Spectroscopy. The Interaction of Electromagnetic Radiation (Light) with Molecules (1) Electromagnetic Radiation-wave description propagation c = 3 x 10 10 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) 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
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
(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
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
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
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
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) 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% 2.0 4000 1400 600 (cm-1) 2.5 7 16 ( m) Spectrum: plot of energy (or its equivalent, probability or efficiency of photon absorption Intensity,, ) vs
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
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.