wbt 11

12 The Raman spectrum can be used to provide information regarding the symmetry properties of vibrations. This information derives from the measurement of the depolarization ratio ρfor each Raman band. The ρreflects the degree to which the polarization properties of the incident radiation change after scattering. It is often used to distinguish between totally symmetric and non-totally symmetric vibrations. wbt 12

13 Vibration-rotation spectroscopy Infrared spectra of linear molecules Linear molecules belong to either the D h (e.g. CO 2 ) or the C v (e.g. HCN) point group. Considering the vibrational selection rules and the character tables, the allowed transition from the zero-point level (Σ g+ in D h, Σ + in C v ) are Σ u+ Σ g+ and Π u Σ g+ in D h Eq. (6.69) Σ + Σ + and Π Σ + in C v Eq. (6.70) For all types of Σ vibrational levels the stack of rotational levels associated with them is given by F v (J) = B v J(J + 1) D v J 2 (J + 1) 2 Eq. (6.71) The rotational selection rule is ΔJ = ±1 Eq. (6.72) wbt 13

14 Rotational transitions accompanying a Σ u+ Σ g+ IR vibrational transition in a D h linear molecule. For C v the g and u subscripts and s and a labels should be dropped. wbt 14

15 The 3 01, Σ u+ Σ g+ IR band of HCN and two weaker, overlapping bands. v 3 is the C H stretching vibration. The transition is of the Σ + Σ + type showing clear P-and R-branch structure like a diatomic molecule. There are two hot bands; one shows P, R, Q branch with the band center at about 3292 cm -1 and the other a P and R with the band center at about 3290 cm -1. wbt 15

16 Rotational transitions accompanying a Π u Σ g+ IR vibrational transition in a D h linear polyatomic molecule. For C v the g and u subscripts and s and a labels should be dropped. wbt 16

17 The Π u stack of levels differs from the Σ + stacks in two aspects: (1) there is no J = 0 level and (2) each of the levels is split, with the splitting increasing with J. The Π u stack of levels corresponds to electronic orbital quantum number Λ = 1. Thus, the total angular momentum J cannot be less than 1. This non-zero angular momentum also account for the splitting of the rotational levels, an effect known as l-type doubling and due to Coriolis forces, modifying the term value to F v (J) = B v J(J + 1) B v ± (q i /2)J(J + 1) Eq. (6.75) For the v i = 1 level of a π vibration, where q i is a parameter which determines the magnitude of the splitting of levels and centrifugal distortion has been neglected. The rotational selection rule is ΔJ = 0, ±1. Eq. (6.76) wbt 17

18 Note: Coriolis force F Coriolis = 2mv a ωsinφ, where m is the mass of the particle, v a its apparent velocity with respect to the moving coordinate system, the angular velocity of the coordinate system with respect to a fixed coordinate system, and ω the angle between the axis of rotation and the direction of v a. The Coriolis occurs only for a moving particle (v a 0) and is directed at right angles to the direction of motion and at right angles to the axis of rotation. Introduction of the Coriolis force leads to an additional coupling between rotation and vibration (Coriolis coupling) which is in general much larger than the effect of the centrifugal force. wbt 18

19 The , a Π u Σ g+ IR band of acetylene. v 1 = symmetric CH stretching; v 5 = cis bending vibration The intensity alteration of 1:3 for J even:odd results from the two equivalent H atoms, each with nuclear spin quantum number I = 1/2, as for 1 H 2. wbt 19

20 Normal modes of vibration of acetylene. wbt 20