J . Phys. Chem. 1984, 88, 181-184 at these energies exceeds the relaxation rates from the excited electronic states, then the observed dissociation rate would be determined by the relaxation rate from the electronic excited state, as the latter becomes a "bottleneck" for the overall dissociation process. Acknowledgment. M.A.E. thanks Professor T. Baer for valu-
181
able discussions. The authors thank Ms. J. Yang for her assistance with the computer analysis and plots of the data, Dr. D. K. Sensharma for his assistance in the design of the mass spectrometer, and Dr. M. Stuke for the fruitful interaction during the initial stages of this program. The financial support of DOD army research office (Contract No. DAAG29-83-K-003 1) is greatly appreciated. M.A.E. thanks NATO for a travel award.
Infrared Photodissociation of Methanol Dimers Mark A. Hoffbauer,t Clayton F. Giese, and W. Ronald Gentry* Chemical Dynamics Laboratory, University of Minnesota, Smith and Kolthoff Halls, Minneapolis, Minnesota 55455 (Received: November 15, 1983) The photodissociation spectrum has been measured for methanol dimers in the region of the vg C-0 stretching vibration from 1025 to 1085 cm-I. The absorption peak corresponding to single-photondissociation has a Lorentzian line shape, with a full-width at half-maximum of 13.8 cm-'. The monomer product recoil energies are extremely small-about 0.2% of the initial photon energy-consistent with the expectation that the photon energy is just barely sufficient to break the hydrogen bond. The combined line width and speed distribution data suggest that the state relaxation rate which is responsible for the line width is greater than the rate of vibrational predissociation.
Introduction A van der Waals (vdW) "molecule" A-B, in which the covalently bound A and B molecules are held together by the relatively weak intermolecular forces between them, can be made to undergo decomposition to the products A + B by vibrational excitation of either A or B above the vdW bond energy. This process can be considered to be a special kind of unimolecular reaction, chracterized by a great disparity in the frequencies of vibrational motions within the covalent bond coordinates of A and B and those of the vdW coordinates which express the location and orientation of A and B relative to each other. Energy must be transferred from the high-frequency covalent coordinates into the low-frequency vdW coordinates in order for the dissociation to occur, making systems of this type interesting special cases in which to test ideas about intra-"molecular" energy flow, as well as ideas about unimolecular reactions. A variety of vdW molecules has been studied recently by the technique of infrared photodissociation spectr~scopy,'-'~ and in a few cases dynamical information on the product speed and angle distribution has been obtained as well.2,397310916Experiments in our own laboratory have explored the effects of varying the vibrational mode which is excited initially2 and the number of vibrational degrees of freedom in the ~ y s t e m . ~ Contrary ,~ to what one would expect from assuming instantaneous statistical redistribution of energy among all degrees of freedom and attributing the homogeneous line width to the vibrational predissociation rate, the line widths for photodissociation were found to depend rather strongly on the mode which was excited initially in isotopic ethylene dimers,2 and were not found to depend strongly on the number of system vibrational modes within a series of OCS-alkane cluster^.^ These observations suggest either that a statistical description of unimolecular reaction is not valid for these special cases or that the homogeneous line width is a measure of some more rapid intra-"molecular" relaxation rate, rather than that of the predissociation rate. In all of the cases studied previously the energy of the infrared photon which induces dissociation has been much larger than the vdW bond energy (by a factor of about 2 to 10). This raises the question of whether the unusual dynamics which are reflected in the very large homogeneous line widths for these processes (2-20 Present address: Chemistry Division, Naval Research Laboratory, Washington, DC 20375.
0022-3654/84/2088-0181$01.50/0
cm-') are a consequence of the fact that only a small fraction of the energy deposited initially in some specific vibrational mode of A needs to be transferred to the vdW coordinates in order to cause dissociation. In order to address this issue, we report here our spectroscopic and dynamical measurements on the photodissociation of methanol dimers. Because of the relatively strong hydrogen bonding in this system, the energy of the CO, laser photons used in these experiments is just barely enough to dissociate the dimer. The experiments span the range of frequencies from about 1025 to about 1085 cm-', or photon energies between 2.9 and 3.1 kcal/mol. Although the structures of methanol dimers and trimers have not been determined in detail, molecular beam-electric deflection experiments'* indicate a singly hydrogen-bonded structure for the (1) M. A. Hoffbauer, W. R. Gentry, and C. F. Giese in "Laser Induced Processes in Molecules", Vol. 6, K. Kompa and S. D. Smith, Ed., Springer, Berlin, 1978. (2) M. A. Hoffbauer, K. Liu, C. F. Giese, and W. R. Gentry, J . Chem. Phys., 78, 5567 (1983). (3) M. A. Hoffbauer, K. Liu, C. F. Giese, and W. R. Gentry, J . Phys. Chem., 87, 2096 (1983). (4) M. A. Hoffbauer, C. F. Giese, and W. R. Gentry, J . Chem. Phys., 79, 192 (1983).
(5) T. E. Gough, R. E. Miller, and G. Scoles, J . Chem. Phys., 69, 1588 (1978). (6) T. E. Gough, R. E. Miller, and G. Scoles, J . Phys. Chem., 85, 4041 (1981). (7) T. E. Gough and R. E. Miller, Chem. Phys. Lett., 87, 280 (1982). (8) M. P. Casassa, D. S. Bomse, J. L. Beauchamp, and K. C. Janda, J . Chem. Phys., 72, 6805 (1980). (9) M. P. Casassa, D. S. Bomse, and K. C. Janda, J . Phys. Chem.,85,2623 (1981). (10) M. P. Casassa, D. S. Bomse, and K. C. Janda, J . Chem. Phys., 74, 5044 (1981). (1 1) M. P. Casassa, C. M. Western, F. G. Celli, D. E. Brinza, and K. C. Janda, J . Chem. Phys., 79, 3227 (1983). (12) J. Geraedts, S. Setiadi, S. Stoke, and J. Reuss, Chem. Phys. Lett., 78, 277 (1981). (13) J. M. Lisy, A. Tramer, M. F. Vernon, and Y. T. Lee, J . Chem. Phys., 75, 4733 (1981). (14) M. F. Vernon, J. M. Lisy, H. S. Kwok, D. J. Krajnovich, A. Tramer, Y. R. Shen, and Y. T. Lee, J. Phys. Chem., 85, 3327 (1981). (15) M. F. Vernon, D. J. Krajnovich, H. S. Kwok, J. M. Lisy, R. Y. Shen, and Y. T. Lee, J . Chem. Phys., 77, 47 (1982). (16) D. S. Bomse, J. B. Cross, and J. J. Valentini, J . Chem.Phys., 78,7175 (1983). (17) G. Fischer, R. E. Miller, and R. 0. Watts, Chem. Phys., 80, 147 (1983). (18) J. A. Odutola, R. Viswanathan, and T. R. Dyke, J. Am. Chem. Soc., 101, 4787 (1979).
0 1984 American Chemical Society
182 The Journal of Physical Chemistry, Vol. 88, No. 2, 1984
Letters
dimer and a cyclic structure for the trimer. The dimer structure is therefore similar to that of (H20),, in which the 0-H-0 hydrogen bond is linear.'9 Various experimental and theoretical estimates of the hydrogen bond energy in the methanol dimer ~ ~ we observe singlerange from 2.9 to 4.6 k c a l / m 0 1 . ~ ~Since photon dissociation at a photon energy of 2.9 kcal/mol (vide infra), the true hydrogen bond energy is probably near the lower end of this range. However, our experiments do not permit a rigorous upper limit to be placed on the bond energy, since we do not know how nearly the vibrational temperature of the dimers approaches the measured translational temperature of the beam. For the points which we wish to discuss here, it is sufficient to note only that the photon energy in excess of that required to break the hydrogen bond must be very small.
Experimental Section Our experiments were carried out with a pulsed molecular beam apparatus having a mass spectrometer detector, and one or two line-tunable pulsed C 0 2 lasers. The apparatus, experimental techniques, and data analysis procedures have been previously described in detaiL2 Upon ionization, methanol clusters (CH,OH), readily eliminate C H 3 0 to form (CH30H),-1.H+. Therefore, the neutral dimer and trimer were detected as CH30H2+and CH30H.CH30H2+, respectively, while the monomer was monitored at the CH30H+ parent peak in the mass spectrum. Because of the propensity of methanol to form large clusters in supersonic expansions, rather extreme dilution of methanol vapor in the carrier gas was necessary to perform experiments on the dimer. For the spectroscopic experiments a mixture of about 0.05% C H 3 0 H in 7 atm of H e was used, giving a beam with a translational temperature of about 3 K. The measurements of the speed and angle distribution of the dissociation products were carried out with a source containing about 0.1% C H 3 0 H in 7 atm of Ar, in order to improve the velocity resolution in the centerof-mass (CM) system by, reducing the laboratory speed of the primary beam. The translational temperature under these conditions was about 1 K. Both beams gave mass spectrometer intensity ratios for monomer:dimer:trimer of roughly 100:10:2. Results and Discussion We began this investigation by searching for evidence to support our initial expectation that two photons would be required to dissociate the dimer. A kinetic scheme in which the ground state is connected by a single-photon absorption to an excited state, which in turn is strongly and irreversibly coupled to the continuum, gives the Beer's law expression -lnfi(v) = u(v)F
(1)
wheref,(v) is the fraction of dimer remaining undissociated, U ( V ) is the frequency-dependent absorption cross section, and F is the fluence of the laser beam measured in number of photons per unit area. A two-photon process would yield a dependence on laser fluence which is greater than linear. The measured fluence de(19) (1977). (20) (21) (1951). (22) (23)
T. R. Dyke, K. M. Mack, and J. S. Muenter, J . Chem. Phys., 66,498 J. S.Rowlinson, Trans. Faraday Soc., 45, 974 (1949). W. Weltner, Jr., and K. S . Pitzer, J . Am. Chem. SOC.,73, 2606
C. B. Kretschmer and R. Weibe, J. Am. Chem. Soc., 76,2579 (1954). R. G. Inskeep, J. M. Kelliher, P. E.McMahon, and B. G. Somer, J. Chem. Phys., 28, 1033 (1958). (24) A. D. H. Clague, G. Govil, and H. J. Bernstein, Can. J. Chem., 47, 625 (1969). (25) G. S. Kell and G. E. McLaurin, J. Chem. Phys., 51, 4345 (1969). (26) E. E. Tucker, S. B. Farnham, and S.D. Christian, J . Phys. Chem., 73, 3820 (1969). (27) T. A. Renner, G. H. Kucera, and M. Blander, J . Chem. Phys., 66, 177 _ . . (1977) (28) L. A. Curtiss, J . Chem. Phys., 67, 1144 (1977). (29) William L. Jorgensen, J . Chem. Phys., 71, 5034 (1979). (30) R. J. Day and R. G. Cooks, Int. J. Muss Spectrum. Ion Phys., 35, 293 (1980). \-- ' ' I .
0
0.I
0.2
0.3
FLUENCE (J/cm2) Figure 1. Fluence dependences of the photodissociation yields for methanol dimers and trimers. The solid lines are least-squares fits to the data of the functional form given in eq 2.
pendences are shown in Figure 1 for a laser frequency near the absorption peaks for both the dimer and trimer. Contrary to our initial expectation, In V;) is seen to have a nearly linear dependence on F a t low fluences. At higher fluences, the onset of saturation behavior is observed. The curvature is opposite to that which would be expected for a two-photon process. The solid lines, which fit the data in Figure 1 very well, are least-squares fits of the form
where the parameter forepresents a fraction of the cluster signal (1 5% for the dimer and 7% for the trimer) which is not affected by the laser. There are two probable origins First, if the true hydrogen bond energy is greater than the photon energy, then single-photon dissociation will occur only in those dimers which possess enough internal excitation energy to place them within one photon of the dissociation limit. This effect could in principle be explored by observing the variation of fowith the degree of cooling in the supersonic expansion. In practice, the range of source conditions which gave sufficient dimer signals without severe contamination of the beam with larger clusters was not sufficient to permit a convincing demonstration of this effect. However, this phenomenon has been seen clearly in the (NH3)2 system.j2 Second, there is probably some contribution to the signal at the CH30H2+mass from the much more intense CH30H+ion originating from the monomer (which is not affected by the laser) because the small signal levels in these experiments required us to operate the mass spectrometer at high transmission efficiency and relatively low resolution. Despite the complication introduced in the data analysis by the presence of fo,the dimer photodissociation spectrum u(v) was obtained by measuring the dissociation yields at relatively low laser fluence (0.04 J/cm2) and extracting u(v) from eq 2. The spectrum, (31) "Orientational hole burning" is another phenomenon which can in principle give curvature of the observed sign. This phenomenon has been discussed by J. Geraedts, M. Snels, S.Stolte, and J. Reuss (private communication) and by M. P. Casassa, C. M. Western, and K. C. Janda (private communication). It arises because molecules with different angular momentum projection quantum numbers have different values of (jL.E), where ,liis the transition dipole moment and 3 the laser electric field vector. Although we lack the structural information necessary to estimate this effect quantitatively for (CHIOH)*, the model calculations performed by these groups lead us to believe that the effect should be small compared to the other sources of signal saturation in these experiments. (32) M. J. Howard, S. Burdenski, C. F.Giese, and W. R. Gentry, J. Chem. Phys., in press.
Letters
The Journal of Physical Chemistry, Vol. 88, No. 2, 1984 183 I
I
I / \\
cn L I
L
I
-1 FR EQ U E NCY ( cm? Figure 2. Photodissociation spectrum of methanol dimers, measured with a laser fluence of 0.04 J/cmZ. The solid line is a Lorentzian fit to the data having a peak at 1045.2 i 0.3 cm-' and a full-width at half-maximum of 13.8 i 0.8 cm-l. Peak frequencies of methanol gas (g) and liquid (1) phase are shown at the top of the figure.
shown in Figure 2, displays only a single, broad absorption peak in this frequency range. The peak is fitted well by a Lorentzian line shape having a full-width at half-maximum of 13.8 cm-'. The corresponding uncertainty principle lifetime is 0.38 f 0.03 ps. Both the high ftaction of dissociation which can be achieved and the Lorentzian line shape are consistent with homogeneous broadening of the absorption line. This was confirmed by attempts to observe hole burning in the absorption spectrum caused by a first laser at a fixed frequency while a second laser was scanned over the absorption peak for the remaining dimers.z No hole burning was observed, indicating that any inhomogeneous contributions to the line width which may be present are small compared to the homogeneous width. The only strong methanol monomer absorption in this frequency region is the vg C-0 stretching and this is presumably the mode which is excited in the dimers as well. Because the linear hydrogen bond in the dimer makes the two weakly coupled monomer constituents distinguishable, one would expect the C-0 stretches in the two monomers to be at different frequencies. We searched for dimer dissociation at other frequencies available from our COz laser in the 920-1090-cm-' range, but observed no other absorption peaks. It would appear that either the splitting between the two methanol v8 frequencies is so small that both peaks fit comfortably under the same Lorentzian profile or that the other absorption peak falls at frequencies not accessible to our laser. The dimer peak which is observed is shifted 12 cm-' to the blue relative to the transition frequency of the gas-phase monomer at 1033.5 cm-1.33 A peak shifted to the red by a similar amount would fall in the 9901025-cm-' region where there is a gap in the spectral output of our laser. Even allowing for the estimated f30% uncertainty in the absolute values of the absorption cross sections: the integrated oscillator strength for the dimer is small-only about 50% of that of the isolated It appears likely that part of the total ug absorption intensity of the dimer is to be found outside of the range of frequencies explored in these experiments. The trimer photodissociation spectrum was similar to that of the dimer in both peak frequency and line width. Information on the energetics of the dimer fragmentation was obtained from measurements of the monomer product speed and (33) Jerry Rodgers, Ph.D. Thesis, University of Florida, 1980. This report gives the peak frequency for the ug mode as 1033.5 cm-', and the integrated absorption intensity ( M ) * = 0.03720 D2.
I
I
I
I
I
I
0.1
0.2
I
C H,O3H
\
I
0
I
I
I
I
0,3 0.4 0 5 RE LAT WE KINE TIC ENERGY(me4 Figure 3. CHBOHproduct CM kinetic energy distribution for dissociation of (CH30H), at u = 1045.1 cm-'. Data points are shown for laser polarizations parallel to (X) and perpendicular to ( 0 )the molecular beam axis. The solid line is a fit to the data points of the function given in eq 3.
angle distribution. Even though these measurements were made with Ar as the carrier gas in order to improve the resolution in C M coordinates, the C M recoil speeds were so small that significant product signals were seen only within f3' of the primary beam axis. Collimation of the primary beam to 1O full-width at half-maximum and the use of several skimmers to attenuate the tails of the angular distribution were necessary in order to make these measurements. The monomer product speed and angle distributions were acquired for laser polarizations both parallel to and perpendicular to the molecular beam axis by alternating the laser polarization on successive shots. The two distributions were identical within experimental uncertainty, indicating an isotropic angle distribution in C M coordinates. To analyze the product C M kinetic energy distribution, points on the velocity vector distribution at a C M scattering angle of 90' (perpendicular to the centroid laboratory velocity) were chosen because the resolution in C M speed is best at that angle.2 These points are shown for both laser polarizations in Figure 3. Although the data set is too sparse to permit the form of the energy distribution P(E) to be determined well, we fitted the distribution with a function of the form P(E) a
exp( l S E / ( E ) )
(3)
where ( E ) is the mean CM kinetic energy, because that functional form has previously given good fits to data on other vdW syst e m ~ . * -The ~ least-squares fit gave ( E ) = 0.20 f 0.06 meV (0.0046 A 0.0014 kcal/mol) which represents less than 0.2% of the photon energy. It is likely that the actual mean product kinetic energy is somewhat smaller, because there is some broadening in the product angular distribution due to the finite apparatus resolution. The extremely small product recoil energy is consistent with the expectation that the photon is only barely energetic enough to break the hydrogen bond, and with the propensity which has been both p r e d i ~ t e dand ~~,~~ for whatever excess energy is available to the products to be channeled into internal rather than translational degrees of freedom. Conclusions We realize that there are some aspects of these experiments which are not completely satisfactory-notably the lack of detailed (34) J. A. Beswick and J. Jortner, Adu. Chem. Phys., 47, 363 (1981). (35) G.E. Ewing, J . Chem. Phys., 71, 3143 (1979).
184 The Journal of Physical Chemistry, Vol. 88, No. 2, 1984
knowledge of the internal energy distribution in the dimers prior to excitation, and the lack of sufficient resolution in product kinetic energy to determine quantitatively the shape of the distribution. However, the main points which we wish to make here are qualitative ones, which do not depend strongly on these quantitative details. The first point concerns the comparison of the methanol dimer photodissociation line width with those of much more weakly bound vdW clusters. Even though some small part of the photodissociation line width for methanol dimers may be attributable to inhomogeneous broadening, the homogeneous line width must still be close to 14 cm-’ which corresponds to a lifetime of 0.4ps for the state populated initially by the laser. These figures are within the narrow range of values previously reported for weakly bound clusters of several molecules which absorb in the same range of photon energies.’-” Thus, an important question which we raised above has been answered-the photodissociation line width is not highly sensitive to the amount of excitation energy in excess of that required for dissociation. The second point concerns the interpretation of the homogeneous line width and its associated lifetime. As we have discussed previously:4 it is difficult to adhere simultaneously to the notions that (a) the photodissociation line widths are direct measures of the rates for vibrational predissociation, and (b) the unimolecular dissociation rates are governed by statistical flow of energy within the cluster. The present data strongly reinforce the conclusion that at least one of these two assumptions must be abandoned for infrared photodissociation of vdW molecules. Within the small set of systems for which data are now available, we have clear examples in which the line width does not depend much on the number of vibrational degrees of freedom in the cluster or on the excess energy which is available, but does depend on which vibrational mode is excited at nearly constant photon energy. All of these observations are qualitatively contrary to the predictions of statistical treatments such as the RRK or RRKM theories,36 if the line widths are taken to be proportional to the unimolecular decay rates in these systems. Let us consider these two hypotheses in turn. Even though RRKM theory has been remarkably useful in interpreting data on unimolecular reaction rates for covalently bound molecules, there have been few tests of the theory on a truly microscopic level. Also, these vdW systems are unusual in several respects, and may not be amenable to the same treatments as covalently bound molecules. On the other hand, the most significant difference between ordinary covalent molecules and vdW ~
~
(36)D.G. Truhlar, W. L. Hase, and J. T. Hynes, J. Phys. Chem., 87,2664 (1983),and references therein.
Letters molecules would appear to be the great disparity in the latter between the vibrational frequencies within the monomer units and those of the vdW coordinates. This feature might mitigate against the rapid exchange of energy between the covalent and the vdW modes, making the dissociation reaction anomalously slow. However, since the experimental results indicate instead an extremely rapid decay of the initial monomer vibration by coupling to the vdW coordinates, this feature of the vdW systems would appear not to be a likely source of nonstatistical behavior. The other possibility is that the homogeneous line widths in these experiments are not directly related to the rates of vibrational predissociation. A Lorentzian line shape implies an exponential decay of the transition moment with time,37but the product of that decay is not necessarily a dissociated cluster. The coherent quantum state which is produced upon absorption of the laser photon decays by simultaneous flow of energy and loss of phase coherence, both caused by anharmonic coupling of the initial monomer vibration to the vdW coordinates. When enough energy has accumulated in those vdW coordinates which are asymptotically translational in character, the cluster can be said to be dissociated. However, the amount of energy which must be transferred to the vdW coordinates in order to destroy the initial coherent quantum state might be much smaller than that required to dissociate the cluster. A definitive experiment, which would compare an independently measured cluster dissociation rate with the relaxation rate derived from the line width, has yet to be done. Nevertheless, the special features of the methanol dimer data permit us to make a strong argument in favor of the hypothesis that the state relaxation rate is greater than the rate of vibrational predissociation. If we take the estimated root-mean-square recoil speed of 5 X lo3cm/s as characteristic of the dissociation channel, we find that, even if the products are accelerated away from each other instantaneously, they can move a distance of only 0.2 A during the 0.4ps characteristic lifetime! Even allowing for the experimental uncertainties in the homogeneous line width and recoil energy distribution, we consider it unlikely that these observations can be reconciled with the point of view that the derived lifetime corresponds to actual dissociation of the dimer. Acknowledgment. This research was supported by the National Science Foundation under Grant No. CHE-8205769, and by the Graduate School of the University of Minnesota. Registry No. Methanol, 67-56-1. (37)P.Avouris, W.M. Gelbart, and M. A. El-Sayed, Chem. Rev., 77,793 (1977);E.J. Heller, Acc. Chem. Res., 14,368 (1981),and references therein; P. R. Stannard and W. M. Gelbart, J . Phys. Chem., 85, 3592 (1981).
