In the Laboratory
Vibrational Line Profiles As a Probe of Molecular Interactions Michael S. Bradley and Cheryl Bratu Department of Chemistry, Valparaiso University, Valparaiso, IN 46383 Undergraduate spectroscopy experiments typically explore peak locations to identify compounds (i.e., qualitative organic) (1) or peak areas (or heights) for quantitation (Beer’s law) (2). Typical Raman experiments explore the relationship of polarization and symmetry using chloromethanes (3), while the HCl/DCl gas-phase IR experiment probes rotations and bond length (4). However, vibrational spectroscopy also provides information about the interactions between molecules through shifts in band frequencies and line widths from their gas-phase values (5–8). These aspects are usually neglected because of the complexity of the underlying physical chemistry. Further, line-width analysis requires fitting the curve to Lorentzian/Gaussian/ combination profiles. There are now many excellent curvefitting tools on the market (SpectraCalc, SigmaPlot, etc.), so this barrier is down. We present here a simplified view of intermolecular interactions and outline an experiment that provides a good handle on the subject (9, 10). Theory A vibrational spectrum results from excited molecules that are vibrating coherently (correlated; incoherent motions average to give no net signal). Mathematically, this is expressed by the Fourier integral (5) ∞
S(ω) =
{∞
e{ iωt < A(t)A(0) > dt
where S(ω) is the frequency spectrum and t is time. The angle-bracketed term is the correlation function, which assesses how long motions stay correlated. A is the transition moment operator, the dipole moment in infrared or polarizability in Raman. Correlations drop off, or relax, exponentially fast, decreasing as exp[{t(τC{1 + τa{1)] (11). τC , the coherence or correlation time, represents the influence of dephasing, where motions in the system randomize the phases of the initially in phase oscillators (random phases give rise to no net signal). τa is the actual lifetime (rate of return to the ground state, called the amplitude co-
Figure 1. Comparison of Lorentzian, Gaussian, and experimental line shapes. Note Gaussian is less sharp at peak, but falls off more rapidly than Lorentzian.
herence time) of the excited state. The excited state relaxes by cascading to other motions of lower energy (vibrational, rotational and/or translational; intermolecularly or intramolecularly). The profile of a vibrational line depends upon the relative magnitudes of τa and τC . A band is Lorentzian if reorientation is faster (τC > τa, as in solids, see Fig. 1) (11). Liquids typically fall between these limits, and the bands are best fit by a Voigt profile (a convolution of Lorentzian and Gaussian character) (12). Often, a “mixed” Lorentzian/ Gaussian profile is used, with percentage Lorentzian character a parameter (12, 13). The width of a band depends upon the correlation time: the band is narrow if the correlation time is long. Essentially, the long time allows molecules to experience a more homogeneous potential, averaging out differences between them, and narrowing the band. Water molecules relax rapidly because of the extensive network of hydrogen bonds, so the IR line is very broad. In contrast, the slower relaxation in liquid CCl4, due to the weak intermolecular interactions, results in Raman lines narrow enough to allow the separate C–37Cl and C– 35Cl stretches to be detected (11). The center frequency of a Raman/IR line also responds to environment. Basically, attractive interactions lower the local potential and shift the frequency to lower energy (red shift). Repulsive interactions cause a corresponding shift to higher energy (blue shift) (7). There are many complicating factors, such as hot bands and Fermi resonance, but these are the essential aspects of line shape theory (14). Raman spectra also give information about the symmetry of a vibration (3), through the polarization of the scattering. A symmetric vibration scatters radiation polarized parallel to the plane of incidence (called a polarized mode). An asymmetric vibration generates scattering with all po-
Figure 2. Isotropic spectra for the C–C shift as CCl4 is added (pure acetone not shown). Inset shows the overlap, in the most dilute case, of the CCl4 doublet with the acetone mode. The trace labeled VV is the || spectrum (V and H refer specifically to our laboratory axes); the VH or ⊥ spectrum has been multiplied by 4/3. No residue of the doublet is seen in the isotropic spectra.
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Figure 3. Shift in C=O vibration during dilution (• = CCl4, ■ = methanol data in all plots). The “3.0 mL” point is discussed in the experimental procedure section. The initial small steps with methanol were needed to show the smoothness of the shift.
larizations (a depolarized mode). With collection at a right angle to the excitation, the spectra typically obtained are I|| and I⊥, denoting collection of scattered light polarized parallel and perpendicular to the plane of excitation, respectively (3, 15). Subtraction produces the isotropic spectrum (IISO = I|| – (4/3) I⊥, the factor 4/3 coming from statistical arguments; see ref 15b). Isotropic spectra of depolarized vibrations are flat (no signal), whereas polarized vibrations still appear. We analyze here the isotropic spectra, since these show less interference from background scattering and fluorescence. Further, an interfering depolarized band from the CCl4 solvent is removed when the isotropic spectrum is prepared. We here outline a Raman experiment using solution composition to alter the line shape and frequency of vibrations of acetone. We modify the intermolecular interactions by diluting acetone with methanol and carbon tetrachloride. There is a clear response of the frequency and line width. We use Raman (rather than IR) because of the ease of sample preparation and simplicity of the spectra.
Figure 4. Line width of the C=O mode during dilution. Initial small steps with methanol help show the steepness of the broadening.
I|| and I⊥ were collected first from a cuvette containing 2 mL of acetone. Then 0.1 mL of methanol was added, and another set of spectra was acquired. A motorized micropipet made the additions fast, easy, and accurate. Further 0.1-mL aliquots were added until 0.4 mL had been added, then 0.4 mL-aliquots were added until the cuvette was full. One milliliter of solution was then removed and replaced with 1 mL of water for the last spectra; this appears in the plots as a “3.0 mL” added volume. A second 2-mL sample of acetone was treated similarly, except that the diluent was CCl4, and all aliquots were 0.4 mL. Since intensity is not important, the cell could be removed and stirred. For the same reason, the spectra were not normalized during analysis. The spectra were calibrated (pixels to cm{1) using the procedure reported previously (14). The isotropic spectra were then fit using the mixed Lorentzian/Gaussian profile choice in SpectraCalc (Galactic Industries). The CCl 4 combination bands at 762.0 and 790.5 cm{1 overlapped the C–C signal. However, as seen in the inset to Figure 2, they were depolarized, and subtracted out when the isotropic file was prepared.
Experimental Procedure Reagent grade CCl4, methanol, and acetone (poorer grades often fluoresce) were purchased from Fisher and used with no further purification. The Raman spectra were excited with an argon ion laser, operating at 500 mW and 488.6 nm. The laser was directed vertically up through a 1-cm fluorescence cuvette (clear on all sides and bottom). The Raman scattering was collected at a right angle and directed into a Spex 270M spectrograph (100 µm slit) with an 1800 lines/mm grating and a Princeton Instruments CCD detector. The C=O and C–C vibrations are obtained simultaneously. Polarization geometry of the scattered light was controlled using a Glan– Thompson analyzer, and the isotropic spectra [IISO = I|| – (4/3) I⊥] were calculated for the analysis.
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Results and Discussion Figures 3 through 6 show the response of the band center and line width of the C–C and C=O modes of acetone during dilution with methanol and CCl4 . The C=O mode shows a pronounced red shift upon dilution with methanol, while blue shifts slightly in CCl4. The exact opposite is seen for the C–C mode, which is one reason acetone is pedagogically useful for this experiment. The line broadens in all cases, though much more markedly when methanol is the diluent. The primary source of the line shifts and broadening observed when methanol is added to acetone involves the displacement of the dipole–dipole alignments in pure acetone with hydrogen bonds to methanol molecules (7, 9, 10).
Journal of Chemical Education • Vol. 74 No. 5 May 1997
In the Laboratory
Figure 5. Line shift of the C-C mode for both diluents.
Figure 6. Line width of the C-C mode for both diluents.
This results in a considerable decrease in the local potential energy for the carbonyl, red-shifting the vibration (Fig. 3). The hydrogen bonds effectively couple the vibration of the carbonyl to the solvent motions, so the vibrational energy is lost quickly and the line broadens extensively (Fig. 4, 7–8 cm{1, analogous to the water IR spectrum). There are no hydrogen bonding groups in the CCl4 molecule. Instead, the dipole–dipole interactions present in pure acetone are broken by the intrusion of this diluent. This increases the local potential energy of the C=O, and the band blue shifts, as seen in Figure 3. The line broadens slightly (Fig. 4), due partially to statistical considerations (8): each acetone molecule is surrounded by n neighbors, and its potential is determined by the makeup of those neighbors. There are n + 1 possible configurations of neighbors when two types of molecules are present (AAA…, BAA…, BBA…, etc.). Each configuration possesses a slightly different potential energy. The spectrum results from the sum of the signals from each configuration. As the mole fraction of diluent increases, the distribution of possible nearest neighbors broadens, and the line broadens. There are more profound changes to the overall potential, but these are beyond the scope of this article (7). The C–C mode responds very differently, as shown in Figures 5 and 6. First, it does not develop a lower local potential due to the hydrogen bonding in methanol, having no direct participation in the hydrogen bond. Instead, the tighter network of molecules causes increased numbers of collisions; the C–C line shifts blue owing to these increased repulsive interactions (~4 cm{1). The line broadens because of the enhanced rate of intermolecular collisions, which, in turn, enhances the rate of energy loss. In CCl4 , the acetone dipole–dipole interactions are interfered with, separating the molecules. The C–C mode responds to this more gaslike surrounding by red-shifting slightly. There is little affect on the line width. This experiment was used in the author’s (MSB) “Lasers and Optics in Chemistry” course, spring 1995. Data col-
lection required about two hours. The analysis (calibration, subtraction to get IISO, and curve fit), performed using macros in SpectraCalc, required about one hour. The students left the laboratory with the band center and line width data for entry into a spreadsheet. The instructor required a short, qualitative, analysis of the data. Further quantitative analysis is possible, but the theories presented in refs 5–8 require an understanding of statistical mechanics that is beyond the scope of most undergraduate physical chemistry courses. In keeping with that idea, this exercise is intended to acquaint students with the qualitative information available through line shapes, and dispel the image of vibrational peaks as static phenomena. LIterature Cited 1. Silverstein, R. M.; Bassler, G. C.; Morrill, T. C. Spectrometric Identification of Organic Compounds; 5th ed.; Wiley: New York, 1991. 2. Skoog, D. A.; West, D. M.; Holler, F. J. Fundamentals of Analytical Chemistry, 6th ed.; Saunders (HBJ): Orlando, 1992; Chapter 34 (experiments therein). 3. Shoemaker, D. P.; Garland, C. W.; Nibler, J. W. Experiments in Physical Chemistry, 5th ed.; McGraw-Hill, New York, 1989; Experiment 37, pp 451–460. 4. Ibid. Experiment 38, pp 461–468. 5. Rothschild, W. G. Dynamics of Molecular Liquids; Wiley: New York, 1984. 6. Oxtoby, D. W. Adv. Chem. Phys. 1979, 40, 1. 7. Schweizer, K.; Chandler, D. J. Chem. Phys. 1982, 76, 2296. 8. Knapp, E. W.; Fischer, S. F. J. Chem. Phys. 1982, 76, 4730. 9. Bradley, M.; Krech, J. H. J. Phys. Chem. 1992, 96, 75. 10. Bradley, M.; Krech, J. H. J. Phys. Chem. 1993, 97, 575. 11. Rothschild, W. G. Dynamics of Molecular Liquids; Wiley: New York, 1984; pp 221–228. ˇ 12. Pelikán, P.; Ceppan, M.; Li ˇska, M. Numerical Methods in Molecular Spectroscopy; CRC: Boca Raton, 1993; pp 30–33. 13. SpectraCalc Analysis Routine; SpectraCalc vs. 2.22 © 1978–1990 Galactic Industries Corp., Salem, NH. 14. Herzberg, G. Molecular Spectra and Molecular Structure, II. Infrared and Raman Spectra of Polyatomic Molecules; Van Nostrand Reinhold, 1945, reprinted by Krieger: Malabar, 1991; see especially p 311 (CCl4 data) and Chapter 2 (discussion of vibrational modes and Fermi resonance). 15. (a) Grasselli, J. G.; Bulkin, B. J. Analytical Raman Spectroscopy; Wiley: New York, 1991. (b) Long, D. A. Raman Spectroscopy; McGraw-Hill: New York, 1977.
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