8282
J. Phys. Chem. 1991,95, 8282-8293
Energy (e")
Flgm 3. Sticking probability (logarithmic scale) vs the incident collision energy (in electronvolts) for different f a c e of a pt crystal. The real part of the optical potential takes full cognizance of the atomic arrangement at the different faces. The imaginary part of the optical potential is the same for all three computations,with L = 1.0 eV, zo = 2.0 bohr, and Y = 0.1 bohr. For the (1 11) face the O2molecule can approach the surface closer in than for the other two. Hence at higher energies its sticking probability begins to decrease with increasing energy that is the generic behavior for nonactivated chemisorption.
much simplifies the interpretation of the resulting energy dependence. It implies that only part of the imaginary potential V l ( r ) ,which is in the classically accessible region, z > z,, can influence the removal of molecules from the direct channel. The turning point z, defined by E = Vo(z,)occurs at lower values of z as the energy is increased. At low collision energies the imaginary potential is de facto inaccessible. The Gaussian form of V l ( z )means that 7 is never exactly zero. However, at low energies 7 is itself exponentially small so that P is zero for all intents and purposes. The initial exponential increase of 7 with E leads to the apparent threshold in P seen in Figure 1. We reiterate that results indistinguishable from Figure 1 are obtained using the first-order perturbation approximation for q so that the post threshold increase in P is here entirely due to the behavior of the scattering wave function in the classically allowed region. Why is tunnelling into the forbidden
region unimportant in our model? The answer is that at lower energies when tunnelling will be most important, 7 is exponentially small itself, so that P is essentially negligible. At higher energies the tunneling contribution to 7 remains small yet 7 itself is larger, so that P is determined primarily by the classically allowed contributions to 7. Figure 3 shows the calculated dissociation probability of O2 on three different faces of R. Our purpose was not to reproduce any particular experimental results but to demonstrate that the model can exhibit considerable structure sensitivity. The real potential Vo(z)was calculated as described earlier by summation of pair potentials with respect to all surface atoms over a particular site. To make a direct comparison between scattering from three different faces of the same crystal, an -atop" site was chosen in each case to calculate the real potential Vo(z).The same Gaussian functional form for V,(z)is used throughout. The differences between the calculations for the three different faces are entirely due to the distances of closest approach. For the (1 11) face the molecule can approach closer and thereby sample more of the imaginary part of the potential. It is interesting to note that the same order of reactivity of the three faces is observed experimentallyBfor N2on Fe. Other things being equal, the model predicts that the most important parameter is the distance of closest approach.
Conclusion The optical model is based on the distinction between those molecules that are scattered promptly off the surface and those that are not. The sticking probability is computed in terms of an imaginary component of the molecule-surface potential. In this quantitative study we have established that the activated adsorption can be represented by an imaginary potential that is localized at short molecule-surface distances. There is then no strict energy threshold for adsorption, but there is a de facto threshold above which the sticking probability increases exponentially with collision energy. The sensitive dependence of the probability on the distance of closest approach can explain the significant differences in reactivity exhibited by different faces of the same crystal. Registry No. N2,7727-37-9; Re, 7440-15-5; 02,7782-44-7; Pt, 7440-06-4.
Dependence of Intramolecular Vibrational Relaxation on Central Atom Substitution: v1 and 2v, Molecular Beam Optothermal Spectra of (CH3)&C=CH and (CH,)3SIWH E. R. Tb. Kentel, K. K. Lehmann,* T. F. Mentel, B. H. Pate, and G. Stoles* Department of Chemistry. Princeton University, Princeton, New Jersey 08544 (Received: February 25, 1991) Using the optothermal detection method for molecular beam infrared spectroscopy, we have measured, with rotational resolution, All spectra the fundamental and first overtone of the acetylenic C-H stretch in (CH3),CC=CH and (CH3)@=H. show homogeneous broadening due to intramolecular vibrational energy relaxation (IVR), which results in Lorentzian line shapes for the individual R(J)and P(J)transitions. From the homogeneous line widths we are able to determine the lifetime of the initial vibrational excitation. For (CH3)3CC=CH the lifetimes in the fundamental and first overtone are 200 and 110 ps respectively. For (CH3)pSiC=CHthe lifetimes are 2 and 4 ns for the fundamental and first overtone. All of these lifetimes are long compared to values typically given for IVR lifetimes. Despite the fact that the silicon compound has a higher density of states at both levels of excitation, the line width of the silicon compound is much narrower than that of (CH3)3CCWH. Furthermore, the density of states of the silicon compound increases by more than a factor of IO00 in going from the fundamental to the overtone, and yet the line width of the overtone is narrower than it is in the fundamental. Although we consistentlyfind that the IVR lifetime of the molecule with the heavier central atom is longer, a simple heavy-atom effect for the inhibition of IVR does not appear to fully explain the data.
Introduction The study of intramolecular vibrational energy relaxation in isolated molecules is of central importance in physical chemistry. In particular, the great success of standard statistical reaction rate 0022-3654/91/2095-8282S02.50/0
theory (RRKM)'v2suggests that vibrational energy redistribution is rapid on the time scale of typical chemical reactions. Studies (1) Oref. I.; Rabinovitch,
B. S.Acc. Chem. Res. 1979, 12, 166.
0 1991 American Chemical Society
Intramolecular Vibrational Relaxation
of vibrational relaxation, in both the fmt excited electronic state>-' and the ground electronic state: have shown that the onset of IVR occurs at quite low energies for larger polyatomic molecules. Often extensive IVR is observed in the energy region of the high-frequency vibrational fundamentals. For the ground state it has been seen that the onset of IVR occurs when the density of background rovibrational states reaches about 100 ~tates/cm-'.~ This threshold level predicts the onset of IVR for a very large number of molecules for excitations in a number of different chromophores. Although there is general agreement that the onset of IVR occurs at low energies, there is still very little information on the true homogeneous lifetime of vibrational excitations. Estimation from the contour of gas-phase vibrational bands has been one experimental method used to provide lifetime information. However, evaluations from gas-phase measurements can greatly overestimate the rapidity of the energy relaxation process since the rotational and hot-band congestion can cause extensive inhomogeneous broadening in the measurement. For example, the gas-phase photoacoustic spectra of benzene suggest that IVR is very rapid in the overtones of the C-H stretches.* Molecular beam double-resonanceexperiments, which provided some rotational selectivity, later showed that the homogeneous IVR lifetime of the first overtone was significantly longer than suggested by the gas-phase result^.^ There is inherently some ambiguity about what is meant by the homogeneous lifetime of an isolated molecule. The homogeneous spectrum is clearly defined as the set of transitions arising from a single, well-defined initial state (a single rotational state in the vibrational ground state, for example). Under experimental conditions allowing ultimate resolution (determined by the radiative line width), such a spectrum will consist of a series of sharp transitions as long as the density of states is low enough that only a single state lies within the radiative line-width profile.IO A short laser pulse (short on the time scale of the intramolecular vibrational relaxation) will create a unique nonstationary state (the bright state) due to the excitation of the set of molecular eigenstates lying within the frequency bandwidth of the laser pulse. The Fourier transform of the autocorrelation of the homogeneous spectrum, denoted &,b(t),'l is then equal to the probability of the molecule being in the initially created bright state at time t. Thus such a frequency-resolved homogeneous spectrum directly provides the probability of being in the bright state but does not provide direct information about what other states are populated by the dynamics. &,(I) will always have recurrences on the time scale of the density of states, leading to sharp eigenstates in the spectrum when the resolution is greater than the spacing between background states. For experimental cases where the homogeneous spectrum consists of a large number of eigenstates (intermediate or statistical case IVR) the initial decay of Pbb(t)will be approximately exponential.IO The time scale of this initial decay is given by the inverse full width of the homogeneous spectrum in the frequency-resolvedexperiment. It is often the case that P b ( t ) will have recurrences at one or more times between these two limits reflecting multiple time scales over which the vibrational excitation is transferred between different modes in the molecule. It is certainly overly simplistic and even a little misleading, to describe such rich dynamics in terms of a single "lifetime". In certain cases, however, Pb(t) decays rapidly compared to the long time limit imposed by the density of states, and recurrences do not occur until this time. As discussed by Heller," in this case (2) Subds, A. S.; Schulz, P. A.; Grant, E. R.; Shen, Y. R.; Lee, Y. T. J . Chem. Phys. 1979, 70, 912. (3) Parmenter, C. S. J . Phys. Chem. 1982.86, 1735. (4) Parmenter, C. S. Faraday Discuss. Chem. Soc. 1983, 75, 7. (5) Smalley, R. E. Annu. Rev. Phys. Chem. 1983, 34, 129. (6) McDonald, J. D. Annu. Rev. Phys. Chem. 1979, 30, 29. (7) Kim, H. L.; Kulp, T. J.; McDonald, J. D. J . Chem. Phys. 1987,87,
._.-.
A116
(8) Rcddy, K. V.; Heller, D. F.; Berry, M. J. J . Chem. Phys. 1982, 76, 28 14. (9) Page, R. H.; Shen, Y. R.; Lee, Y. T. J . Chem. Phys. 1988.88,4621. (10) Freed, K. F.; Nitzan, A. J . Chem. Phys. 1980, 73.4765. ( I 1 ) Heller, E. J. Faraday Discuss. Chem. Soc. 1983, 75, 141.
The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8283 the molecular motion has sampled the energy shell almost ergodidly and calling the decay a "relaxation" agrees with common usage of the word. We believe that this situation describes the spectra we report in this paper. It must be remembered that any spectroscopic experiment is sensitive only to recurrences over some window of time determined by the spectral window explored on the one hand (giving the shortest time) and the effective resolution on the other (giving the longest time). Our experimentsare only sensitive for long times up to about 20 ns (determined by residual Doppler broadening, which limits our experimental resolution). For the molecules we are studying, this long time limit is less than the time scale imposed by the density of states. Thus we can rigorously interpret our spectra only as implying a homogeneous relaxation that is effectively irreversible for a time of 20 ns or less. The presence of recurrences on a time scale longer than our experimental limit would imply relaxation processes much slower than those reported herein, which are already the slowest IVR rates that have ever been reported. Recently, high-resolution measurements of the vibrational spectra of larger polyatomic molecules in molecular beams have been performed with the goal of studying the IVR process.l2-I8 In this paper we are interested in these frequency domain experiments and their interpretation in the context of IVR. There has also been much progress in time domain measurements of the IVR process in both the ground electronic state19 and the first excited electronic state;mhowever, we limit the scope of this paper to the results obtained from high-resolution spectroscopy. In these spectra the presence of IVR is indicated by extensive perturbations to the expected zero-order spectrum. These perturbations occur when vibrational states, which otherwise would have no transition strength (the so-called dark states), couple to the optically active vibrational state being studied (the bright state). This coupling allows the vibrational energy to redistribute over the entire molecule since the coupled states often involve the motion of a number of different atoms in the molecule. Through the study of these perturbations the high-resolutionspectrum provides information on the vibrational dynamics of the molecule. The information is often obtained with full-state (J,K) resolution, and so the dynamical information obtained is truly homogeneous. The high-resolution studies reported to date have all shown the presence of several very weak perturbation^.'^-'^ The states that appear in the spectrum due to these vibrational couplings to a single zero-order state are termed the molecular eigenstates. Typically, as the background density of states increase, the number of molecular eigenstates observed will also increase. When the number of molecular eigenstates reaches about 10, the molecule is said to be in the "intermediate regime" of IVR.'O It has been shown that in this regime the lifetime of the initial excitation can be determined by calculating the time evolution of a coherently excited superposition of the eigenstatessZ1 When the exciting optical pulse is short compared with this lifetime, the initial decay of the prepared state is approximatelyexponential at early times with a decay rate given by a Fermi Golden Rule formula.lOJ Since it is often possible to assign the high-resolution spectrum with rotational quantum numbers, this calculation can be performed homogeneously; that is, only the eigenstates with the same (12) deSouza, A. M.; Kaur, D.; Perry, D. S. J . Chem. Phys. 1988,88, 4569. (13) Go, J.; &hardy, G.A.; Perry, D. S. J . Phys. Chem. 1990,94,6153. (14) Bethardy, G. A.; Perry, D. S. J. Mol. Specfrosc. 1990, 144, 304. (15) McIlrov, A,; Nesbitt, D. J. J . Chem. Phvs. 1989. 91. 104. (16) McIlrG, A.; Nesbitt; D. J. J . Chem. Phs. 1990; 92; 2229. (17) Lehmann, K. K.; Pate, B. H.; Scoles, G. J . Chem. Soc., Faraday Trans. 1990. 86. 2071. (18) Lehmann, K. K.; Pate, B. H.; Scoles, G. J. Chem. Phys. 1990, 93, 2 152. (19) Stewart, G. M.; Ensminger, M. D.; Kulp, T. J.; Ruoff, R. S.; McDonald, J. D. J. Chem. Phys. 1983, 79, 3190. Stewart, G.; Ruoff, R.; McDonald, J. D. J. Chem. Phys. 1984,80,5353. Kulp, T.; Ruoff, R.; Stewart, G.; McDonald, J. D. J . Chem. Phys. 1984,80, 5359, 5359. (20) Felker, P. M.; Zewail, A. H. J . Chem. Phys. 1985,82, 2961. Felker, P. M.; Zewail, A. H. J . Chem. Phys. 1985,82,2975. Felker, P. M.; Zewail. A. H. J. Chem. Phys. 1985,82,2994. Felker, P. M.; Lambert, W. R.; Zewail, A. H. J . Chem. Phys. 1985.82, 3003. (21) Lahmani, F.; Tramer, A.; Tric, C. J . Chem. Phys. 1974, 60, 4431.
8284 The Journal of Physical Chemistry, Vol. 95, No. 21, 199‘1
good quantum numbers, typically the rotational quantum numbers, are included in the calculation. In this way the homogeneous lifetime of a few molecules have been calculated.’= The reported lifetimes have ranged from a few hundred picoseconds to a few nanoseconds. These homogeneous lifetimes are longer than the few picosecond lifetimes often assumed for IVR. When the density of states is very high, the molecule enters the statistical regime of IVR.’O In this case there is irreversible flow of the energy out of the initially excited mode. This decay takes the form of an exponential decay and a Lorentzian lineshape will be observed in the spectrum. We have recently observed true Lorentzian broadening due solely to IVR in the fundamentals of (CH3)$CWH and (CH3)$iC=CH.18 In other studies the spectra have been fit to convolutions of Lorentzian line shapes with a predicted rigid-rotor spectrum.I6 The observed lifetimes have been on the order of a few picoseconds to a few nanoseconds. The question of the homogeneous IVR line width for vibrational excitations is of obvious importance for the prospects of performing laser-enhanced, mode-specific, chemistry of large molecules: a longstanding goal of experimental physical chemistry. It has recently been shown that direct overtone excitation of HOD leads to a great enhancement of a mode-specific reaction with H atoms.23 However, HOD is a molecule that is too small to show IVR at the level of excitation used in the experiment, so the energy must remain localized until a collision occurs. For larger molecules a prerequisite for similar mode-specific reactions becomes that the IVR rate be slower than the collision rate, so that the energy will still be localized in the reaction coordinate when a possible reactive collision occurs. Since for typical gas pressures (- 1 atm) there will be about 10’O collisions/s, IVR lifetimes on the order of a few hundred picoseconds or longer are required. In the early 198h chemical activation studies on molecules with heavy central atoms showed non-RRKM reaction rates suggesting that the presence of a heavy atom could serve to localize energy in one of the ligand^.^^,^^ These initial results led to a number of additional experimental ~ t u d i e s ~and ~ * ~to’ much theoretical directed toward determining if a “heavy-atom effect” operates in these systems to decrease the IVR rate. However, both the experimental and theoretical results were somewhat ambiguous. Part of the problem is separating the effect of simply changing the mass from the chemical effects that accompany the substitution of a larger atom, such as reduced bond strengths and longer bond lengthsDJ5 Possible evidence of a heavy-atom effect for reducing IVR has also come from gas-phase photoacoustic studies of the overtones of molecules containing heavy A study of the relaxation rates of alcohols and silanols in solution also showed a longer lifetime for the heavier species.38 Still, the question of whether heavy-atom substitution inhibits IVR, as well (22) Pate, B. H.; Lehmann, K. K.; Scolcs, G. To be published in J. Chem.
Phys. (23) Sinha, A.; Hsiao, M. C.; Crim, F. F. J . Chem. Phys. 1990,92,6333. (24) Rogers, P.; Montague, D. C.; Frank, J. P.; Tyler, S.C.; Rowland, F. S . Chem. Phys. Lett. 1982,89,9. (25) Rogers, P. J.; Selco,J. I.; Rowland, F. S.Chem. Phys. Lett. 1983,97, 313. (26) Wrigley, S.P.; Rabinovitch, B. S.Chem. Phys. Lett. 1983,98, 386. (27) Wrigley, S.P.; Oswald, D. A.; Rabinovitch, B. S.Chem. Phys. Lett. 1984, 104, 521. (28) Lopez, V.; Marcus, R. A. Chem. Phys. Lett. 1982, 93, 232. (29) Swamy, K. N.; Hase. W. L. J . Chcm. Phys. 1985, 82, 123. (30) Lopez, V.; Fairen, V.; Lederman, S. M.; Marcus, R. A. J . Chem. Phys. 1986,84, 5494. (31) Lederman, S.M.; Lopez, V.; Voth, G. A.; Marcus, R. A. Chem. Phys. Lett. 1986, 124, 93. (32) Lederman, S.M.: Lopez, V.; Fairen. V.: Voth, G.A,; Marcus, R. A. Chem..Phys. 1989. 139, 171.(33) Uzer. T.; Hynes, J. T. Chem. Phys. 1989, 139, 163. (34) Uzer, T.; Hynes, J. T. J. Phys. Chem. 1986, 90,3524. (35) A discussion of these results can be found in Faraday Discuss. Chem. Soc. 1983, 75, 155 (General Discussion Section). (36) Manzanares, I. C.; Yamasaki, N. L. S.;Weitz, E.; Knudtson, J. T. Chem. Phvs. Lett. 1985. 117. 411. (37) Manzanares, I. C.;Yamasaki, N. L. S.;Weitz, E. J . Phys. Chem. 1989, 93, 4133. (38) Heilwcil, E. J.; Casassa, M. P.; Cavanagh, R. R.; Stephenson, J. C. J . Chem. Phys. 1986.85, 5004. ~
Kerstel et al. as which physical properties actually define the heavy-atom effect, are open problems. In this paper we report homogeneous lifetime data for isolated molecules using high-resolution, molecular beam optothermal spectroscopy. We have measured both the fundamental and first overtone of the acetylenic C-H stretch in 3,3-dimethylbutyne (tert-butylacetylene) and (trimethylsilyl)acetylene, where the central atom is substituted by silicon. The ability to measure the lifetime at two levels of excitation allows us to see if a mass dependence alone can account for our results or whether other mechanisms are important in determining the IVR lifetime of the vibrational excitation. These molecules provide a convenient model system for studying the vibrational energy relaxation of molecules containinga heavy central atom. Most of the background states involve motions of the trimethyl end of the molecule since most of the vibrational modes related to the acetylene chromophore have high frequencies. For the vibration to kinetically reach these modes it must pass through the central atom. Since we are exciting a low-lying vibrational motion that is localized in the terminal C-H end of the acetylene, we expect that central atom substitution will cause only small differences in the nature of the motion initially excited. Since the central atom is on the symmetry axis and near the center of mass of the molecule, there are only small changes in the rotational constants. The symmetry of the two molecules is also the same. Therefore, direct comparison of the spectra can be made, allowing us to clearly determine the effect of central atom substitution.
Experimental Section The molecular beam infrared spectrometer uses the technique of optothermal bolometric d e t e ~ t i o n . ’ ~ .In~ short, a well-collimated molecular beam, of a carrier gas (He) seeded with the molecule that is to be studied, is crossed with infrared laser radiation. A bolometer detector placed further downstream detects changes in the internal energy of the molecular beam. Using two color center lasers, the tuning range comprises both the fundamental and the first overtone vibrational excitation region of (among others) acetylenic C-H stretches. In this section we will describe first the molecular beam machine, followed by the laser and data acquisition systems. Because of the particular advantages offered by this technique for overtone spectroscopy, we will conclude this section by comparing it in some detail to other methods. Molecular Beam Machine. The molecular beam machine, showing in Figure 1, consists of two vacuum chambers, each pumped by a 5000 L s-’ oil-diffusion pump, backed by a single rotary/Roots combination. In one chamber the sample gas is expanded through a 30-pm diameter nozzle (a Structure Probe, Inc., electron microscope aperture) at a typical backing pressure of 10 bar, with dilution ratios in the range 0 5 1 % . The molecules used in this study were obtained from Aldrich Chemical Co. The vapor phase was used without further purification. The beam source and gas-inlet line assembly can be heated, to approximately 400 K at the nozzle, in order to prevent excessive clustering, while maintaining high throughput rates. For the study of van der Waals molecules, for which the machine was originally designed, the source is also equipped with a cryogenic cooler. A 0.5-mm-diameter conical skimmer, located 12 mm downstream, collimates the polecular beam, which enters the second chamber and is detected by a liquid helium cooled (1.5 K) composite-type silicon bolometer (Infrared Laboratories) located 44 cm from the nozzle. Measurement of the dc current through the bolometer as a function of its bias voltage revealed a noise-equivalent power of 5 X W Hz-II2 and a sensitivity of 5.5 X IO5 V W-I. The W Hz-’/’ manufacturer’s (measured) specifications are 3 x and 7.7 X lo5 V W-I, respectively. The 3-dB point in the fre(39) Gough, T. E.; Miller, R. E.; Scoles, G. Appl. Phys. Lett. 1977, 30, 338.
(40)Miller, R. E. In Atomic and Molecular Beam Methods; Scoles, G., Ed.; Oxford University Press: Oxford Vol. 2, Chapter 6, in press.
Intramolecular Vibrational Relaxation
The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8285
,wF=-\--[ n
quency response curve occurs near 400 Hz. The detector “sees” the molecular beam through a 1.5 X 3 mm slit in its liquid helium cooled shielding. To further reduce the amount of black-body radiation and scattered laser light, a second aperture, measuring 1.5 X 4 mm and held at liquid nitrogen temperature, is placed approximately 65 mm in front of the bolometer. Even with these measures in place, the output power level of our overtone (1.5 pm) laser is sufficiently high to produce an appreciable background signal, on the order of 10 times the noise level. Changes in the baseline, sometimes observed in overtone spectra, therefore reflect changes in the output power as the laser is scanned. The infrared laser radiation is crossed with the molecular beam by weakly focusing it into a plano parallel mirror multipass arrangement, thereby increasing the detection sensitivity by 1 order of magnitude over a single-pass crossing. Due to the slightly nonorthogonal crossings, the resolution is limited by a residual Doppler broadening amounting to 10 MHz at 3 pm and 20 MHz at 1.5 pm. The laser is amplitude modulated at 280 Hz, in a window in the noise spectrum. The detector signal is preamplified and fed into a lock-in amplifier (Stanford Research 510). Typical root-mean-squared noise levels in a 1-Hz bandwidth are around 60 nV. Expanding 1% acetylene in helium at a stagnation pressure of 10 bar, we achieve a S / N ratio of lo4 on the P(l) transition for the fundamental (the 3-pm v 3 band) and about 5 X lo3 for overtone (the 1.5-pm v, v3 band) excitation. However, taking into account that in this particular case the fundamental transition is saturated, the overall sensitivity for overtone excitation is about 8 times below that of fundamental excitation. This is consistent with the number calculated considering the two transition dipoles and the available laser power. Laser System and Data Acquisition. Infrared laser radiation is provided by two commercial color-center lasers. The first, a Burleigh FCL- 120, relies on laser action in the 1.5-pm region of TIo(1) color centers in a KCl host. It is pumped with the fundamental output at 1.064 mm and 1.9 W of a Spectra-Physics 3460, continuous-wave(CW) Nd:YAG laser. Mode locking of the pump laser and an optical isolator both provide protection against relaxation oscillations caused by optical feedback. This
+
0
color center laser is tunable, single-mode, from 1.45 to 1.58 pm and provides about 150 mW of power at 1.53 pm, measured at the machine. Its free running line width is estimated to be 6 MHz (from a molecular beam acetylene absorption with a single orthogonal laser crossing) and is believed to be caused mainly by pump laser power fluctuations. The second laser, the more common Burleigh FCL-20, uses three crystals to achieve a combined single-mode tuning range from 2.3 to 3.45 pm. In the region of the fundamental acetylenic C-H stretch, around 3.0 pm, we obtain 18 mW (again measured at the machine) when pumping the RbC1:Li-F,(II)-crystal with 2 W from the 647.1-nm line of a Spectra-Physics Model 171 Kr+ laser. The free-running line width is on the order of 1 MHz. The singlemode scanning of these lasers is completely computer controlled. To ensure lasing on the proper cavity mode in the course of a scan, it is essential that the intracavity etalon, and to a lesser extend the grating, accurately track the scanning cavity mode. To this end, both etalon and grating are advanced in a feed-forward manner. In addition, the etalon transmission is actively locked to the lasing cavity mode with a feedback loop, as described previously by Kaspar et al.4’ One aspect of the operation of our lasers that deserves to be described in detail is the way in which the scans are linearized in frequency. This is an important issue for high-resolution spectroscopy, as tuning of the intracavity elements can cause frequency jumps of which the exact magnitude is unknown but that are of the same order of magnitude or larger than the desired spectral precision (Le., typically 1 order of magnitude better than the experimental line width). When, for example, the Littrow mount grating is advanced, an associated small change in cavity length generally causes the laser to rescan anywhere from 0 to 20 MHz of the spectrum. The exact step size is unpredictable, due to the finite mechanical accuracy of the sine-drive/grating combination. A common solution to this problem has been to scan the laser to a nearby transmission of a long, temperature-stabilized (41) Kaspar, J. V. V.;Pollock, C. R.;Curl, Jr., R. F.;Tittel, F.K. Appl. Opt. 1982, 21, 236.
8286 The Journal of Physical Chemistry, Vol. 95, No. 21, 199'1 etalon, so the scan can be resumed at exactly the same point after the grating has been advanced." A similar procedure then has to be followed when the end mirror and intracavity etalon piezo ramp voltages need to be reset. This makes the necessary software rather complicated and slow. To overcome these problems, we continuously monitor the laser frequency with two scanning etalons (spectrum analyzers), using an electronic circuitry, originally designed and built by W. S.Woodward for the laboratory of R. E. Miller.'2 A 150-MHz FSR etalon (Burleigh CFT 500) serves as the frequency reference, while an 8-GHz etalon is used to correctly identify the 150-MHz etalon order. The electronic circuitry receives the piezo ramp and the scanning etalon detector signals. It produces as its output for each scanning etalon the piezo ramp voltage for which (the first) transmission occurred. In this way, a continuous frequency map of the scan is obtained and stored with the data (bolometer signal and gas-cell transmissions). The linearity of the spectrum now only depends on the linearity of the I50-MHz etalon piezo scanning over one FSR and the frequency stability of the etalon. The etalon is therefore temperature stabilized to 0.01 OC and hermetically sealed. A nonlinearity in the response of the 150-MHz etalon piezo can be made very small by adding an independent quadratic term to its ramp voltage. This frequency monitoring scheme allows for a relatively simple and efficient programming of the loop that controls the singlemode scanning and can achieve scan speeds up to 10 cm-'/h. When the scan is completed, the discontinuities in the frequency spectrum are removed by (partially interactive) software routines. The data are subsequently transferred to the spectral fitting program D E C O M P ~to~ extract the linepositions and lineprofile (Voigt) parameters. Comparison with Other Methods. It is only recently that high-resolution spectroscopic studies of larger molecules have been carried out under sub-Doppler molecular beam conditions with the explicit purpose of studying IVR in the ground electronic state. The experimental challenges are substantial: especially in the sparse and intermediate regimes, ultimate resolution and sensitivity are required to observe all states (perturbation) that appear in the spectrum and that are often due to very weak high-order couplings. Furthermore, an accurate determination of the rotational constants (in particular the aA*sand aB's) is useful in determining the character of the perturbing state@). Therefore, even though extreme cooling of the intermolecular degrees of freedom can greatly reduce the spectral congestion and improve the S/N on low-J and low-K lines, it is actually desirable to obtain as "warmwa spectrum as the S / N and resolution will permit. With the above in mind, we will discuss hereafter the factors that are important in evaluating the two related experimental techniques employed to date in these high-resolution IVR studies: direct absorption and energy deposition. In approximate order of importance, for high-resolution studies of stable molecules, these factors are as follows: (i) Sensitivity. In the direct absorption method, the laser is passed (in a multipass arrangement) through the high-density region of an unskimmed, free-jet expansion. Molecular absorption is measured by the resulting attenuation of the laser beam. Since the optical density of the free jet is very low, extreme demands are placed on the detection system and in particular the laser amplitude stability. It is immediately seen that the sensitivity in this case does not depend on the available laser power (as generally the noise level is limited by laser amplitude noise, rather than the NEP of the detection system). The sensitivity is ultimately limited to the laser shot-noise level. With a carefully designed twebeam detection system Nesbitt and -workers obtained a near shot-noise limited minimum detectable absorption of 1.4 X lod Hz-'IZ for their difference-frequency, slit-jet spectrometer.u This figure may seem low compared to the sensitivity of a color-center laser (42) Circuit designed by W.S. Woodward,Digital Specialties, 1702 Allard Rd., Chapel Hill, NC. (43) DeCOMP was provided by P.Bernath and was originally written by J. Brault, National Optical Astronomy Observatory, Tuscon, A Z 85719. (44) Lovejoy, C. M.; Nesbitt, D. J. J . Chcm. Phys. 1987, 86, 3151.
Kerstel et al. (output power = 10 mW in the 3-pm region) optothermal spec~.~ the trometer that can be better than 1O-Io H Z - ~ / However, beam flux in an optothermal apparatus is limited by the requirement of a well-collimated beam and by the degrading of the bolometer responsivity together with an increase in its noise level that would accompany a very large beam intensity. In contrast, the density-length product appearing in the Lambert-Beer absorption law can be made very large in the pulsed slit-jet expansion, direct absorption, experiment. This is of particular concern when the species under study are van der Waals molecules, the production of which is highly favored by expanding large quantities of gas. Recently, Bevan and co-workers reported on a CW slit-jet spectrometer using a frequency modulated diode laser in the 5-pm region4swith a sensitivity comparable to that of the pulsed slit-jet, difference frequency, spectrometer of Nesbitt and co-workers. However, when the transition dipole matrix element of the molecular excitation is much smaller, as is the case for overtone excitation (typically by a factor of 40-100), the sensitivity of the direct absorption method is irrevocably reduced by the same factor, while in an optothermal spectrometer this loss can be compensated for by an increase in the power of the laser source (when this is available). The spectrum of the 2ul band of the HCN dimer,& obtained with our spectrometer, as well as later overtone studies of acetylenic mole~ules,~~' which have shown excellent S/N ratios, serve to prove this point. (ii) Resolution. Pioneering studies of the kind as those discussed here were camed out with a 3-pm color-center laser in combination with a pulsed, free-jet, pinhole expansion in the laboratory of D. S. Perry.'2I4 In these experiments the expansion was not skimmed to form a collimated molecular beam. Instead the laser was multipassed through the free-jet, close to the pulsed valve opening, to maximize the absorption density-length product. Without further measures, the experimental resolution is entirely determined by the Doppler broadening (approximately 300 MHz for 1-butyne12),due to the stream lines fanning out in two dimensions. The same laboratory demonstrated that a resolution of 12 MHz can be achieved, with a sliced-jet pinhole expansion, without seriously reducing the s e n ~ i t i v i t y . In ~ ~this ~ ~ simple and elegant approach to the problem of Doppler broadening, a narrow metal blade was inserted in the center of the expansion, just before the laser crossing, to deflect molecules from the center line of the expansion that absorb with near-zero Doppler shift (as opposed to retaining only this group of molecules by beam collimation). The result is a spectrum in which the Doppler broadened lines show a narrow dip in the center. In the slit-jet expansion method the residual Doppler broadening is reduced to about 30 MHz (for heavier molecules), when the laser beam propagates parallel to the long axis of the slit. This results from the tendency of the one-dimensional expansion to strongly narrow the velocity distribution in the direction of the laser beam. In the case of optothermal detection, the contribution to the overall line broadening from the frequency instabilities of the laser source, the Doppler effect, and transit-time broadening can be made very small (on the order of 100 kHz or less, by stabilizing the laser with the help of an external cavity, by seeding in a heavier carrier gas to reduce the beam velocity, by further collimation of the molecular beam, and by increasing the size of the molecular beam-laser interaction region). However, in most practical situations it is difficult, though not impossible, to reduce the observed line width to much less than 1 M H Z . ~ (iii) Cooling of Internal Degrees of Freedom. McIlroy and Nesbitt found that their linear jet produces a nearly perfect (45) Wang,Z.; Eliadcs, M.; Carron, K.;Bevan, J. W.Rev. Scf. Instrum. 1991,62, 21.(46) Meyer, H.; Kerstel, E.R.Th.; Zhuang, D.;Scoles, G. J. Chem. Phys. 1989, 90,4623. (47) Kerstd, E. R.T.;Lchmann, K.K.;McIlroy, A.; Nesbitt, D. J.; Pate. B. H.;Scoles, G., manuscript in preparation. (48) Mercorelli, L. R.; Hammand. S. A.; Perry, D. S. Chem. Phys. Lett. 1989, 162, 277. (49) Kaur. D.: dcSouza. A. M.: Wanna. J.: Hammand. S.A.: Mcrcorelli. L.;Pe&y, D.'S. Appl. Opi. 1990,.29, 119.
The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8287
Intramolecular Vibrational Relaxation equilibrium in the rotational (J as well as K ) state po ulations and the (parallel) translational temperature of the jet.' The K N = 0 and 1 (J" = 1-7) intensities of the P and R branch of the u2 transition in pmpyne are well described by a single temperature, indicative of Boltzmann statistics. It is generally accepted that the pinhole expansion tends to produce J and K state distributions that are not equilibrated. The higher J levels are relatively overpopulated, whereas J and K 'temperatures" (assuming that the population of the corresponding levels can be characterized with one temperature) are different, the K temperature generally being higher. As pointed out before, this is not necessarily a disadvantage. In fact, we have recorded spectra (of propyne), while deliberately raising the rotational 'temperature" by expanding a very rich mixture (10%) against a high background pressure, with the explicit purpose of observing as high J states as possible. Moreover, given a sufficiently high spectral resolution, the ability to accurately predict intensities based on Boltzmann statistics is relatively unimportant, since then the spectral assignment can almost entirely rely on the matching of ground-state combination differences. Where intensities are of crucial importance, as in the evaluation of anharmonic coupling matrix elements via a Lawrence-Knight deconvolution scheme or a calculation of a lifetime from the time evolution of eigenstates, all states in question belong to the same zero-order 'bright" state and have the same quantum numbers J and K.16 On the other hand, the study of the methyl stretches of I-butyne by Perry and co-workers convincingly shows the advantages of being able to cool the sample to rotational temperatures as low as I K in a pinhole expansion." The lowest temperature reported for a slit-jet is about 5 K. The effect of this difference in temperature, in terms of spectral congestion, is best appreciated when realizing that the partition function scales with PI2. (iv) Experimeetal Considerations. The vacuum requirements for a pulsed pinhole expansion direct absorption experiment are very modest compared to both the Roots-blower pumped slit-jet direct absorption experiment and the CW, differentially pumped, pinhole expansion in an optothermal apparatus. On the other hand, Stark spectroscopy and separated fields (Ramsey fringes) type of experiments are more easily carried out in a collimated molecular beam a p p a r a t u ~ . ~ The * ~ ~same is true for doubleresonance experiments that require more space and could be compromised when the interaction region is not entirely collision free. The CW linear jet, because of its large gas consumption (10L103 times that of a pinhole expansion), is unattractive when expensive or difficult to obtain and/or handle samples are to be studied. The very modest demands for laser power in a direct absorption experiment allowed Nesbitt and co-workers to build a difference-frequency laser that is tunable over a wide range (2.2-4.2 pm), covering most fundamentalexcitations of interest. The price paid for the increased tuning range is the complexity of the laser system. The work of several groups shows that is has become possible to overcome the limited sensitivity of earlier diode laser system^."^"^ Given the rapid and ever-evolving progress in diode laser (single-mode) tunability, frequency coverage, ease of handling, and the lowering of their cost, this technique holds good promise for the near future. We conclude that, certainly at the overtone excitation level, the optothermal spectrometer, combined with the high-power (150 mW) 1.5-pm oolor-center laser, is superior to the direct absorption technique. But even at the fundamental excitation level our technique appears to offer some advantages. This is perhaps best illustrated by the u I 1-butyne spectrum. Perry and co-workers
P
(50) Gough, T. E.; Orr, B. J.; Isenor, N. R.;Scoles,G . J. Mol. Spctrosc. 1983, 99, 143. (51) Adam, A. G.; Gough, T. E.; Isenor, N. R.;Scoles, 0. Phys. RN.1985, A33, 1451. (52) Hodge, J.; Havman. G.D.: Dvkc T R * H n w a d R 1 I r h p m %P Faradav Trans. 2 1'
. . --
. ...
(54) Sncls, M.; Meerts, W. L. Appl. Phys. 1988. B45,27.
were able to identify in their sliced-jet spectrum s K statts belonging = to the P(2) transition and sharing the same upper state McIlroy and Nesbitt observed seven states belonging to the same lo, 202transition.Is Recently, in our laboratory we have been able to identify 22 components of this transition in a 0.2-cm-' frequency region. The transitions were assigned by combination differences with R(0). The weakest assigned features had a signal-to-noise of about 3:l. The strongest transitions were measured with a signal-to-noise of about 80:l.
-
Expected Features of the Observed Spectra Before presenting the experimental results, it is useful to discuss the type of spectra that we expect to observe. Both the fundamental and overtone excitations of the acetylenic C-H stretch produce parallel-band, symmetric-top spectra.5s These spectra are characterized by a central Q branch with P and R branches to the low- and high-frequency sides, respectively. Each individual P(J) or R(J) transition also has a set of K components. For the P branch each P(J) consists of K components with K = 0 to (J - 1). In the R branch the R(J) transitions include K components for K = 0 to J. For a rigid rovibrator the transition frequencies for these lines are given bySS V ~ , ~ ( J ,=Kv0) + ( B f+ B")m + ABm2 + (AA - AB)P (1) Here centrifugal distortion terms, which generally produce only small corrections at low J,K values, have been neglected. For P-branch transitions m = -J, and for R-branch transitions m = J 1. The intensities of the individual K components are given by the Honl-London factors and the ground-state populations.ss In this paper we are most interested in the structure of the individual P(J) and R(J) transitions since lifetime information is available from the line width of these transitions. Within the individual P(J) or R(J)transitions the individual K components will be spaced according to the final term in eq 1. Physically, the acetylenic C-H stretch primarily involves motion of the H atom along the symmetry axis of the molecule. This motion is expected to produce only a small, negative change in the B rotational constant. Since the uI normal mode involves only parallel motion of atoms on the symmetry axis, the magnitude of L 4 is expected to be much less than that of AB. These physical notions are borne out by the constants of CF,CCH, which has a very similar mass distribution. For this molecule AB = -4.320 MHz and AA = -0.26 MHz." For the compounds studied here, the ratio of (d'/aB) should be smaller still. Therefore, the K structure in the R(J)and P(J) transitions will degrade to the high-frequency side of the transition. The degradation of intensity arises from the fact that the low-K components have greater Hbnl-London factors and larger ground-state populations. The transition frequencies of the Q branch are given byss VQ(J,K) = yo + ABJ(J 4- 1) + (AA - AB)@ K # 0 (2) Under the same assumptions for AA and AB as above, the Q branch will degrade to the low frequency side. According to the second term in eq 2, the Q-branch lines move toward lower frequencies as J increases and their intensity decreases due to reduced population and intensity factors. As K increases, these J series move further out to the low-frequency side due to the second and third terms in eq 2 since a K progression begins with the J = K term. The molecular symmetry group of these molecules, allowing for torsional motion of the methyl groups, is Glb2. We have recently reported the character table for this group and the statistical weights of the torsional levels.% The presence of torsional motion has a large effect on the observed spectrum. Indeed, in our preliminary report on the acetylenic C-H stretch fundamentals of (CH,),CC=CH and (CHJ3SiC=CH we showed that the spectra are quantitatively Lorentzian with no observed eigenstates.** However, the classification of these molecules in the C,
+
~
( 5 5 ) Herzberg, G . Molecular Spctro and Molecular Structure II. Infrared and Raman Spectra of Polyotomic Molecules; Robert E. Krieger Publishing Co., Inc.: Malabar, FL, 1945; Chapter IV.2. (56) Lchmann, K. K.;Pate, B. H.J . Mol. Spectrosc. 1990, 144, 443.
8288 The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 point group, which corresponds to the neglect of torsional motion, does not provide a sufficient density of states to explain the lack of individually resolved eigenstates. In the C3, classification of ( C H 3 ) 3 C m H ,the average spacing of AI eigenstates, which is the manifold that can couple to the acetylenic C-H stretch via anharmonic interactions, is 51 MHz, and so a fairly resolved spectrum would be expected, especially considering the expected Thomas-Porter fluctuations in the intensities of the individual eigenstate~.~’The effect of including torsional states is that the ground state is 27-fold degenerate and consists of six different symmetry species. This means that we measure the superpasition of six different spectra. The spectrum is then expected to have a density of lines that, in the absence of vibration-rotation splittings (for example, the 1-type doubling of E vibrational states), is 24 times the density of states. If vibrational-rotation splittings are large, the number of lines observed can be as much as 122 times the density of A, states. This factor accounts for the observation of ‘filled-in” rotational profiles for both ( C H 3 ) 3 C m H and (CH3),SiC=CH, Clearly, to obtain smooth rotational profiles, the bright state must be coupled to a sizable fraction of the vibrational bath states that lie within the narrow homogeneous line width. Our goal in this study is to obtain homogeneous lifetimes for the vibrational energy relaxation following excitation of the acetylenic C-H stretch. However, in light of the previous discussion it is obvious that there is potential for extensive inhomogeneous broadening in our measurements. First of all, each individual P(J) and R(J) transition definitely contains inhomogeneity due to the presence of many K components. This inhomogeneous component should increase with J as additional K components are included with a spacing that goes as P. However, we will show that for tert-butylacetylene the widths of the P(J) and R(J) transitions are independent of J. The conclusion then is that the homogeneous IVR broadening is much greater than the K structure inhomogeneity. When the line width increases with J, as occurs for the silicon-substituted compound, we can estimate the K structure inhomogeneity using the measured spectroscopic constants and the assumptions discussed above. In this way we hope to be able to distinguish the effect of inhomogeneous broadening due to the K structure from the possibility of rotationally mediated IVR mechanisms (Coriolis effects). Inhomogeneity due to the different torsional levels should also be considered. It is conceivable that the transitions from the six different torsional symmetry species could have different center frequencies. However, it is unlikely that we will observe such effects. For trimethyl carbon compounds the barrier to internal rotation is sufficiently large that microwave studies fail to observe ground-state splittings even at the kilohertz leveL5* For the silicon compound the barrier drops and torsional splittings may be measurable. For example, the spectrum of (CH3)3Si-H has been mentioned in a previous microwave study but was said to be left unassigned due to the complex structure of the transitions, presumably due to torsional ~ p l i t t i n g s . ~Still, ~ to produce a measurable effect in our infrared spectra, it is necessary that the barrier to internal rotation in the ground and excited vibrational states be sufficiently different so that the splitting pattern changes between the two states. Accordingly, we do not expect to have torsional inhomogeneity in our spectra. For the spectrum of (CH3)3SiCECHthe natural abundances of the Si isotopes should be taken into account (there are two heavier isotopes of about 4% natural abundance in addition to the major isotope %i, which is in 92% abundance). A normal-mode calculation for the Si compound indicates that the isotope shift for the acetylenic C-H stretch should be small even compared with the observed line width. Since the major isotope will dominate the spectrum, we expect at most to observe small effects in the residuals to our fits. (57) Engel. Y. M.; Levine, R. D. J. Chem. Phys. 1988,89,4633. (58) Nugent, L. J.; Mann, D.E.: Lide Jr., D. R.J. Chem. Phys. 1%2,36,
965.
(59) Lide Jr., D. R.;Mann. D. E.J . Chem. Phys. 1958, 29, 914.
Kerstel et al.
TABLE I: Measured SpcetroscoPic Constantsa ( C H M m H VI
3329.371 08 (94) 0.089 560 (43) 0.089 439 (48) . . -50.85 -0.000096 (20)
; ” E’ XI I an
2Vl VO
E” E’
6557.0247 (12) 0.090006 (46) 0.089865 (56)
(CH,),SiC=CH “I
2‘E’‘ XI I an
3312.462913 (64) 0.065 4848 (32) 0.065 4300 (38) -52.30 -0.0000566 (18)
2Vl
‘;’ B’
6520.305 26 (IO) 0.0655171 (49) 0.065 400 4 (49)
“All values are in c d . Reported errors in the constants for the vibrational levels are 20.
Last, hot-band transitions may also be present. For example, the hot-band coming from the lowest frequency vibration is observed both in our spectrum of propyne4’ and trifluoropropyne.22 These hot bands appear at lower frequency. So we may possibly observe small hot-band absorptions, probably to the low-frequency side of the transitions. By carefully considering all of the sources of inhomogeneity, we aim at making reliable estimates of the homogeneous lifetimes from our spectra. In the following section these considerations will be used when assigning the homogeneous line width. This line width is then used to obtain the dynamical lifetime information.
Experimental Results Figure 2 shows the fundamental and first overtone spectra of both (CHJ3CC=CH and (CH3)3SiC=CH. The parallel-band, symmetric-top rotational structure is apparent; however, the K structure of the individual R(J) and P(J) transitions is not resolved. In spite of the fact that, for the sake of comparison, the full spectra have been compressed to fit the size of the figure, it is obvious that the width of the tert-butylacetylene compound is much larger than that of the silicon-substituted compound. From the spectra the band origin, rotational B constant, and change in rotational constant upon vibrational excitation (AB) can be determined. These spectroscopicconstants are listed in Table I. Also given in Table I is the anharmonicity, XIl,calculated from the band origins of the fundamental and first overtone. The value of about -50 cm-I for this parameter is the same as the value previously found for a number of symmetric-top terminal acetylenes from photoacoustic spectroscopy data that included up to the fifth overtone of the acetylenic C-H stretch.@ For interpreting our data in terms of the dynamics of the vibrational motion, we are most interested in the line shape of the spectral features. In the statistical limit of intramolecular vibrational relaxation a Lorentzian line shape is predicted.1° The line width of the profile provides the relaxation rate. In our previous preliminary communication of the fundamental spectra of these two molecules we showed that the line shapes were Lorentzian.l* The lifetimes reported in the previous publication are a factor of 2 too long. The lifetime we gave was the correct T2lifetime calculated from a Lorentzian profile. When spectral broadening comes only from population relaxation of the upper state (3)
where T is the lifetime associated with the exponential IVR decay of population and r is the full width at half-maximum (fwhm) of the Lorentzian line shape. The spectra reported here were taken with much colder expansions than were used in the previous measurements.’’*’* The colder expansion has allowed us to measure the lower rotational (60) Hall, R. R. Ph.D. Thesis, Rice University, 1984; University Microfilms International, 8416524.
The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8289
Intramolecular Vibrational Relaxation
V.1
.-Em W
Y
-
,
3327.49
3328.49
~
~
3329.49
Wavenumber/cm- 1
.
~
3330.49
,
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6555.45
-
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6558.45
~
,
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Wavenumber/cm- 1
i
6558.45
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.-E
.-E
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transitions where the inhomogeneity from K structure is reduced, providing better estimates of the homogeneous IVR lifetime of these two molecules. The R(7) transitions of the fundamentals and the R(5) transitions of the overtones are shown in Figure 3 along with the residuals from the best fit to a single Lorentzian. The fit is performed by using a nonlinear least-squares algorithm.6l For the terr-butylacetylene the fit runs from the midpoint between two successive rotational transitions to the midpoint of the next two transitions in order to provide as much baseline as possible. For the overtone spectra a sloping baseline is used in the fit since, due to the greater power of the 1.5-pm laser, a slowly variable background signal due to scattered light is present. All four fits include about 2000 data points each. All of the measured R branch lines were fit, and the line widths are plotted in Figure 4. Generally the lowest J line width reported is not very well determined due to low signal-to-noise. We find that the line width of the silicon-substituted compound is significantly narrower than that of tert-butylacetylene in both the fundamental and first overtone. Combined with our previous results for the fundamental of tert-butylacetylene,'* we find that the line width remains nearly constant at about 800 MHz from R( 1) to R( 18). The lack of J dependence of the width indicates that the dominant mechanisms for IVR are anharmonic. Furthermore the K structure inhomogeneity is obscured by the IVR broadening. We conclude that the homogeneous IVR lifetime of rert-butylacetylene in the fundamental is 200 ps. This value
agrees very well with the lifetimes observed for other terminal acetylenes at u = 1.16 The line widths of (CH,),SiC=CH in the fundamental show a steady increase as a function of J. We believe that this increase is due to unresolved K structure and not to Coriolis IVR mechanisms. Coriolis mixing matrix elements increase as [J(J + 1) - K(K f 1)11/* for xy-axis interactions or as K for z-axis interactions.'j2 The observed line widths do not increase that rapidly as J increases. Furthermore, at the higher J values the line shape starts to develop a shoulder to the high-frequency side as expected for K structure based on the measured AB value. The line widths expected for K structure can be estimated through a simulation of the data. Under the assumption that hA The full density 25 MHz (6 ns) in the fundamental. of states is 162 times the density of AI states. While for the fundamentals we do see a decrease in the line width when the mass of the central atom is increased, a heavy-atom a small matrix element controlling the relaxation since it would effect alone does not appear to explain the data. First, the factor most likely be greatly detuned in the overtone. We, therefore, of 2.3 mass increase from C to Si narrows the line width by loOo%, believe that our data imply that there is no single state (or small while the factor of 4.2 mass increase from Si to Sn only narrows set of states) that act as a doorway for the intramolecular vithe width by about 40%. Second, a mass effect cannot explain brational relaxation. why (CH3)3CC=CH broadens in the overtone but (CH3),SiIn conclusion we have no natural explanation of the trends in C=--CH narrows. Again, although the mass of the central atom line widths observed in these molecules. It must be cautioned that may reduce the IVR rate, we cannot conclude that it is the the tin results are only preliminary, and the lifetime may be dominant effect in determining the IVR lifetime of these systems. considerably longer than we estimate if other explanations are Although the intent of our experiment was to simply increase found for the observed line shape. Future double-resonance or the mass of the central atom, the substitution of silicon (and tin) time-resolved measurements may answer these questions. causes other changes in the structure of the molecule. Perhaps Methyl group rotation has been implicated in enhancing IVR the greatest effects are related to the lengthening of the bond in a few cases.”-73 In particular, the chemical timing experiments between the methyl groups and the central atom. The distance of Parmenter et al. on p-fluorotoluene and p-difluorobenzene increase reduces the barrier to rotation of the methyl group. The strongly suggest that the presence of the methyl group enhances barrier for (CH3),CC=CH has been measured to be 1434 cm-I, the IVR rate.’* However, time-resolved fluorescence experiments and the barrier of (CH,),SiC=CH can be taken to be about the of p-fluorotoluene in a free-jet expansion did not confirm this same as that of (CH3),SiH which is 871 ~ m - I . 6The ~ barrier for finding.74 Later theoretical work suggested that the thermally (CH,),SnH has been calculated to be 217 ~ m - I . 6 A ~ questionable populated torsions in pfluorotoluene made good acceptor modes assignment for the methyl torsional mode fundamental in .’~ these results suggest that the in the IVR p r o c e s ~ . ~ ~Although (CD ),Sn=H (70 an-’) implies a barrier almost identical with freedom of the torsion is important, it is difficult to reconcile our thisjO If we take the height of the torsional barrier to be represults with the previous work. First, pfluorotoluene has a leading resentative of the strength of other steric interactions across the v 6 Fourier term in the torsional barrier and so is only slightly central bond, we predict a central-atom dependence to the rate hindered; the measured barrier is 4.77 cm-’.” Second, our spectra of energy relaxation similar to that predicted by the mass effect. are taken in a molecular beam where the torsional states are, most A simple heavy-atom effect, where the kinetic couplings are relikely, not thermally populated. Last, we find that a lower barrier duced, would predict a line-width decrease proportional to (1/ results in a decreased IVR rate. mcmtnlItm). For this mass effect the line widths are expected to Clearly there is much work left to be done before achieving a be in the ratio 104.3:l for central atoms C, Si, and Sn respectively. detailed understanding of the factors that determine the intraThe ratios of the barrier heights are 6.6:4.5:1 and are very similar molecular vibrational relaxation rate. However, our data do serve to the ratio for the mass effect. Neither of these predictions is to show that the total density of states has little importance for in good agreement with the experimental data, which for the the dynamics of vibrational relaxation. The normal modes of fundamental have a ratio of about 303:l. Other estimates of the ( C H 3 ) 3 C m H 6 6 * 6and 7 (CH,),SiCbCH@’ have been assigned. steric interactions could be made, but without knowledge of which From these data and the barriers to methyl group rotation we have modes are most important in coupling vibrational energy across calculated the density of states for these two molecules in the the central atom, it is difficult to choose between them. fundamental and first overtone. In this calculation the energy Another change that occurs as the mass of the central atom levels of the methyl torsion are calculated separately?* The rest increases is a lowering of the frequencies of many of the modes. of the modes are treated as harmonic vibrations. The labels of The central-atom substitution results in an increased mass and the molecular symmetry group G162are used.56 In Table I1 the longer bond lengths, and also a reduction in force constants of results of this calculation are presented for the A, levels. The modes involving motion of the central atom. Swamy and HaseZ9 density of states alone fails to explain any of the data. At the have found that the ‘heavy-atom blocking” of vibrational energy fundamental and first overtone the silicon compound has a much transfer found in classical trajectory c a l c ~ l a t i o ndoes s ~ ~not ~ ~ ~ ~ higher ~ density of states than does (CH3),C=H, and yet a t occur unless one changes the force constants as well as the mass both levels of excitation (CH,),SiCWH has a longer IVR of the central atom. If small, near-resonant mixing of some specific mode or modes controls the vibrational energy transfer, then the (71) Walters, V. A.; Colson, S.D.; Snavely, D. L.;Wiberg, K. B.; Jamison, rate will strongly depend upon the mode frequencies. Examination 8. M. J . Phys. Chem. 1985,89, 3857. of fundamental frequencies for all three molecules reveals no (72) Parmenter, C. S.; Stone, B. M. J. Chem. Phys. 1986, 84, 4710. low-order resonances that could provide a doorway for the energy (73) Reid, S. A.; Kim. H. L.;McDonald, J. D. J . Chem. Phys. 1990,92, relaxation. Furthermore, the small change in line width of the 7079. (74) Baskin, J. S.; Rose, T. S.;Zewail, A. H.J . Chem. Phys. 1988,88, overtone bands (where the detuning will change by 100 cm-I due 1458. to anharmonicity) compared to the line width in the fundamental (75) Moss,D. B.; Parmenter, C. S.;Ewing, G. E. J. Chem. Phys. 1987, of the same molecule argues against a high-order resonance with 86, 51. (76) Martens, C. C.; Reinhardt, W. P. J . Chem. Phys. 1990, 93, 5621. (77) Ghosh, P. N. J. Mol. Spectrosc. 1990, 142, 295. (78) The program for calculating the torsional energy levels for a V3hmer (69) Ouellette, R. J. J . Am. Chem. Soc. 1972, 94, 7674. was written by D. S. Perry, Department of Chemistry, University of Akron, (70) Belyakov, A. V.; Bogoradovskii, E.T.; Zavgorodnii. V. S.; Apal’kova, Akron, OH 44325. G. M.; Nikitin, V. S.;Khaikin. L. S. J . Mol. Srruct. 1983, 98, 27. ~~
J. Phys. Chem. 1991, 95, 8293-8299 lifetime. For each individual compound there is a large increase in the density of states in going from the fundamental to the first overtone (more than a factor of IOOO), and yet (CH3),CC=CH broadens only slightly (a factor of 2) and the silicon-substituted compound narrows. The inability of the total density of states to explain the lifetime trend of the data and the above-mentioned insensitivity of the line width on the identities of the final states of the full bath illustrate the minor role that the full density of states plays in the dynamical process of vibrational energy redistribution in these molecules. There is clearly a minimum density of vibrational states (about 100-1OOO per cm-') required for a vibrational energy relaxation to occur since several coupled states lying within the frequency region given by the homogeneous line width are required for a true relaxation process. For lower state densities, the time evolution of the excitation will show negligible energy transfer (small-molecule limit) or quantum beats with a few frequencies. There is ample experimental evidence for substituted acetylene compounds that the acetylenic C-H fundamental will relax into all symmetry-allowed vibrational states (and perhaps rovibrational states) that fall within the homogeneous width.12J6J8.22The time-averaged state in this case is like a microconanical ensemble and thus has a statistical distribution of vibrational energy among the vibrational modes. Increasing the density of states beyond this minimum will be expected only to increase the volume of phase
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space into which the molecular excitation decays. In summary, using the optothermal technique, we have measured both the fundamental and first overtone spectra of (CH,),C*CH and (CH,),SiC=CH. All of the spectra show broadened transitions that are Lorentzian, with some inhomogeneity in some cases. The four spectra show a wide variety of interesting behavior with respect to the homogeneous IVR lifetime. In all cases the lifetimes are rather long, ranging from 100 ps up to about 4 ns. Lifetimes on the order of nanoseconds ensure that, at reasonable pressures (about 1 atm), collisions with vibrationally excited molecules can occur. These long IVR lifetimes may allow mode-selective, laser-enhanced, bimolecular chemistry to occur. More experimental and theoretical work is necessary to understand in further detail the measured lifetimes in terms of the intramolecular forces and dynamics.
Acknowledgment. We thank D. S.Perry for providing us with the program for the calculation of torsional energy levels. It is a pleasure to thank Prof. J. Schwartz for his generous help in synthesizing the tin-substituted compound. T.F.M. thanks the Deutsche Forschungsgemeinshaft for research support. This work was supported by the NSF under Grants CHE87-09572 and CHE85-53757. Registry No. (CH,),CC=CH, 917-92-0; (CH,),Si=H, 54-2; (CH,),SnC=CH, 11 12-00- 1.
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Calculation of the Vibrational Levels of Electronically Excited Ar-OH(A2E+) Using a Proposed Potential Energy Surface and Analytic Discrete Variable Representatlonst Y. Guan and J. T. Muckelman* Chemistry Department, Brookhaven National Laboratory, Upton, New York 11973 (Received: December 27, 1990; In Final Form: April 16, 1991)
The vibrational levels of a potential energy surface recently proposed by Bowman et al. [ J . Phys. Chem. 1990, 94, 22261 for the electronically excited van der Waals complex Ar-OH(A2Z+) are calculated by using analytic discrete variable representations. The results, together with those of previous calculationsand with experimental spectroscopic data on vibrational band origins, are used to suggest further refinements in the potential energy function.
Introduction Recently Bowman et al.' attempted to "invert" experimental spectroscopicdata to obtain a potential surface for the electronically excited state of the van der Waals complex Ar-OH(A2Z+). Their approach was to perform an exact calculation of vibrational energy levels using a flexible functional form for the potential and to search in the multidimensional parameter space for the optimum set of parameters. The functional form of the potential they employed was guided significantly by an ab initio calculation of the surface by Degli Esposti and The experimental data to which the fit was carried out were the fluorescence excitation spectra of Berry et al." and of Fawzy and Heaven,7J who also reported spectra for Ar-OD(A*Z+). These data consisted of band origin energies assigned to a series of van der Waals stretching vibrations3 ("A" bands7a) and some unassigned band origins ("U" bands7.*) which Fawzy and Heaven attributed to the excited bending vibration. Berry et aL5 subsequently confirmed this assignment through product state distributions following vibrational predissociation of the complex. Using the van der Waals stretching assignments made by the two experimental groups for the A bands, corresponding to energy 'This research was carried out at Brookhaven National Laboratory under Contract No. DE-AC02-76CH00016 with the U S . Department of Energy and supported by its Division of Chemical Sciences.
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intervals v, to v, - 1 for v, from 2 to 6 for Ar-0H3g8 and A P O D ~ ~ and assigning most of the reported U band^^.^ to highly excited van der Waals stretching states in the first excited bending state, Bowman et al.' were able to vary selected potential parameters and repeatedly diagonalize the matrix representation of their trial Hamiltonian operator in a fairly large basis until reasonable agreement with the experimental intervals and rotational constants was obtained. The basis they employed was optimized to yield reliable representations of states with the linear Ar-H-O configuration, the geometry believed to have the only substantial Franck-Condon factors with the electronic ground state. In fact, their variations of the trial potential affected only this region of configuration space. Only energy intervals involving states as( 1 ) Bowman, J. M.; Gazdy, 9.;Schafer, p.; Heaven, M. C. J. Phys. Chem. 1990, 94, 2226; correction, 1990, 94, 8858. ( 2 ) Degli Esposti, A.; Werner, H.-J. J . Chem. Phys. 1990, 93, 3351. (3) Berry, M. T.;Brustein, M. R.; Adamo, J. R.; Lester, M. I. J . Phys. Chem. 1988, 92, 5551. (4) Berry, M. T.; Brustein, M. R.; Lester, M. I. Chem. Phys. Lett. 1988, 153, 17. (5) Berry, M. T.; Brustein, M. R.; Lester, M. I. J . Chem. Phys. 1989, 90, 5879. (6) Berry, M. T.; Brustein, M. R.; Lester, M. I. J. Chem. Phys. 1990,92, 6469. (7) Fawzy, W. M.; Heaven, M. C. J. Chem. Phys. 1988,89, 7030. (8) Fawzy, W. M.; Heaven, M. C. J . Chem. Phys. 1990, 92,909. (9) Lin, Y.; Kulkarni, S . K.; Heaven, M. C. Unpublished results.
0 1991 American Chemical Society
