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J . Pkys. Chem. 1988, 92, 1388-1392
Large Av’TramMons and Isotope EffeCts in the Crossed Beams Inelastk Scattering of I,” (v’ = 35) from H, and D2 Douglas J. Krajnovich,? Kirk W. Butz, Hong Du, and Charles S. Parmenter* Department of Chemistry, Indiana University, Bloomington, Indiana 47405 (Received: December 10, 1987)
Rotationally and vibrationally inelastic scattering from the level v’ = 35 with J’ = 8-1 1 in the B 0,’ electronic state of I, have been followed in a crossed molecular beams experiment using H2 and D2target gases. Center-of-mass collision energies are 89 and 103 meV, respectively. I2 B 0,’ is excited by a laser pump and the inelastic scattering is followed by dispersed B X fluorescence. The signal-to-noiseis good enough to obtain relative cross sections for I2 scattering for Av”s extending to k7. The cross sections are remarkably symmetricwith respect to gain vs loss of vibrational quanta. They decrease exponentially with increasing lAvl for each target, but H2 has a steeper decline. Collision momentum rather than velocity differences appears to be responsible for this isotope effect. The mean vibrational energy change per state-changing collision is only about -9 cm-I for both H2 and D2,a small fraction of the 60-cm-’ vibrational quantum size. Rotationally inelastic scattering produces 2-3 times more rotational excitation with the heavier isotope D,,a consequence of angular momentum conservation.
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Introduction By a large margin, most of our information about state-resolved vibrational energy transfer has been obtained from bulb experiments with broad thermal collision energy distributions. An important segment of this bulb work is based on electronic spectroscopy since it uses the optical pump, dispersed fluorescence probe technique’ for both diatomic and polyatomic molecules. Among the former, none is more spectroscopically accessible than I,, and accordingly, many data now exist for collisions between I2 and various atomic/molecular targets. We mention in particular the extensive bulb measurements2 by Brown, Klemperer, Steinfeld, and co-workers in the 1960s and early 1970s, all of which concern vibrational and rotational state changes within the B 0,’ electronic state. Their most detailed data concern the initial levels u ’ = 25 and 43. Additional bulb experiments by Derouard and Sadeghi3 and by Pritchard and co-workers4 (among others) place emphasis on state-resolved rotational energy transfer in the B electronic state. The general applicability of the bulb technique is beautifully illustrated by the I2 studies. By simple tuning of a light source (laser), a broad choice for initial-state selection is available. In turn, the detection of final states has both high selectivity and high sensitivity. Often, all of the dominant transfer channels can be followed. On the negative side, the broad thermal collision energy distribution inevitably obscures important aspects of the scattering dynamics. In addition, thermal inhomogeneous broadening can blur both the initial- and final-state resolution. This problem in particular imposes limitations on the choice of molecules, especially polyatomics, accessible to the bulb method. To gain relief from these restrictions while preserving the advantages of the optical pump and dispersed fluorescence probe, we are exploring the extension of this venerable technique to a crossed molecular beam environment. Preliminary results on the H e I,(B) and H, glyoxal (SI) systems’-s demonstrate that the inelastic scattering signal is indeed large enough to follow vibrational state changes with the narrow collision energy distributions of crossed molecular beams. The discovery of a surprising equivalence for rotationally and vibrationally inelastic scattering from glyoxals is an early reward of the crossed beams approach, giving an example of dynamics that would be difficult to uncover in a bulb experiment. We now extend the beam studies to the scattering of I2 B-state molecules from two isotopic targets, namely, H2and D,. I2 molecules were pumped to the initial B-state vibrational level v’ = 35 by a pulsed dye laser. The relative probabilities of populating various final v’levels were obtained from an analysis of the dispersed fluorescence spectrum. Some information was also obtained on the extent of rotational energy transfer in both the vibrationally
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‘Present address: IBM Almaden Research Center, 650 Harry Road, San Jose, CA 95120.
0022-365418812092-1388$01.50/0
elastic and the vibrationally inelastic channels. Distinctions occur with the two isotopic targets, and they are well beyond those that could be generated by the small differences in collision energy. Since the potential energy surface is identical for H, and D,, differences in the inelastic scattering must be related to the reduced mass of the collision pair. The rotational differences are a straightforward consequence of angular momentum conservation, and the vibrational differences are believed to be due to a collisional momentum-transfer effect. Our studies are preceded by crossed beam studies in the ground electronic state of I, by Gentry, Giese, and co-workers.6 These workers combined a rotatable beam source design to vary continuously the collision energy with laser-induced fluorescence as a high-resolution final-state probe. Their reported crossed beam data are for collisions of IZ(vf’= 0) with He, H,, and D2. Experimental Section A pulsed molecular beam of iodine was generated by using a miniature solenoid valve to expand an 12/Hemixture (4% I,) at 200 Torr through a 0.5 mm diameter orifice. The solenoid valve was maintained at 90 OC to prevent condensation of iodine crystals. The target beam was formed by pulsing 1000 Torr of pure H2 or D2 through a second 0.5 mm diameter orifice at room temperature. Both beam sources were differentially pumped. The molecular beams were collimated by skimmerlike apertures and then crossed at right angles in the main scattering chamber. The excitation source was an excimer-pumped dye laser system. The molecular beams and laser beam were coplanar, with a 4 5 O intersection angle between the laser and each molecular beam. Baffle arms reduced stray light and defined the laser beam to a 3 mm diameter at the interaction volume. The dye laser, with a measured bandwidth of 0.25 cm-’ fwhm, was tuned 1.8 cm-’ to the red of the B O,+(v’= 35) X’Zg+ ( u ” = O),band origin. For such a pump, J’levels between 8 and 13 (within v’ = 35) should contribute to our initial conditions. The dye laser energy
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(1) Krajnovich, D. J.; Parmenter, C. S.; Catlttt, D. L., Jr. Chem. Reu. 1987,87, 237. (2) (a) Brown, R. L.; Klemperer, W. J . Chem. Phys. 1964,41, 3072. (b) Steinfeld, J. I.; Klemperer, W. Zbid. 1965,42, 3475. (c) Kurzel, R. B.; Steinfeld, J. I. Ibid. 1970,53,3293.(d) Steinfeld, J. I.; Schweid, A. N. Ibid. 1970,53,3304.(e) Kurzel, R.B.; Degenkolb, E. 0.;Steinfeld, J. I. Ibid. 1972, 56,1784. (0 Rubinson, M.; Garetz, B.; Steinfeld, J. I. Ibid. 1974,60,3082. (3)Derouard, J.; Sadeghi, N. Chem. Phys. 1984,88,171;J. Chem. Phys. 1984,81,3002. (4)Dexheimer, S. L.;Durand, M.; Brunner, T. A.; Pritchard, D. E. J . Chem. Phys. 1982,76,4996. Dexheimer, S.L.; Brunner, T. A,; Pritchard, E. D.Ibid. 1983,79,5206. (5) Butz, K. W.; Du, H.; Krajnovich, D. J.; Parmenter, C. S. J. Chem. Phys. 1987,87,3699. (6)Hall, G.;Liu, K.;McAuliffe, M. J.; Giese, C. F.; Gentry, W. R. J . Chem. Phys. 1984,81, 5577. Hall, G.; Liu, K.; McAuliffe, M. J.; Giese, C. F.; Gentry, W. R.Ibid. 1986,84, 1402.
0 1988 American Chemical Society
The Journal of Physical Chemistry, Vol. 92, No. 6, 1988 1389
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Frequency /cm-‘ Figure 1. Inelastic dispersed fluorescence spectra for Iz*(v’ = 35) scattering from Hzand Dz The dots represent a 3-point sliding average of the raw experimental points. The solid curves are calculated fits to the data. The “dip” near (39,O) is an experimental artifact caused by the fact that some I2 molecules were directly pumped to v’ = 39 via the (39,l) hot band transition.
was maintained between 1.0 and 1.5 mJ per pulse. The center-of-mass (c.m.) collision energies were estimated from calculated beam velocities. The iodine beam was assumed to have no “velocity slip” between I2 and He giving u(12) = 1.05 X lo5 cm/s. The work of Kolodney and Amirav’ on Heseeded I2 beams suggests that the amount of velocity slip should be much less than 10% under our experimental conditions. The lab velocities of the neat H2 and D2 target beams depend on the extent of rotational cooling. Neumark et a1.* used a time-of-flight technique to measure the velocities of H2 and D2 beams formed by expanding 95 psi of each gas through a 70 pm diameter nozzle. The product of their stagnation pressure (Po) and nozzle diameter ( D ) is similar to our experiments, and since the degree of rotational relaxation in a supersonic expansion depends mainly on the value of P@, it is reasonably accurate to estimate H2and D2 beam velocities from their results. We obtain 4 H 2 ) = 2.74 X lo5 cm/s and u(D2) = 1.97 X lo5 cm/s. With these beam velocities, the most probable c.m. collision energies are 2.06 kcal/mol(89 meV, 720 cm-’) for the H2+ 12* experiment and 2.36 kcal/mol (103 meV, 830 cm-’) for the D2 + 12* experiment. The fluorescence collection and detection system will be described in detail el~ewhere.~Briefly, fluorescence was imaged into a 1.7-m scanning monochromator and detected by using a (7) Kolodney, E.; Amirav. A. Chem. Phys. 1983,82, 269. (8) Neumark, D. M.; Wodtke, A. M.; Robinson, G . N.; Hayden, C. C.; Lee, Y.T.J . Chem. Phys. 1985,82,3045. Neumark, D. M.; Wodtke, A. M.; Robinson, G . N.; Hayden, C. C.; Shobatake, K.; Sparks, R. K.; Schafer, T. P.; Lee, Y.T. Ibid. 1985, 82, 3067. (9) Butz, K. W.; Du,H.; Krajnovich, D. J.; Parmenter, C. S., to be pub-
lished.
high-gain Hamamatsu R2079 PMT. Total fluorescence was imaged with a separate system onto a low-gain RCA 7326 PMT. The PMT outputs were charge-integrated and digitized on a shot-by-shot basis by a two-channel gated detection system interfaced to an IBM PC. The PC also controlled the timing of the molecular beam and laser pulses and the scanning of the monochromator. The weak signal from inelastically scattered 12* molecules was isolated by triggering the target solenoid valve only on alternate laser pulses and by subtracting the normalized dispersed fluorescence signals measured with the target beam O N and OFF. By “normalized”, we mean that the dispersed fluorescence signal was ratioed to the total fluorescence signal on a shot-by-shot basis. This procedure eliminates quenching contributions to the inelastic fluorescence spectrum. The data acquisition sequence was identical for the H2and D2 experiments. The spectrometer entrance and exit slit widths gave a 7.2-cm-’ fwhm triangular slit function, and the monochromator was scanned in discrete 2-cm-’ steps. Data was accumulated for 400 laser shots at each frequency point (half each with the target beam on and off). The total counting time was about 4 h for each target.
Results and Analysis A comparison of our results on 12*(u’ = 35) inelastic scattering from H2and D2is given in Figure 1. Only the subtracted inelastic dispersed fluorescence signal is shown. The solid curves in Figure 1 are calculated fits to the data. The spectral range of Figure 1 encompasses three vibrational bands from the initially pumped level v’ = 35 to the ground electronic state: (35,O) at 19023 cm-’; (35,l) at 18809 cm-’;
1390 The Journal of Physical Chemistry, Vol. 92, No. 6,1988 TABLE I: Data for Inelastic Scattering of the Level = 8-11 in B O.+ I, from H, and D, Target Gases aEvibt
Av’ +7 +6 +5 +4 +3 +2 +1 0 -1 -2 -3 -4
cm-’ +367 +321 +272 +222 +170 +115 +58.6
0 -60.8 -124 -1 89 -256 -325 -396 -469
-5 -6 -7
H, target u(v’)” 0.21 0.46 0.90 1.79 3.85 8.31 (33) [10.0] 3.88 2.17 1.oo 0.48 0.29 0.10
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D2target cm-I
11 11 11 11 11 10 10 11 10 11 11 11 11 11
a(v’)“
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0.42 0.65 0.97 1.50 2.63 4.61 9.66 (24) [10.0] 4.67 2.86 1.58 0.86 0.76 0.38
26 26 26 26 26 26 24 19 24 26 26 26 26 26 26
“Relative inelastic scattering cross sections. Those for Au’ = -1 are arbitrarily set to 10.0. Those for Av‘ = 0 are for pure rotationally inelastic scattering. They are properly scaled to the vibrational cross sections but have larger uncertainty. bAverage rotational energy as a consequence of inelastic scattering.
( 3 5 , 2 ) at 18 597 cm-’. Large negative “dips” occur in the difference spectrum at (35,O) and ( 3 5 , 2 ) due to inelastic depletion of the initially pumped level. These negative dips have been set to zero signal in Figure 1. Hardly any dip is observed at the (35,l) transition, however, due to the extremely small Franck-Condon factor (FCF). All of the positive signals in Figure 1 come from new B-state levels populated during single inelastic collisions. The positive signals on the low-frequency sides of the (35,O) and ( 3 5 2 ) bands are due to pure rotationally inelastic scattering within v’ = 3 5 . The vibrationally inelastic scattering manifests itself at other (v’, u”) transitions. For example, peaks labeled Av’= + I , ..., +7 in Figure 1 correspond to (36,0), ..., (42,0), respectively. Similarly, the peaks labeled &’= -1, -2, -3 are largely due to (34,0), (33,0), and (32,O). Larger negative A d changes also occur, but the (v‘, 0) fluorescence from these low-lying levels is overlapped by (v’,2) and (v’,3) emission from higher v’levels. The Av’= -1 peaks for H2 and D2 in Figure 1 have been arbitrarily scaled to the same height. The actual Av’ = -1 signal level was about 12 and 7 photons per laser pulse for H2 and D2, respectively. (For comparison, the 35-0 elastic fluorescence signal was about 1400 photons/pulse. ) In order to extract quantitative vibrational state populations from the fluorescence spectra, account must be taken of three factors. The Einstein A coefficient for spontaneous emission at each u’ transition was calculated by using precise literature values for the (v’”’’) transition frequencies,1° FCFs,Io and the electronic transition dipole moment as a function of the R centroid.lO*” Correction for the dependence of the Iz (B state) fluorescence quantum yield on rotational and vibrational quantum numbers was made with extensive data published by Vigut and co-workers.I2 Finally, the wavelength dependence of the overall detection sensitivity was obtained by measuring a series of 12*(v? resonance fluorescence spectra and noting the systematic discrepancies between t h e measured and calculated (v’,~’’)band intensities. All of these intensity correction factors were incorporated into a computer program that was used to fit the experimental spectra. The fits were obtained with sets of adjustable scaling parameters, one set for each final v’. These parameters are related to the (relative) inelastic scattering cross sections. Three parameters
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(10) Gerstenkorn, S.; Luc, P. Facteurs Franck-Condon de la MolZcule de I’lode, 1984. (A copy of this unpublished table was kindly provided to us by Dr.J. Verges.) ( 1 1) Tellinghuisen, J. J . Chem. Phys. 1982, 76, 4736. (12) ViguZ, J.; Broyer, M.; Lehmann, J. C. J. Phys. 1981,42,949. ViguC, J., private communication.
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The Journal of Physical Chemistry, Vol. 92, No. 6,1988 1391
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can, for example, be folded over almost directly onto the hu’(up) cross sections. A similar representation would occur if the cross sections were plotted against PE, since the size of the vibrational quantum (about 60 cm-’) varies only slowly in the range of the data. Approximately symmetric final-state distributions are expected to occur whenever (i) the collision energy is large compared to the vibrational level spacing, and (ii) the translational collision velocity is large compared to the velocity of internal vibrational motion. The first condition is well-satisfied in our experiment, and the second is met marginally. The significance of condition (ii) is that the collision has an equal probability of occurring during the expansion and compression strokes of the oscillator’s vibrational motion. For the onedimensional (1-D) collinear case, an impulsive collision during the expansion stroke will damp the vibrational motion (V T relaxation), while impulsive collisions during the compression stroke should result in T V excitation. For 1-D perpendicular collisions, just the opposite is true, but there is still symmetry between the T V and V T cross sections. Classical trajectory calculations show that the final-state symmetry survives three-dimensional averaging, in agreement with experiment.’ hE(up) and AE(down)for Vibrationally Inelastic Scattering. While it may be stretching a point with a stretched diatomic, the data might be considered as a glimpse into the hE(up)-PE(down) problem long discussed in connection with collisional vibrational activation-deactivation of reactive, highly excited (i.e., 15 000 cm-I) polyatomic molecules. The problem there concerns the distribution of hE~b, the vibrational energy gain/loss, for inelastic collisions and also the resulting average ( per colli~ion.’~*’~ The small quantum size in I2relative to the collision energy begins to replicate the vibrational pseudocontinuum of the polyatomic problem. Our experiments further concern a highly excited anharmonic oscillator, with a high quantum number (u’ = 35) and an energy content (3360 cm-’) that is near a dissociation limit (De = 4381.1 cm-I for the B state). Further, when the classical turning points at 2.667 and 4.128 A are compared with re = 3.0247 A, it is apparent that large atomic excursions occur within this oscillator. It can be seen that due to the symmetry of the final vibrational state distribution, the mean vibrational energy transferred per inelastic collision is small, even though the total vibrationally inelastic scattering cross section is large. Using the u(u? factors and values from Table I, it is easy to calculate ( h E , i b ) = -9 cm-’ for both H2 and D2 The experimental error associated with the ( h E ~ b values ) should not be greater than f 5 m-’.Thus, the mean vibrational energy transfer is in the direction of V T relaxation for these monoenergetic collisions, but it amounts to only a small fraction of the local vibrational quantum spacing. Future extension of these experiments over a range of collision energies will provide the data needed to estimate the ( h E ~ b values ) for thermal systems. Exponential Scaling. Another characteristic immediately apparent by inspection of Figure 2 concerns the relative magnitudes of cross sections for increasing Au’. The vibrationally inelastic cross sections for both target gases scale closely to an exponential in Au’. Since scaling against Au‘is roughly equivalent to scaling against hE, the cross sections are a simple manifestation of the energy gap or momentum gap lawsls so often used to describe vibrational energy transfer processes. Narrower Final-State Vibrational Distributions for H2. The relative cross sections in Figure 2 scale more steeply for the H2 target gas. The effect is so pronounced that the narrower final-state vibrational distribution can be seen easily in the raw experimental spectra. This difference cannot be attributed to the small difference in collision energies between H2 and Dz. The conclusion follows from the fact that inelastic scattering for H e + I,* at Ec,,,,= 89 meV gives results that are almost identical
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(13) Sce, for example: Troe, J. J. Chem. Phys. 1982,77,3485. Heymann,
M.;Hippler, H.;Troe, J. Ibid. 1984, 80, 1853.
(14) See for example, Barker, J. R. J . Phys. Chem. 1984, 88, 11. ( 1 5 ) Ewing, G.E. J . Phys. Chem. 1986, 90, 1790.
with the D2 + 12* results a t Ec.m = 103 meV. The difference between the He-12* and D2-I,* potential energy surfaces should be small at these relatively high collision energies. Thus, it appears that the factor mainly responsible for the shape of the final vibrational state distribution (in this narrow range of collision energies) is the reduced mass of the collision pair. This reduced mass effect is interesting to consider. Varying the reduced mass at fixed collision energy affects both the collision velocity and the collision momentum. At the same c.m. collision energy, the collision velocity is 2 times larger for H2 than for D2. If the H2 collision energy is cut in half (relative to D2), then the H2 and D2 collision velocities become identical while the H2 momentum is half that of D2. If the H2 collision energy is doubled, then the H2 and D2 collision momenta become identical while the H, velocity is twice that of D2. Which factor, velocity or momentum, is mainly responsible for the observed isotope effect in the vibrationally inelastic scattering? In the case of light particle scattering from 12*, the collision momentum factor almost certainly dominates. In the 100 meV collision energy range, both H2 and D2 can uoutrunn the 1-1 vibrational motion at u’ = 35. The projectile comes in, strikes an almost stationary I2 molecule, and gets out. The collision energy is high enough to ensure that the interaction is almost purely repulsive. Under these conditions, the outcome of a collision should not depend too sensitively on the range of the repulsive potential (or equivalently, on the time of the repulsive interaction). Rather, the amount of energy transferred to or from the 12* molecule should be determined by the impulsive momentum transfer during the collision. If this interpretation is correct, then H2 + 12* scattering at collision energies around 200 meV should give a final vibrational state distribution similar to D2 + 12* at 100 meV. Experiments to test this hypothesis are in progress. Rotationally Inelastic Scattering with H2 and D2 Target Gases. Rotationally inelastic scattering affects only the 12*, since the collision energy is far too low to result in significant rotational excitation of H2 or D2. Between these target gases, the heavier partner D2 results in 2-3 times more rotational excitation of I,. Recall that J’levels between 8 and 13 were initially pumped. The initial B-state rotational energy, then, is - 2 cm-’, as compared to the final I,* rotational energy of 10-1 1 cm-I for H2 collisions and 18-26 cm-’ for D2. There does not appear to be a strong dependence of the average rotational excitation energy on the vibrational quantum number change, IAu 1. The only exception appears to be the low value of E , obtained for the Ad = 0 channel with D2. Not surprisingly, the extent of rotational excitation in collisions of I,* with H2 or D2 is determined mainly by conservation of angular momentum. For purposes of illustration, assume a coplanar collision between I,* and H2 or D,, an_d assume that the initial 12*rotational angular momentum vector 4 is aligned parallel to the initial orbital angular momentum vector L,.Finally, assume a classical impact parameter b = 1.5 8, that is equal to one-half the 12*equilibrium bond separation. (This value should be representative of the range of impact parameters involved in the inelastic scattering.) For H2 collisions at 89 meV and b = 1.5 A, L, = 14h. For D2 collisions at 103 meV and b = 1.5 A, L, = 21 h. The maximum amount of rotational excitation will occur when all of the initial orbital angular momentum is converted into additional rotational angular momentum of the 12* giving Jf = J , + I,,. Using the initial value J , = 1Oh corresponding to our experimental conditions, we obtain Jf = 24h and E,,, = 12 cm-I for H2collisions and Jf = 3 1h and E,, = 20 cm-’ for D2 collisions. These crude estimates are in semiquantitative agreement with our experimental values for the mean Iz* rotational energy (Table I). The bulb measurements of Dexheimer et al! and of Derouard and Sadeghi3 lend additional support to the rather obvious conclusion that dynamical, rather than energetic constraints, determine the extent of rotational energy transfer in collisions between light particles and heavy molecules. Acknowledgment. We thank John Dorsett and the entire staff of the Indiana University Chemistry Department mechanical
J. Phys. Chem. 1988, 92, 1392-1394
1392
instrument shop for their expert help in the construction of the apparatus. We also thank Robert Ensman for electronics design support. D.J.K. acknowledges helpful correspondence with Prof. J. Tellinghuisen and Dr. J. ViguE on several aspects of I2 spec-
troscopy and predissociation. Financial support from the National Science Foundation and from the donors of the Petroleum Research Fund, administered by the American Chemical Society, is greatly appreciated.
Pressure-Induced Vibrational Fundamental and Overtone Frequency Shifts of Iodine Mofecules in Solution D.Ben-Amotz, M. R. Zakin, H. E. King, Jr., and D. R. Herschbach*+ Corporate Research Science Laboratory, Exxon Research and Engineering Company, Annandale, New Jersey 08801 (Received: December 18, 1987)
From resonance Raman scattering, we obtain frequency shifts for the fundamental and first two overtones of iodine in methylcyclohexane solutions (5-30 mM) at pressures up to 12 kbar. The shifts (relative to 1 bar solutions) are positive, indicating dominantly repulsive interaction. For the fundamental, &/dP = 0.36 f 0.01 cm-'/kbar, in good agreement with the value 0.40 f 0.04 obtained from a hard-sphere model due to Schweizer and Chandler. The observed pressure derivatives for the first and second overtones are larger by factors of about 2 and 3, respectively. This is consistent with a theoretical prediction of Buckingham and offers evidence that the usual form adopted for the solutesolvent interaction potential, which contains only terms linear and quadratic in the vibrational displacement, is adequate for treating pressure-induced frequency shifts. We also analyze the gas-liquid shifts seen by Kiefer and Bernstein in extensive overtone spectra of iodine solutions at 1 bar. These shifts are all negative, indicating dominantly attractive interaction, and for the higher overtones show marked deviations from the Buckingham criterion.
Introduction When a gas-phase molecule enters a solution, its bonds usually expand slightly and its vibrational frequencies shift downward, because at ordinary densities attractive solutesolvent interactions are usually dominant. These shifts can be offset and reversed by compressing the solution to reduce the mean distance between molecules and thereby enhance repulsive interactions. The pressure dependence of vibrational frequencies thus offers information about the solutesolvent interaction potential. Previous experiments in pursuit of this theme dealt with shifts of fundamental frequencies. Here we report shifts for some overtone frequencies which probe the dependence of the interaction potential on the vibrational displacement of the solute molecule. Theoretical treatments of vibrational frequency shifts induced by compression or solvation typically consider a diatomic molecule immersed in a benign solvent.I4 The solute-solvent interaction potential is usually assumed to have the form V,,, = F[ + GF2, where [ = ( r - re)/reis the displacement from the equilibrium bond distance of the isolated (gas-phase) solute molecule and the force constants F and G are averaged over the solvent configuration. For V,,, of this form, the corresponding shifts in the vibrational energy levels obtained from second-order perturbation theory are proportional to the quantum number ( n + 1 / 2 ) and linear in the I: and G quantities. Thus, as first pointed out by Buckingham,2 for any such the frequency shifts of the fundamental and successive overtones should be in the ratio 1:2:3.... As long as a second-order treatment is adequate, this prediction holds regardless of the magnitude of anharmonicity, either in the solute molecule vibrational potential or in the dependence of the solutesolvent interaction on the solvent configuration. By virtue of this Buckingham criterion, overtone spectra thus offer a means to test the basic assumption concerning the form of the solutesolvent interaction.
vnt
Experimental Procedure and Results In this study we used resonance Raman scattering to measure frequency shifts at pressures up to 12 kbar for the fundamental Exxon Faculty Fellow from Harvard University, Cambridge, MA.
0022-3654/88/2092- 1392$01.50/0
to 3 X and first two overtones of iodine solutions (5 X M) in methylcyclohexane, a benign solvent that remains liquid over this pressure range. Comparable spectra at 1 bar pressure have been obtained for a much wider range of overtones for iodine in cyclohexane and other solvents by Kiefer and Bernstein.Io For our pressure dependence measurements, we used a diamond anvil cell of the Merrill-Bassett type" and employed the ruby fluorescence technique'* to determine the pressure (at 23 "C) before and after each Raman measurement. The temperature of the solutions during selected experiments was determined by comparing the intensity of the low-frequency Stokes and antiStokes bands of methylcyclohexane. The spectra were obtained by focusing a 514.5-nm argon ion laser line at 50-100 mW into the sample cell using a 5-cm focal lengthfll.2 camera lens which was also used to collect the backscattered Raman light. The spot diameter of the laser, within the 500-pm sample cell diameter, was 50 pm, and the path length in the sample was between 100 and 200 pm. The scattered light was filtered and dispersed by a Spex 1877 triple monochromator with a 2400 grooves/mm dispersion grating. The signal was collected by an EG&G 1420 optical multichannel analyzer and 1630 controller system. The frequency shifts of the iodine overtones were meashred relative to a 0.01 M solution in methylcyclohexane at 1 bar and calibrated (1) Fishman, E.; Drickamer, H. G. J. Chem. Phys. 1956,24, 548. Benson, A. M.; Drickamer, H. G. J. Chem. Phys. 1957,27, 1164. Wiederkehr, R. R.; Drickamer, H. G. J. Chem. Phys. 1958, 28, 31 1. (2) Buckingham, A. D. Proc. R . Soc. London, A 1957,248,169; 1960,255, 32; Trans. Faraday SOC.1960,56, 7 5 3 . (3) Pullin, A. D. E. Spectrochim. Acta 1958, 13, 125. (4) Dijkman, F. G.; van der Maas, J. H. J . Chem. Phys. 1977,66, 3871. ( 5 ) Oxtoby, D. W. J. Chem. Phys. 1979,70, 2605; J Phys. Chem. 1983, 87, 3028. (6) Fujiyama, T. J. Raman Spectrosc. 1982, 12, 199. (7) Schweizer, K.S.;Chandler, D. J . Chem. Phys. 1982, 76, 2296. (8) Zakin, M. R.; Herschbach, D. R. J . Chem. Phys. 1986, 85, 2376. (9) LeSar, R. J. Chem. Phys. 1987,86, 4138. (10) Kiefer, W.; Bernstein, H. J. J . Raman Spectrosc. 1973, I , 417. (11) Merrill, L.; Bassett, W . A. Rev. Sci. Instrum. 1974, 45, 290. (12) Barnett, J. D.; Block, S . ; Piermarini, G. Rev. Sci. Instrum. 1973, 1, 44.
0 1988 American Chemical Society
