Spectroscopy. The Interaction of Electromagnetic Radiation (Light) with Molecules

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1 Spectroscopy. The Interaction of Electromagnetic Radiation (Light) with Molecules (1) Electromagnetic Radiation-wave description propagation c = 3 x cm/sec magnetic () and electric (E) field vectors wavelength (cm) distance traveled during one cycle frequency (z) number of waves per unit time = c/ monochromatic one polychromatic - many different 's

2 (2) Electromagnetic Radiation-corpuscular description quanta or photons; energy = h = hc/ (Joules) intensity is proportional to number of photons (3) Electromagnetic Spectrum (4) Energy of Molecules degrees of freedom (= 3n, where n = number of atoms in molecule) divided among: translation : average kinetic energy = 1/2 kt x 3 degrees of freedom = 3/2 kt or 3/2 RT (per mole) rotation : 3 degrees of freedom (2 for linear

3 molecules) vibration : 3n - 6 degrees of freedom (3n - 5 for linear) electronic : electron configuration isomers quantum restrictions - only certain energies allowed (molecules have allowed energy states) Boltzmann distribution - population distribution in assemblage of molecules with quantized energy states, given by n i /n o = (g i /g 0 )e-( ε/kt) kt (a) (b) The distribution of molecules throughout (a) widely spaced and (b) closely spaced allowed-energy levels. (5) Light-Induced Transitions (spectroscopy) Requirements (a) photon energy must match energy difference between a populated and a higher allowed energy state

4 (b) some interaction mechanism must exist Vibrational Spectroscopy : IR spectroscopy Diatomic molecules eg. -Cl average bond length 1.27Å amplitude of oscillation 0.11Å has characteristic frequency of vibration classical ball and spring model ooke's law F = -k r k is restoring force constant (corresponds to bond force constant in molecule) r = displacement from r o, the most stable distance (bond length in molecule) classical harmonic oscillator has specific vibrational frequency which is a function of k, m 1, m 2

5 quantum mechanical harmonic oscillator energies of allowed states vib = h (v + 1/2) v = 0, 1, 2, 3,...vibrational quantum number zero point energy = 1/2 h fundamental frequency = (1/2 )(k/ ) 1/2 k = force constant reduced mass = (m 1 m 2 )/(m 1 +m 2 ) light absorption energy difference between adjacent levels vib = h 's in infrared region of spectrum; energies ca 10 kcal./mole >> RT E of light acts on oscillating dipole of vibrating molecule when in phase and promotes transition

6 intensity depends on the probability of absorption which is proportional to change in dipole moment with vibration / r) Boltzman populations essentially only v=0 populated selection rule transitions with v 1allowed, mainly v = 0 to v = 1, gives rise to fundamental band overtone band v > 1 (not allowed), weak, vib = 2h Structrural dependence of fundamental frequency = (1/2 )(k/ )1/2 stronger bonds: k larger, _ larger, larger e.g. of F-F < of C ( similar) larger atoms: larger, smaller, smaller e.g. of Cl-Cl < of F-F one degree of vibrational freedom for diatomic molecules; one fundamental frequency (8) Polyatomic molecules (3n-6 fundamental modes) vibrational motion described by a number of frequencies like those for diatomic molecules, which can be stretching modes (similar to diatomic molecules) or bending modes (bond angle deformations; smaller k's, lower 's) Triatomic examples nonlinear : degrees of vibrational freedom= 3n-6 = 3

7 e.g. S 2 expect : two degenerate (i. e. same ) S= stretching modes and a bending mode see: mechanical coupling of the stretching modes to give symmetrical and asymmetrical coupled modes SYMMETRICAL STRETC IR ACTIVE BEND IR ACTIVE ASYMMETRICAL STRETC IR ACTIVE bands: bend at 519 cm -1 sym stretch at 1152 cm -1 asym stretch at 1361 cm -1 ( sym stretch < asym stretch) all IR active : have dipole moment change linear molecule : degrees of freedom = 3n-5 = 4 e.g. C 2

8 SYMMETRICAL STRETC IR INACTIVE BEND TW MDES IR ACTIVE ASYMMETRICAL STRETC IR ACTIVE bend (two degenerate modes) at 668 cm -1 asym stretch at 2349 cm -1 both IR active but sym stretch is inactive in the IR Mechanical coupling of two or more vibrations typical examples: C N S N + - C - C C C C C C C N C N C C C, C C, C C N etc all of the above involve coupling of stretch-stretch modes stretch-bend N bend-bend

9 (9) Qualitative Analysis Many different vibrational modes (3n-6) vibrational motion can be localized (involves deformations at neighboring atoms in molecule); gives rise to characteristic IR absorption for that structural unit existing in any molecule. motion can be delocalized, because of extensive mechanical coupling of similar C-C, C-, C-N, modes etc., depends on subtle details of the particular structure; these give rise to fingerprint bands in the IR that are characteristic of the specific molecule IR spectra UV VIS NIR 100% IR 0 FIR MW Per Cent Transmitance characteristic region fingerprint region Absorbance 0% (cm-1) ( m) Spectrum: plot of energy (or its equivalent, probability or efficiency of photon absorption Intensity,, ) vs

10 Beer-Lambert law A= cl A = log(1/t) T=(I/I o ) %T A = absorbance, T = transmitance, I = intensity usual conditions not very quantitative use qualitative indications such as st(rong), m(edium), w(eak), etc., relative to most intense peak in spectrum to describe intensity bands (why not lines?) position : = (1/2 )(k/ ) 1/2 intensity : dipole moment change determines this C= > C=N > C=C shape: sharp, broad, etc. lack of bands is extremely informative characteristic region: show functional groups, many compounds can have similar spectra fingerprint region: delocalized moles, not characteristic of small unit, but of molecule as a whole (some exceptions, especia lly C- bending modes), only very closely related compounds are similar; characteristic of specific molecules

11 characteristic bands: localized vibrational modes, is characteristic of functional group; no mechanical coupling (or constant mechanical coupling effect) -X; effect of small C-,, N, S, etc. results in high bands C-X (X = heavy atom); effect of large C-Cl, CBr, CI, C-g, etc. low often in FIR X=Y; effect of large k (force constants for double bonds approximately twice that of single bonds) C=C, C=, C=N, etc. X Y; effect of larger k C C, C N Correlations of group vibrations to regions of infrared absorption.

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