J . Phys. Chem. 1986, 90, 3301-3313 and
I*’)
as (x f iy). Elementary considerations then show that (4)
and the other matrix elements are zero. Hence both types of transitions have intensities given by
I(E”,AI”IILA~,,~E’,A~~)IZ )(+”IA2/’1+’)12(FC++ + FC--)’
(5)
FC is the Franck-Condon factor, that is, the overlap of the lv,l) basis functions associated with the appropriate electronic components I*) of the two eigenstates in question. Relative intensities calculated from eq 5 (for arbitrarily scaled electronic matrix elements) are listed in Table I and compared graphically with experiment in Figure 1. While it is difficult to gauge the accuracy of experimental intensities, it is clear that theory fails badly for a couple of bands, even though more qualitative broader trends are reasonably reproduced. One possible explanation is that the excited-state assignment of Thompson et al. needs refining. We have investigated this possibility but have yet to find a set of upper state coupling parameters that improves the intensity agreement, while retaining a fit to observed excited-state energy levels. More likely to be of greater importance than further optimization within the simple picture of the two-state isolated degeneracy demanded by Hamiltonian (1) is the inclusion of coupling to additional electronic states. Redissociation is evident in the experimental data of Morse et aL20 and Crumley et Configuration interaction involving excited states of 3d manifold can be expected to be important. In fact, Walch and Laskowski2* suggest on the basis of their calculations that the lowest allowed excited state is of electronic term symmetry ’Al’. Additional intensities from a greater number of the excited-state levels will be necessary to more fully resolve the vibronic character of the excited state.
3301
Conclusions To summarize, we have constructed a Jahn-Teller vibronic Hamiltonian that successfully accounts for all of the resolved level structure of the Cu3 electronic ground state. The parameters of this fit ( k = 1.86, g = 0.223 in reduced units of the zeroth order frequency wo = 137 cm-I) describe a surface moderately stabilized by distortion ( D = 305 cm-’) with barriers to pseudorotation (1 11 cm-l) just less than the zero-point energy (1 18 cm-’). The symmetric stretching frequency is assigned to be ws = 269.5 cm-I. Theoretical intensities, using Thompson et a1.k parameters to generate eigenfunctions for excited state levels, agree roughly with experiment, tending to confirm the published fit to the excited state structure. Deviations, however, point to possible added complexity in the optical spectrum due to multistate interactions in the excited state. Since completion of this work we have learned of a parallel effort by T r ~ h l a and r ~ ~co-workers to assign the Cu3 emission spectrum on the basis of a surface derived from the ab initio calculations of Walch and Laskowski. Their slightly optimized coupling parameters of k = 1.56 and g = 0.247 &firm the present more comprehensive assignment and show that the ab initio results give a reasonably correct description of vibronic coupling in Cu3.
Acknowledgment. We are grateful to E. Rohlfing and J. Valentini for providing their spectra in advance of publication, and to K. S. Haber for stimulating discussions. We thank D. Truhlar for communication of his results. This work was supported by the National Science Foundation under Grant No. CHE-8213162. (35) Truhlar, D. G.; Thompson, T. C.; Mead, C. A. to be submitted for publication.
FEATURE ARTICLE Infrared Laser Photodissociation and Spectroscopy of van der Waals Molecules R. E. Miller Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 2751 4 (Received: February 14, 1986; In Final Form: April 10, 1986)
Infrared-laser-inducedvibrational predissociationof weakly bound van der Waals molecules has become a topic of considerable interest, both experimentally and theoretically. In particular, the partitioning of the excess energy in the fragments and the vibrational relaxation lifetimes have attracted much attention. The spectroscopy of these systems is also of interest since it can provide valuable molecular structure information which is important in obtaining a detailed understanding of the dynamics. This article is intended to provide a concise account of our present understanding of these processes as well as to point out where future research in this area might be directed.
Introduction Weakly bound van der Waals molecules have fascinated scientists for many years, in part as a result of the promise they hold for bridging the gap, in a more or less continuous fashion, between the gas and solid (or liquid) states of matter.’ As pointed out by Levine,2 the idea of detecting these molecular aggregates by using spectroscopic methods dates back into the early l i t e r a t ~ r e . ~ (1) G. D. Stein, Phys. Teach., 17, 506 (1979). (2) H. B. Levine, J. Chem. Phys., 56, 2455 (1971).
0022-3654/86/2090-3301$01.50/0
Indeed, as so beautifully demonstrated for the Ar, the spectroscopy of atomic and molecular clusters holds much promise in obtaining accurate intermolecular potential surfaces. In larger systems, where the dimensionality of the potential becomes so large ~~
~~
~
~
(3) J. 0. Hirschfelder, F. T. McClure, and I. F. Weeks, J . Chem. Phys., 10, 201 (1942). (4) Y. Yanaka and K. Yoshino, J . Chem. Phys., 53, 2012 (1970); Y. Yanaka, K. Yoshino, and D. E. Freeman, J . Chem. Phys., 59, 5160 (1973). ( 5 ) E. A. Colburn and A. E. douglas, J . Chem. Phys., 65, 1741 (1976). (6) G. C. Maitland and E. B. Smith, Mol. Phys., 22, 861 (1971). (7) R. A. Aziz and H. H. Chen, J . Chem. Phys., 67, 5719 (1977).
0 1986 American Chemical Society
3302 The Journal of Physical Chemistry, Vol. 90, No. 15, 1986 that a detailed characterization is no longer possible, studies of this type can, in many cases, lead to a t least the equilibrium structure. More recently, the study of the dynamics of these systems has also become an area of intense activity. Despite there being a long interest in systems of this type, it is only in recent years that the experimental and theoretical methods have become sufficiently refined to provide the necessary data required for a detailed understanding of even the simplest systems. With the advent of free jet molecular beam source^,^^^ and a wide variety of compatible spectroscopic m e t h o d ~ , lthe ~l~ field of cluster research has taken on a completely new appearance. By making use of these methods, it is now possible to obtain detailed structural information for a wide range of van der Waals systems, as well as detailed dynamical information concerning the possible dissociation channels open to their excited states. The power of these methods can be appreciated if one considers that, by using the numerous forms of free jet sources that have been developed in recent years including those based on laser vaporization,16thermospray, and electrospray,l' it is now possible to form clusters of essentially any size and composition. As a result of the dramatic advances that have occurred in the field of cluster spectroscopy, it is impossible to discuss the results obtained by using all of the latest techniques in a single article. For this reason, the author has chosen to concentrate on the developments in the field of infrared spectroscopy and the infrared-induced photodissociation of weakly bound clusters. Even within this field, the discussion is restricted somewhat in that the extensive literature that has been assembled on the infrared matrix spectroscopy of c l ~ s t e r s isl ~not ~ ~included. ~ However, in order to aid the reader in exploring the areas neglected in this discussion, a brief introduction to the types of optical spectroscopies used in the study of van der Waals molecules will be given in the next section. i n view of the purpose of these articles, it is not our intention to discuss in detail all work that has been done on the infrared spectroscopy and the dynamics of van der Waals molecules. Instead, the emphasis is on introducing the uninitiated to the recent developments in the field and giving the reader some idea of what developments might be expected in the near future. However, the reference list has been made rather complete so that the article should also be useful to those in the field by giving a concise description of where we stand at the present time (see Table I). A Short Overview of Cluster Spectroscopy As already indicated, the spectroscopy of weakly bound van der Waals molecules is by no means a recent field of endeavor. In fact, one of the first spectroscopic studies of this type was carried out in 1962 by Rank et al.zOon several hydrogen halide-rare gas complexes using conventional infrared techniques. Although no spectroscopic assignment was made in these studies, it was possible (8) J. B. Anderson, R, P. Andres, and J. B. Fenn, Adu. Chem. Phys.. 10, 275 (1966). (9) H. Ashkenas and F. S. Sherman, RareJed Gas Dyn., Suppl., 32, 84 ( 1966). (10) R. E. Smalley, L. Wharton, and D. H. Levy, J. Chem. Phys., 63,4977 (1975). (1 1) D. L. Feldman, R. K. Lengel, and R. N. Zare, Chem. Phys. Lerr., 52, 413 (1977); E. E. Marinero, C. T. Rettner, and R. N. Zare, Phys. Reu. Lett., 48, 1323 (1982). (12) J. S . Muenter and W. Klemperer, J. Chem. Phys., 52, 6033 (1970). (13) A. C. Legon, Annu. Rev.Phys. Chem., 34, 275 (1983). (14) T. E. Gough, R. E. Miller, and G. Scales, Appl. Phys. Lett., 30,338 (1977). (15) I. F. Silvera and F. Tommasini, Phys. Reu. Lett., 37, 136 (1976); P. Huber-Walchli and J. W. Nibler, J. Chem. Phys., 76, 273 (1982). (16) T. G. Dietz, M. A. Duncan, D. E. Powers, and R. E. Smalley, J. Chem. Phys., 74,651 1 (1981); M. C. Heaven, T. A. Miller, and V. E. Bondybey, J. Phys. Chem., 87, 2072 (1983). (17) T. R. R i m , Y. D. Park, L. Peteanu, and D. H. Levy,Int. Symp. Mol. Beams, Proc., 10th. I-Cl (1985); M. Yamashita and J. B. Fenn, J . Phys. Chem., 88, 4671 (1984). (18) V. E. Bondybey and L. E. Brus, Adu. Chem. Phys., 41,269 (1980). ( 19) R. L. Redington and D. F. Hamill, J. Chem. Phys., 80, 2446 (1984). (20) D. H. Rank, B. S. Rao, and T. A. Wiggins, J . Chem. Phys., 37,251 1 (1962); D. H. Rank, P. Sitaram, W. A. Glickman, and T. A. Wiggins, J. Chem. Phys., 39, 2673 (1963).
Miller to estimate the heats of formation for several of these species. A number of other systems have since been studied in this way.z1 The main limitation of this method arises from the fact that the concentration of clusters is generally very low in equilibrium gases. This problem has traditionally been overcome by making use of long path length optical systems. Unfortunately, the resolution obtained by using conventional infrared spectrometers is generally rather poor so that it is difficult to assign the spectra in all but the very simplest systems.z2 As will become clear shortly, this problem has been overcome to a large extent by making use of high-resolution tunable infrared laser^.*^-^^ The extremely high spectral brightness of these sources makes it possible to obtain spectra at essentially Doppler-limited resolution. A problem inherent to both methods, however, is that the range of clusters that can be easily formed in an equilibrium gas is rather limited. With the advent of free jet techniques, the production of a wide variety of clusters has become routine. Initially, these methods had little impact on the field of infrared spectroscopy due to the fact that the sensitivity of the conventional techniques was insufficient to permit their use with molecular beams. The molecular beam electric resonance technique, on the other hand, is ideally suited to this type of study, and as a result, a vast literature has been accumulated on the detailed rotational spectroscopy of molecular cluster^.^^^^^ More recently, Fourier-transform microwave ~pectroscopy'~ has also provided a very powerful method for obtaining such spectra. These high-resolution radio-frequency and microwave spectra have been extremely useful in determining both molecular structuresz7and intermolecular p o t e n t i a l ~ ~for ~J~ these systems. With the advent of widely tunable visible and UV laser systems, the laser-induced fluorescence method (LIF)29 has become a powerful technique for studying van der Waals molecules. Indeed, it is nearly a decade now since Levy and c o - ~ o r k e r spublished ~~,~~ their pioneering work on the detailed electronic spectroscopy and dissociation dynamics of the H e I Zsystem. It was in this beautiful set of papers that the vibrational predissociation of van der Waals systems was first investigated in detail. Indeed, this system became a benchmark for theoretical investigation^)^-^^ and has already been discussed extensively in the l i t e r a t ~ r e . Since ~ ~ that time
(21) J. L. Himes and T. A. Wiggins, J . Mol. Spectrosc., 40, 418 (1971); R. D. Pendley and G. E. Ewing, J. Chem. Phys., 78,3531 (1983); C. A. Long and G. E. Ewing, J . Chem. Phys., 58,4824 (1973). (22) A. R. W. McKellar and H. L. Welsh, J . Chem. Phys., 55,595 (1971); A. R. W. McKellar and H. L. Welsh, Can. J . Phys., 50, 1458 (1972); A. R. W. McKellar and H. L. Welsh, Can. J. Phys., 52, 1082 (1974); A. R. W. McKellar, Faraday Discuss. Chem. Soc., No. 73, 89 (1982), and references contained therein. (23) A. S. Pine and W. J. Lafferty, J. Chem. Phys., 78, 2154 (1983); A. S. Pine, W. J. Lafferty, and B. J. Howard, J . Chem. Phys., 81, 2939 (1984). (24) N. Ohashi and A. S. Pine, J . Chem. Phys., 81, 73 (1984). (25) E. K. Kyro, P. Shoja-Chaghervand, K. McMillian, M. Eliades, D. Danzeiser, and J. W. Bevan, J . Chem. Phys., 79, 78 (1983); E. Kyro, R. Warren, K. McMillan, M. Eliades, D. Danzeiser, P. Shoja-Chaghervand, S. G. Lieb, and J. W. Bevan, J . Chem. Phys., 78, 5881 (1983); B. A. Wofford, J. W. Bevan, W. B. Olson, and W. J. Lafferty, J . Chem. Phys., 83, 6188 (1985). (26) T. R. Dyke, Top. Curr. Chem., 120, 85 (1984). (27) W. Klemperer, J. Mol. Strucr., 59, 161 (1980). (28) J. M. Hutson and B. J. Howard, Mol. Phys., 45, 769 (1982); J. M. Hutson and B. J. Howard, Mol. Phys., 45, 791 (1982). (29) D. H. Levy, Annu. Rev. Phys. Chem., 31, 197 (1980). (30) R. E. Smalley, D. H. Levy, and L. Wharton, J. Chem. Phys., 64,3266 (1976); M. S. Kim, R. E. Smalley, L. Wharton, and D. H. Levy, J. Chem. Phys., 65, 1216 (1976). (31) K. E. Johnson, L. Wharton, and D. H. Levy, J. Chem. Phys., 69,2719 (1978); J. E. Kenny, K. E. Johnson, W. Sharfin, and D. H. Levy, J . Chem. Phys., 72, 1109 (1980); W. Sharfin, K. E. Johnson, L. Wharton, and D. H. Levy, J . Chem. Phys., 71, 1292 (1979). (32) J. A. Beswick and J. Jortner, Chem. Phys. Lett., 49, 13 (1977); J . Chem. Phys., 68,2277,2525 (1978); J. Chem. Phys., 69,512 (1978); J. Chem. Phys., 70, 3895 (1979). (33) E. Seger and M. Shapiro, J . Chem. Phys., 78, 4969 (1983). (34) G. E. Ewing, J. Chem. Phys., 71, 3143 (1979). (35) S. B. Woodruff and D. L. Thompson, J . Chem. Phys., 71,376 (1979). (36) R. Ramaswamy and A. E. DePristo, J. Chem. Phys., 72,770 (1980). (37) G . C. Schatz, V. Buch, M. A. Ratner, and R. B. Gerber, J . Chem. PhyS., 79, 1808 (1983).
Feature Article
The Journal of Physical Chemistry, Vol. 90, No. 15, 1986 3303
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3304 The Journal of Physical Chemistry, Vol. 90, No. 15, 1986 there have been a large number of studies carried out using this method. In cases where the rotational lines are resolved, the spectra can be used to obtain information on both the molecular structure39 and the electronically excited state predissociation dynamics.40 As indicated above, the conventional infrared methods are somewhat limited in sensitivity, thus making their use with molecular beam techniques somewhat difficult. For example, the fluorescence method, which is so powerful at shorter wavelengths, is rather insensitive in the infrared due in part to the long fluorescence lifetimes of the vibrationally excited states. In addition, infrared photon detectors are orders of magnitude less sensitive than the photomultipliers used in the visible and UV regions of the spectrum. The advantage of infrared spectroscopy, however, is that it is more universal since most molecules have infrared-allowed transitions within the tuning range of the available lasers. Despite the low optical density characteristic of a molecular beam, several early absorption experiments were carried out in which multiple beam sources were used to increase the absorption path l e ~ ~ g t h More . ~ ~ .recently, ~~ the absorption method has also been used in conjunction with a free jet source.43 In both cases, the principal sensitivity limitation is associated with the amplitude noise of the laser. In view of its inherently low amplitude noise the diode laser is ideally suited to studies of this type. Further improvements in the absorption method have been made by using pulsed nozzles to increase the optical density of the free jet prepared gas sample. This has the added advantage that the molecular absorption can be modulated so that phase-sensitive dei n t e g r a t i ~ ncan ~ ~be used to reduce the noise t e ~ t i o nor~gated ~ bandwidth. Although the detection of infrared fluorescence is made difficult by the factors discussed above, experiments have been carried out in free jet expansions using this detection scheme. By resolving the infrared fluorescence from a laser-excited molecular beam, McDonald and c o - ~ o r k e r have s ~ ~ been able to probe, in a very detailed way, the dynamics of intermolecular vibrational relaxation in several organic molecules. As shall be seen in a later section, this process is also believed to play an important role in the vibrational relaxation of van der Waals molecules. To the author’s knowledge, however, the fluorescence method has not been used to obtain infrared spectra of van der Waals molecules. In view of the sensitivity of the molecular beam electric resonance technique, which is based on the detection of the change in state of the molecules in the beam, one might expect that higher sensitivity in the infrared region of the spectrum could be obtained by using some other indirect detection method. The approach taken by Gough, Miller, and Scoles14 in the late 1970s is based on the fact that a near-infrared photon has rather high energy compared with thermal molecular energies. As a result, upon exciting a molecule to an excited vibrational state, one finds its total energy is increased substantially. This suggests that if a liquid helium cooled bolometer is positioned on the molecular beam path, the infrared spectrum can be recorded by observing the molecular energy change resulting from the absorption of an infrared photon. This technique, which has become known as the optothermal method,I4 makes use of the fact that the fluorescence lifetime in the infrared is very long so that molecules which absorb an infrared photon between the source and the detector remain excited during (38) D. H. Levy, Ado. Chem. Phys., 47, 323 (1981). (39) See for example C. A. Haynam, D. V. Brumbaugh, and D. H. Levy, J . Chem. Phys., 79, 1581 (1983). (40) See for example L. Young, C. A. Haynam, and D. H. Levy, J . Chem. Phys., 79, 1592 (1983). (41) F. Y. Chu and T. Oka, J . Appl. Phys., 46, 1204 (1975). (42) A. S. Pine and K. W. Nill, Opr. Commun., 18, 57 (1976). (43) D. N. Travis, J. L. McGurk, D. McKeown, and R. E. Denning, Chem. Phys. Left., 45, 287 (1977). (44) Y . Mizugai, H. Kuze, H. Jones, and M. Takami, Appl. Phys. E , 32, 43 (1983). (45) G. D. Hayman, J. Hodge, B. J. Howard, J. S. Muenter, and T. R. Dyke, Chem. Phys. Lett., 118, 12 (1985). (46) G. M. Stewart, M. D. Ensminger, T. J. Kulp, R. S . Ruoff, and J. D. McDonald, J . Chem. Phys., 80, 5353, 5359 (1984).
Miller their flight to the bolometer. The fact that the bolometer surface is at 2 K ensures that the molecules stick to the detector so that their energy is completely delivered to it. Under typical operating conditions, the minimum detectable power for these bolometer detectors lies in the range 10-12-10-14W/Hz112. This indicates that an absorption of approximately 1 in 10” of a IO-mW laser can be detected by using a time constant of 300 ms. In the case of cluster spectroscopy, the bolometer detects the decrease in beam flux resulting from vibrational prediss~ciation.~~ Recoil of the fragments out of the molecular beam results in a decrease in the translational (as well as internal and condensation) energy which is detected by the bolometer. It was by use of this method that the first cluster vibrational predissociation spectrum was observed in the ground electronic state.47 Since then it has been used in a number of laboratories to investigate many different cluster system^.^*-^' Since the beam flux is directly affected by the dissociation of a van der Waals molecule, it is possible to observe the spectrum of these clusters with other beam detectors. Indeed, the mass spectrometer has become a very popular detector in studies of this type because of its ability to supply some degree of species selectivity. As a result, a large number of clusters have been measured in this w a ~ . ~ * -A~w’ ord of caution is necessary here.
(47) T. E. Gough, R. E. Miller, and G. Scoles, J . Chem. Phys., 69, 1588 (1978). (48) T. E. Gough, R. E. Miller, and G. Scoles, J . Phys. Chem., 85,4041 (1981). (49) R. E. Miller, R. 0. Watts, and A. Ding, Chem. Phys., 83, 155 (1984). (50) G. Fischer, R. E. Miller, and R. 0. Watts, Chem. Phys., 80, 147 (1983); J . Phys. Chem., 88, 1120 (1984). (51) R. E. Miller, R. F. Vohralik, and R. 0. Watts, J . Chem. Phys., 80, 5453 (1984). (52) R. E. Miller and R. 0. Watts, Chem. Phys. Lett., 105, 409 (1984). (53) D. F. Coker, R. E. Miller, and R. 0. Watts, J . Chem. Phys., 82,3554 (1985). (54) G. Fischer, R. E. Miller, P. F. Vohralik, and R. 0. Watts, J . Chem. Phys., 83, 1471 (1985). (55) T. E. Gough, D. G. Knight, and G. Scoles, Chem. Phys. Lerf.,97,155 (1983). (56) T. E. Gough, M. Mengel, P. A. Rowntree, and G. Scoles, J . Chem. Phys., 83, 4958 (1985). (57) Ph. Brechignac, S.DeBenedictis, N. Halberstadt, B. J. Whitaker, and S. Avrillier, J . Chem. Phys., 83, 2064 (1985). (58) M. A. Hoffbauer, W. R. Gentry, and C. F. Giese in Laser-Znduced
Processes in Molecules, K. Kompa and S . D. Smith, Eds., Springer-Verlag, West Berlin, 1978, Springer Ser. Chem. Phys. Vol. 6, p 252. (59) M. A. Hoffbauer, K. Liu, C. F. Giese, and W. R. Gentry, J . Chem. Phys., 78, 5567 (1983). (60) M. A. Hoffbauer, K. Liu, C. F. Giese, and W. R. Gentry, J . Phys. Chem., 87, 2096 (1983). (61) M. A. Hoffbauer, C. F. Giese, and W. R. Gentry, J . Chem. Phys., 79, 192 (1983). (62) M. A. Hoffbauer, C. F. Giese, and W. R. Gentry, J . Phys. Chem., 88, 181 (1984). (63) M. J. Howard, S.Burdenski, C. F. Giese, and W. R. Gentry, J, Chem. Phys., 80, 4137 (1984). (64) A. Mitchell, M. J. McAuliffe, C. F. Giese, and W. R. Gentry, J . Chem. Phys., 83, 4271 (1985). (65) R. D. Johnson, S.Burdenski, M. A. Hoffbauer, C. F. Giese, and W. R. Gentry, J . Chem. Phys., 84, 2624 (1986). (66) W. R. Gentry in Resonances, D. G. Truhlar, Ed., American Chemical Society, Washington, DC, 1984, ACS Symp. Ser. No. 263, p 289. (67) M. P. Casassa, D. S.Bomse, and K. C. Janda, J . Chem. Phys., 74, 5044 (1981). (68) M. P. Casassa, C. M. Western, F. G. Celii, D. E. Brinza, and K. C. Janda, J . Chem. Phys., 79, 3227 (1983). (69) C. M. Western, M. P. Casassa, and K. C. Janda, J. Chem. Phys., 80, 4781 (1984). (70) M. P. Casassa, D. S . Bomse, and K. C. Janda, J . Phys. Chem., 85, 2623 (1981). (71) M. P.Casassa, C. M. Western, and K. C. Janda, J . Chem. Phys., 81, 4950 (1984); M. P. Casassa, F. G. Celii, and K. C. Janda, J . Chem. Phys., 76, 5295 (1982).
Feature Article
As a result of the very weak binding energy of van der Waals molecules, electron impact ionization leads to considerable fragmentation of the clusters. Because of this, not even the mass spectrometer can completely discriminate the spectrum of smaller clusters from the interference due to the larger ones. It should also be mentioned here that infrared lasers can be used in conjunction with a molecular beam electric resonance apparatus to obtain spectra of van der Waals molecule^."^^' As is the case for the optothermal detection method, this technique has the advantage that it is sensitive not only to predissociating clusters but also to stable molecules. Ground electronic state dynamics has also been studied by using visible and UV laser fluorescence techniques. For example Brinza et al. have r e p ~ r t e dthe ~ ~laser-induced ,~~ fluorescence spectrum of Ne-C1,. These spectra clearly show features attributable to metastable, vibrationally excited Ne-C1, which is present in the molecular beam. This implies that the vibrationally excited, ground electronic state clusters have lifetimes in excess of the flight time from the source to the laser crossing region. Laser-induced fluorescence has also been used to probe the internal states of the molecular fragments formed from both ~ l t r a v i o l e and t ~ ~ infrared vibrationalg7 predissociation of a van der Waals molecule. In addition, multiphoton ionization detection has been used in conjunction with an infrared photolysis laser to investigate, in real time, the lifetime of a vibrationally excited van der Waals mole ~ u l e The . ~ ~ results of these studies will be discussed in detail in a later section. Very recently, there have also been some exciting advances in the application of far-infrared lasers to the study of van der Waals molecules. By way of an introduction to these experiments, the measurements of Boom et al.98on Ar-HCl should be pointed out. (72) M. P. Casassa, C. M. Western, and K. C. Janda in Resonances, D. G. Truhlar, Ed., American Chemical Society, Washington, DC, 1984, ACS Svma. Ser. No.263. D 305. ' (f3) J. M. Lisy, A.'Tramer, M. F. Vernon, and Y. T. Lee, J . Chem. Phys., 75,4733 (1981). (74) M. F. Vernon, D. J. Krajnovich, H. S.Kwok, J. M. Lisy, Y. R. Shen, and Y. T. Lee. J. Chem. Phvs.. 77.47 (19821. (75) M.F. Vernon, J. M.-Lisy, H. S.Kwoc D. J. Krajnovich, A. Tramer, Y. R.Shen, and Y. T. Lee, J. Chem. Phys., 75, 4733 (1981). (76) 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). (77) R. H. Page, J. G. Frey, Y. R. Shen, and Y. T. Lee, Chem. Phys. Lerr., 106, 373 (1984). (78) M. F. Vernon, J. M.Lisy, D. J. Krajnovich, A. Tramer, H. S.Kwok, Y.R.Shen, and Y. T. Lee, Faraday Discuss. Chem. Soc., No. 73 (1981). (79) J. Geraedts, S. Stolte, and J. Reuss, Chem. Phys. Lerr., 97, 152 (1983). (80) J. Geraedts, S.Setiadi, S.Tolte, and J. Reuss, Chem. Phys. Len, 78, 277 (1981). (81) J. Geraedts, S.Tolte, and J. Reuss, 2.Phys. A, 304, 167 (1982). (82) J. Geraedts, M. Waayer, S.Stolte, and J. Reuss, Faraday Discuss. Chem. SOC..No.73. 375 (19811. (83) J. Geraedts,' M. N. N. b e l s , S.Stolte, and J. Reuss, Chem. Phys. Lert., 106, 377 (1984). (84) W. L. Liu, K. Kolenbrander, and J. M. Lisy, Chem. Phys. Leu., 112, 585 (1984). (85) D. S.Bomse, J. B. Cross, and J. J. Valentini, J. Chem. Phys., 78,7175 (1983). ' (86) J. M. Philippoz, J. M. Zellweger, H. van den Bergh, and R.Monot, J. Phys. Chem., 88, 3936 (1984). (87) P. Melinon, J. M. Zellweger, J. M. Philippoz, R.Monot, and H. van den Berah. Inr. S v m n Mol. Beams. Proc.. 9rh, 8 (19831.
(88) p. Melinon, R.Monot, J. M..Zellweger, and H. van den Bergh, Chem. Phys., 84, 345 (1984). (89) G. B. Spector, B. B. Brady, and G. W. Flynn, J . Phys. Chem., 89,
1875 (1985). (90) R. L. Deleon and J. S.Muentcr, J. Chem. Phys., 80, 6092 (1984). (911 G. T. Fraser, D. D.Nelson, A. Charo, and W. Klemperer, J . Chem. Phys., 82, 2535 (1985). (92) (a1 U. Buck and H. Mever. Phvs. Reu. Lerr.. 52. 109 (1984): (b1 F. Huisken; H. Meyer, C. Lavenstiin, R. Sroka, and V. Buck, J. 'Chem. k i y s . , 84, 1042 (1986). (93) T. E. Gough and R. E. Miller, Chem. Phys. Lett., 87, 280 (1982). (94) D.E. Brinza, B. A. Swartz, C. M. Western, and K. C. Janda, J. Chem. Phys., 79, 1541 (1983). (95) D. E. Brinza, C. M. Western, D. D. Evard, F. Thommen, B. A. Swartz, and K. C. Janda, J . Phys. Cbem., 88, 2004 (1984). (96) D. S.King, J. Chem. Phys., 82, 3629 (1985). (97) D. S. King and J. C. Stephenson, J. Chem. Phys., 82,5286 (1985).
The Journal of Physical Chemistry, Vol. 90, No. 15. 1986 3305
In this study a Fourier-transform spectrometer was used in conjunction with a liquid helium cooled bolometer to measure the far-infrared spectrum in a cooled gas cell. The spectral region covered by this study was 13-150 cm-'. This region is of considerable interest in the study of clusters since it is here that the low-frequency vibrations of the van der Waals molecules are situated. From the point of view of probing the intermolecular potential this spectral region is therefore extremely important. In the near-infrared studies, on the other hand, information on the intermolecular potential is more difficult to obtain since it generally represents only a small perturbation for the monomer frequencies. Unfortunately, the early studies of Boom et al. did not enable detailed assignments to be made. Recently, however, Klemperer and co-workersWhave observed transitions in Ar-HC1 using a far-infrared laser in conjunction with a molecular beam electric resonance apparatus. The ability to preselect the state of the molecules makes the assignment of these spectra considerably easier. Saykally and co-workersIm have also detected transitions in Ar-HCl using a free jet source in the cavity of a far-infrared laser. The high- Q characteristic of these lasers greatly enhances the absorption, making this a very sensitive and promising technique. In these experiments, a bolometer detector is used to monitor the far-infared laser output. Since the energy of a single far-infrared photon is insufficient to dissociate the cluster, it is clear that these studies do not give information on the vibrational predissociation dynamics. As a result, the near- and far-infared techniques can be thought of as complementary. Unfortunately, these techniques are all rather new and to date no comprehensive studies of this type have been carried out for any of these systems. Infrared-Laser-Induced Vibrational Predissociation van der Waals molecules form an interesting class of molecules in that they have one bond which is considerably weaker than all the others. This difference in binding energy is in fact so large that the vibrational frequencies associated with the chemical bonds in the molecule are larger than the dissociation energy of the weak van der Waals bond. As a result, the molecule becomes metastable upon vibrationally exciting one of the monomer units. Assuming that the vibrationally excited state of the monomer is coupled to the ground state, via the intermolecular potential, the excited van der Waals molecule will therefore dissociate. It was first suggested by Klempererlo1that this form of vibrational predissociation might be observed in a molecular beam experiment by using an infrared laser to excite (HF), and a mass spectrometer to detect the subsequent decrease in intensity of the corresponding mass peak. As indicated in the previous section, much of the data to be discussed in this paper were obtained by using variations of this idea. Before discussing the ground electronic state dynamics of these systems, it is worth spending a few moments summarizing what has been learned about the 1,-He system in the excited electronic state. Indeed, the wealth of experimental and theoretical data that exists for this system makes it an ideal starting point, particularly in view of the fact that much of what has been learned about this system can be carried over into the ground state. For I,-He it is known that vibrational predissociation proceeds via the lowest possible change in vibrational quantum number.31 That is to say, if the energy of a single vibrational quantum is sufficient to dissociate the molecule, then the single-quantum channel completely dominates. Only when the energy of a single quantum is not enough to dissociate the molecule does the two-quantum channel become important. This is clearly consistent with the energy gap picture for V-T and R-T collisional relaxation which has proven so useful in unifying collisional dynamics.*02 In view (98) E. W. Boom, D.Frenkel, and J. van der Elsken, J . Chem. Phys., 66, 1826 (1977). (99) M. 'D.Marshall, A. Charo, H. 0. Leung, and W. Klemperer, J. Chem. Phys., 83,4924 (1985). (100) D. Ray, R. L.Robinson, D. Guo, and R. J. Saykally, J. Chem. Phys., 84. 1171- 119x6). -., ._ (101) W. Klemperer, Ber. Bunsenges. Phys. Cbem., 78, 128 (1974).
3306 The Journal of Physical Chemistry, Vol. 90, No. 15, 198'6 of the similarity between the collisional processes and the vibrational predissociation of a van der Waals molecule, it is perhaps not surprising that the energy or momentum gap ideas have also been applied to the latter.34 From the width of the observed transition^,^' it was possible to estimate the vibrational predissociation lifetimes for the various vibrational levels within the excited electronic state. These lifetimes were found to decrease with increasing quantum number. This result is consistent with the energy gap picture since the anharmonicity of the upper electronic state potential gives smaller vibrational quanta with increasing quantum number. Therefore, in view of the fact that the single-quantum channel dominates, the amount of excess energy available to the fragments after breaking the van der Waals bond decreases as the vibrational quantum number increases. This in turn decreases the translational energy (or momentum) gap, thus making the predissociation lifetime shorter. The correlation between the size of the vibrational quantum and the predissociation lifetime is probably so strong for the case of 12-He owing to the lack of fragment internal degrees of freedom. In the case of more complex van der Waals molecules, formed from polyatomic molecules, the high density of low-frequency vibrations makes an effective depository for this excess energy. The analogous process in collisional dynamics is V-V relaxation. In these cases, it appears as if the correlation between the size of the vibrational quantum and the vibrational relaxation lifetime is much weaker. The first system for which infrared vibrational predissociation was observed was (N20), by use of the optothermal detection technique.47 In this study the u3 mode of N 2 0 was excited with a tunable diode laser. As predicted by Klemperer,'o' infrared excitation of the dimer leads to a decrease in the beam flux reaching the bolometer detector. In this study only very broad limits could be placed on the predissociation lifetime. On the one hand, the clusters clearly dissociated before reaching the detector so that on the basis of the time of flight an upper limit of approximately 0.1 ms can be placed on the lifetime. At the other extreme, the lower limit can be obtained from assuming that the width of the observed spectrum was entirely due to lifetime broadening associated with the finite lifetime. Unfortunately, this s, thus leaving the lifetime rather lower limit is approximately uncertain. As indicated in the Introduction, a large body of data has now been compiled for a variety of polyatomic van der Waals molecules. Taken together with the theoretical work that has been carried out in this area, these results are beginning to tell us what the important factors are that control the detailed dynamics of these systems. In the next several sections, we will discuss the experimental and theoretical results which have helped us to understand the partitioning of the excess energy in the fragments and the lifetime of the excited state of the complex. Atom-Diatom Molecule Systems As indicated previously, there is ample evidence to support the statement that vibrational predissociation tends to proceed via the channel which gives the least excess translational energy or momentum34 in the fragments. E ~ i n g ' ~first . ' ~suggested ~ that a simple golden rule calculation could be used to explain this fact. This model has been widely quoted in the literature owing to the simple physical basis on which it rests. In Figure 1, we have once again reproduced a figure taken from ref 104 which beautifully explains the important concepts. In this figure r represents the van der Waals coordinate, and the two potential surfaces represent intermolecular potentials for the ground and vibrationally excited states of the monomer units. &(r) and R,(r) are the vibrationally excited metastable state and continuum state wave functions, respectively. In a simple golden rule calculation the transition rate from the metastable state to the dissociative state can be (102) T. A. Brunner and D. Pritchard, Adv. Chem. Phys., 50,590 (1982). (103) See for example H. K. Shin, J. Chem. Phys., 78,795 (1983). (104) G. E. Ewing, J. Chem. Phys., 72,2096 (1980). (105)G . E. Ewing, Faraday Discuss. Chem. Soc., No. 73,325 (1982).
Miller
I
'
'
!I'
'
'
'
'
'
I
4000
-
2000
x 01 L
I
0)
=
W
o
0
2
4
6
/a
A-BtC
7
8
1
0
Figure 1. Potential energy surfaces, wave functions, and energies pertinent to the vibrational predissociation of AB-C. Adapted with permission from ref 104.
calculated from the matrix element involving these two state functions. The coupling term in this matrix element is obviously closely related to the intermolecular potential. Assuming that the coupling term is slowly varying with r, in comparison to the frequency of the continuum wave function, then (qualitatively at least) one would expect that the predissociation rate would depend on the overlap integral between the two state functions. Since the frequency of the continuum wave function increases with increasing AET (Le., excess translational energy or more precisely with the translational momentum), this will lead to a decrease in the value of the overlap integral and hence the predissociation rate. For the case of H d 2 , translational momentum is rather small as a result of the relatively small vibrational energy associated with the iodine stretching vibration (approximately 100 cm-'). As a result, the predissociation lifetime is rather short (approximately 100 ps). At the other end of the spectrum of diatomic-rare gas clusters, we have the H2-Ar system.22 In this case, the diatom vibrational energy is very large (approximately 4100 cm-I) so that, on the basis of what we have said so far, we would expect that the vibrational predissociation rate would be rather slow. Indeed, LeRoy et a].'" have carried out converged close-coupling calculations on this system for both the rotational and vibrational predissociation rates, and they find that the latter of these is some 3 orders of magnitude slower than that of the former. Rotational predissociation is found to be rather fast (lifetimes in the range 50-200 ps), however, as expected, considering the relative sizes of the rotational and vibrational quanta. Very recently, similar C C calculations have been carried out on the He-HF system by Gianturco et al.'07 In this case, the well depth is so small that the intermolecular potential only supports a single state, namely the J = 0 state. All other rotational states were found to undergo rapid rotational predissociation. Other rare gas-diatom systems that have been recently studied by using accurate C C calculations are Ar-HC1Io8 and He-CO and He-N,.Iw In all cases, reasonably accurate intermolecular potentials were used, having been obtained from state-to-state differential scattering data and/or rotational spectroscopy. As (106) R. J. LeRoy, G. C. Corey, and J. M. Hutson, Faraday Discuss. Chem. SOC.,No.73,339 (1982); R.J. LeRoy in Resonances, D. G. Truhlar, Ed., American Chemical Society, Washington, DC, 1984, ACS Symp. Ser. No. 263, p 231 and references contained therein. (107) F. A. Gianturco, A. Palma, P. Villarreal, and G . Delgado-Barrio, Chem. Phys. Leff., 111, 399 (1984). (108) C. J. Ashton, M. S . Child, and J. M. Hutson, J . Chem. Phys., 78, 4025 (1983). (109) F. A. Gianturco, private communication.
The Journal of Physical Chemistry, Vol. 90, No. 15, 1986 3307
Feature Article a result, these are ideal systems for experimental photodissociation studies since direct quantitative comparisons with theory should be possible. During the course of writing this paper the author has become aware of two very recent experiments on Ar-HCll'O and Ar-HF."' Clearly, a detailed understanding of the spectroscopy and dynamics of these diatomic molecule-rare gas systems is forthcoming.
Polyatomic van der Waals Molecules; Partitioning of the Excess Energy The majority of infrared studies carried out in molecular beams have involved van der Waals systems formed from polyatomic molecules. In these cases, the question of how the energy is partitioned in the fragments is rather complex owing to the fact that the fragments have more than one vibrational degree of freedom. For example, in the case of (N20), excited with one quantum of the u3 vibration, Ewing112 suggested that several different vibrational relaxation channels needed to be considered. A few of these are reproduced here. N20(001). ..Nz0(000) -* NzO(OOO) + N20(000) + AEv-T(1693 cm-') (1) N20(OO1) ...N20(000) -* N20(010) N2(000)
+
+ AEV-,, (1104 cm-')
(2)
N20(00 1)...NzO(000) -* N20(010) N20(010)
+ AEv+ (515 cm-I)
(3)
N,O(OO 1)...NzO(000) -* N20(100) NzO(OOO)
+ AEv-v (408 cm-I)
(4)
+ +
In calculating the energy available for partitioning between the translational and rotational degrees of freedom for these channels, he assumed a zero-point energy for the van der Waals bond of for the complex of 580 cm-'. 49 cm-' and a binding energy (0,) In this treatment, the rotational degrees of freedom were neglected. For clusters which fragment to give molecules with small rotation constants, this assumption is probably quite a reasonable one since in order for the rotational degrees of freedom to form a depository for appreciable energy very high J states would have to be populated. For lighter systems, such as (HF),, this approximation is clearly inappropriate. In an effort to quantify the energy gap arguments presented above, Ewing made use of Fermi's golden rule to explain in some detail the tendency for producing vibrationally excited fragments and hence small translational excitation. Although this type of calculation is by no means rigorous, it does give some valuable insight into which of the available channels are the most probable and, in a semiquantitative way, explains much of the available data. For example, if the coupling term in the matrix element appearing in Fermi's golden rule is simply taken as the derivative of the Morse potential used to describe the intermolecular potential, then the rate for the channel labeled 4 is found to be about 6 orders of magnitude faster than that obtained for the purely translational channel labeled as 1. However, the predissociation lifetimes obtained by using this expression for the coupling term are still much longer than those observed experimentally. If, on the other hand, a dipole-dipole coupling term is included, then the lifetimes are found to decrease by another 6 orders of magnitude into the range obtained from the experiments. Beswick and Jortnerll3 have carried out more rigorous calculations on the vibrational predissociation of (N20), and also find that, for the most efficient V-V channel, the lifetime is in the range 10-5-106 s, overlapping with the experimentally determined Clearly, the low-frequency vibrations within the monomer unit can be important in increasing the rate at which vibrational predissociation occurs. Unfortunately, no direct experimental measurement of the fragment vibrational distribution resulting (1 10) A. S.Pine, private communication. (1 11) C. M. Lovejoy, M. D. Schuder, and D. J. Nesbitt, to be submitted for publication. (112) D. A. Morales and G . E. Ewing, Chem. Phys., 53, 141 (1980).
Frogment Angular Distributions
'
lJ-LddJ 2 4 6 8 IO Loborotory Angle (Degrees)
Figure 2. Angular distributions of water cluster fragments following infrared-laser-inducedvibrational predissociation. The detected masses are ( 0 ) H30+, (A) (H20)2H+, (0)(H20)3H+,and ( 0 ) (H20)4H+. Adapted with permission from ref 74.
from the infrared-induced vibrational predissociation has yet been carried out. However, as we will now see, a considerable amount has been learned about the other degrees of freedom of the fragments. Let us now consider in some detail the results of a number of experiments specifically designed to address the problem of energy partitioning. In order to establish what fraction of the available energy appears as relative translational energy of the fragments, several investigators have measured the fragment velocity and angular distributions. For example, as seen in Figure 2, Lee and c o - ~ o r k e r s ' ~reported ~ ~ * this type of data for (HzO), excited near 3.7 pm. Clearly, the fragments are highly peaked in the forward direction despite the fact that the excess energy available after breaking the bond is very large. Similar results have also been reported by Gentry and co-workers for (CzH4)259and OCS c1usters6O excited with a pulsed CO, laser near 10 pm. These results confirm that it is the internal degrees of freedom which are the most effective in accepting the available excess energy. However, since there is no state selection of the fragments in these experiments, it is not possible to conclusively decide on the relative importance of the rotational and vibrational degrees of freedom. However, as suggested by Beswick and Jortner,II3 for dimers formed from polyatomic molecules with small rotational constants it is unlikely that appreciable energy is carried away in the rotational degrees of freedom since this would involve very large changes in the rotational quantum number. On the other hand, for (C2H4)2, excited at 10 pm, there are no low-frequency vibrations accessible tQ the fragments so that in this case rotations will clearly be very important. To obtain a complete characterization of the energy partitioning for these systems, it is obviously necessary to probe the internal degrees of freedom of the fragments. Very recently, King and Stephensong7have reported a two-laser experiment in which they dissociate NO-C$4 using a C02 laser (exciting the v, mode of C2H4) and then probe the rotational distribution of the fragment NO using laser-induced fluorescence. As shown in Figure 3, the rotational distribution is well-characterized by a Boltzmann distribution with a temperature of 75 K. Clearly, most of the excess energy must be deposited elsewhere. By recording Doppler profiles for the nascent N O they have also been able to obtain the amount of kinetic energy released in the fragments. The results clearly show that there is once again very little kinetic energy released in the dissociation process. Unfortunately, the CzH4 fragment cannot be probed in these experiments. From energy (113) J. A. Beswick and J. Jortner, J . Chem. Phys., 74, 6725 (1981).
Miller
3308 The Journal of Physical Chemistry, Vol. 90, No, 15. 1986 I
I
I
I
Rotational Distribution
+
16'
-
16~
-
0
100
200
300
400
internal Energy (cm-'1
Figure 3. The NO fragment rotational distribution resulting from vibrational predissociation of NO-C2H4. Adapted with permission from
ref 91. balance considerations, it is clear, however, that the C2H4 fragment carries away approximately 300 cm-' in internal energy. In view of the fact that the lowest vibrational frequency of ethylene is 826 cm-l, it is clear that this energy must reside in rotation. King and Stephenson suggest that the rotation is primarily about the a axis for which the rotational constant is 4.8 cm-I. The other two rotational constants are considerably smaller ( B = 1.0 cm-' and C = 0.83 cm-I) so that states of much higher J would need to be excited in order to account for the estimated internal energy. This clearly would be less favorable. King and co-workers114have also measured Doppler profiles and rotational-state distributions of N O produced by infrared predissociation of In this case, a complete characterization of the system is obviously possible. In view of this, it is likely that this system will be the subject of considerable theoretical study in the near future. To date, however, these results have not been published. It is important that we note here that, in both of the systems for which the internal states of the fragments have been probed, all of the V-V channels of the type discussed above are closed. As a result, we still do not have any conclusive experimental data which confirm that for large polyatomic systems it is the V-V, rather than the V-R,T, channels which are most important. Recently, Hutson et a1.Ii5 have carried out coupled channel calculations on Ne-C2H4 and Ar-C2H4. Considering the excitation of the band correlating with the Y, mode of ethylene, the calculations clearly show that rapid dissociation occurs to form a vibrationally excited (ul0) ethylene fragment. Note that this channel is believed to be closed for (C2H4)2,59but due to the lower binding energies for these mixed clusters, is open in these cases. Clearly, the study of energy partitioning in the vibrational degrees of freedom of polyatomic fragments is an area which will receive considerable theoretical and experimental attention in the future.
Predissociation Lifetimes A critical question that we have not yet addressed in any detail is the following: How long does it take for this dissociation process to occur and what are the factors that control its rate? However, in the course of examining how energy is partitioned among the various degrees of freedom of the fragments, some aspects of this question have unavoidably been discussed. Indeed, in the previous sections, we found that the predissociation lifetime and the detailed energetics of the available relaxation channels are inseparably connected. For the case of rare gas-diatomic molecule systems, the predissociation lifetimes seem to be adequately explained by the available theoretical methods.32-37~115~L16 As a result, it is likely (1 14) D. King, private communication. (115) J. M. Hutson, J . Chern. Phys., 81, 4474 (1984).
that good quantitative agreement between theory and experiment will be possible for these systems. In this section, we wish to examine the available data for the more complex van der Waals systems typically studied using the infrared laser-molecular beam techniques. Although a considerable amount of data has been obtained for these systems, the above question is still a long way from being answered. As will become clear in the following discussion, there are still some real mysteries remaining, and we are a long way away from being able to predict lifetimes for particular excited vibrational states of a given system. Part of our lack of understanding is associated with the fact that none of the experimental techniques presently available fulfill all of the requirements of an ideal method for determining the lifetimes. The ideal experiment, of course, would involve measuring the decay of the excited-state dimer in real time. Although this type of experiment has been carried out for some systems,64%97J14 the time resolution has been insufficient to resolve the predissociation decay. As a result of these limitations, we have been forced to obtain information concerning the predissociation lifetime from experiments carried out in the frequency domain. In the case where all of the spectroscopic fine structure is completely resolved, this method works rather well. Indeed, we saw for the case of He-I, that quantitative lifetimes could be obtained by measuring the width of transitions that are broader than the limit imposed by instrumental effects. In this type of measurement, the inverse of the homogeneous line width can be attributed to the short lifetime in the excited state of the dimer. Even here, however, the results are not conclusive in that it is not always possible to correlate the line width with the particular relaxation channel of interest. For example, in complex systems it is possible that intramolecular vibrational relaxatiod6 is responsible for the observed line width rather than the vibrational predissociation process. In cases where the rotational fine structure is not resolved, the problem is even more severe since there is always some uncertainty as to the source of the broadening. In most of the systems studied so far the width of the vibrational band is consistent with that expected from a rotational contour at a temperature characteristic of a free jet expansion. As a result, there is always some contribution to the observed line width from the unresolved rotational contour and much of the uncertainty in the lifetimes quoted in the literature is associated with the fact that we are often unsure of the relative importance of these two broadening mechanisms. Strictly speaking, therefore, from this type of measurement, we are only able to quote a lower limit to the predissociation lifetime. For most of the spectra recorded without rotational resolution, this limit is approximately lo-', s. At the other extreme, we know that for experiments carried out with the beam detector positioned directly on the molecular beam the lifetime must be shorter than the flight time from the laser to the detector if a decrease in flux is to be observed. In the case where the detector is positioned off the main beam, the fragments can only be detected if dissociation occurs within the field of view of the detector. Unfortunately, the limit imposed by these time-of-flight arguments is approximately 10-4-10-6 s, which leaves a considerable range of uncertainty. Let us begin by discussing those systems for which the rotational fine structure has been resolved so that rather good estimates of the lifetime can be made. In addition to the atom-diatom molecule systems discussed in the previous section, rotationally resolved spectra have also been obtained by using long path length absorption cells for (HCl)2,24HF-C0,25and HF-HCN.25 For these cases, there is no evidence of broadening that can be associated with vibrational predissociation. This is perhaps not all that surprising, in view of our earlier discussions of the energy or momentum gap models for vibrational predissociation, since in all cases a high-frequency vibration is being excited in a molecule which has a very low density of rotational and vibrational states. An extremely interesting system that has been studied in considerable detail is the H F dimer. (HF), was one of the first ( 1 16) A. S Pine, to be submitted for publication.
The Journal of Physical Chemistry, Vol. 90, No. 15. 1986 3309
Feature Article
/
p" 1'1'
p"
-020
I
I
I
-015
-010
-005
I
I
1
010
015
1
0 005 A v (ern-')
I
020
Figure 5. A small section of the high-resolutionspectrum of acetylene dimer.I3 Resolution of the spectrum is limited by Doppler broadening resulting from the velocity spread of the molecular beam.
F Figure 4. (HF), equilibrium geometry. Arrows show relative motions of the atoms corresponding to the v I and v2 vibrations. Adapted with
5ooo -0.59
permission from ref 23. dimers to be investigated by the molecular beam electric resonance As a result, its equilibrium geometry is well-charmethod."' acterized and is shown here in Figure 4. This molecule clearly has two vibrational modes ( u l and v2) associated with H-F stretches. In one case ( q ) the motion is essentially that of the free hydrogen while in the other it is the hydrogen-bonded H which undergoes large-amplitude vibrations. Pine and L a f f e r t ~find ~~ that the widths of the rovibrational transitions in the u1 band are essentially Doppler limited whereas those in the u2 band are noticeably broader. When these results are combined with the beam measurements of DeLeon and Muenter,go the estimated predissociation lifetime of the dimer lies in the range 3-0.5 ns when the u2 mode is excited and 300-30 ns for u, mode excitation. This difference might seem surprising if we only consider the energetics of this system since the two modes are only separated by 60 cm-l out of 3900 cm-'. However, if one considers the structure shown in Figure 4 and the vibrational displacements for the two modes, this difference in lifetimes becomes more clear. Large-amplitude motion of the bonded hydrogen may lead to dissociation more rapidly than vibration of the (much more decoupled) nonbonded hydrogen. In terms of the Fermi's golden rule picture of the dissociation process, the difference in lifetimes is probably best represented by a difference in the matrix element coupling terms for the two modes. Recently,11sa rather complete close-coupled calculation has been carried out for this system which gives a lifetime for uz excitation which is in rather good agreement with that obtained experimentally. As we shall see shortly, the available data seem to suggest that this mode dependence of the lifetime exists in many other systems. Indeed, in some of the larger polyatomic clusters the existing data suggest that there are even more dramatic examples of mode-dependent vibrational relaxation rates. Now the following question should be raised: What happens to the vibrational predissociation rate as the size and complexity of the cluster are increased? Until recently, all of the molecular beam results indicated that for dimers formed from polyatomic molecules the predissociation rate is so fast that is completely eliminates any rotational fine structure, thus leaving only a broad unresolved band. Recently, at the Australian National University, we were able to extend the observation of rotational fine structure to rather complex systems, indicating that the predissociation lifetimes are not universally short for these larger systems. The first system investigated a t high resolution was the acetylene dimer.51 Although the restricted tunability of the laser prevented a unique assignment of the spectrum from being made, the line width of the observed transitions indicates that the lifetime is in the 1-100-ns range. A small portion of the spectrum obtained under single-mode conditions is shown in Figure 5 . Similarly, we have seen sub-Doppler resolution transitions for C 0 2 and NzO dimerd2 indicating lifetimes in excess of 100 ns. For the case of (117) T. R. Dyke, B. J. Howard, and W. Klemperer, J . Chem. Phys., 56, 2442 11972). (1 (8) N.' Halberstadt, Ph. Brechignae, J. A. Beswick, and M. Shapiro, J . Chem. Phys., 84, 170 (1986). ~
fie
J/cmZ
952.9 cm-I
= 4000 -
Laser
ii
c c c 0
< 3000 ul L
c
0
.
0
0
0 0
u" 2000-
0 0
i
loo0-
500
o On 0
Off
0
t
0
$
i
600700 Time ( p s e c )
800
900
Figure 6. Time-of-flight distributions of (C2H4), obtained with the dissociating laser off and on. With laser on, 99.9% of the dimer ion disappears. Adapted with permission from ref 59.
(C3H4)Z (methylacetylene dimer)54 spectral features as narrow as 375 MHz were observed, suggesting that the lifetime is at least 0.4 11s. More recently, rotationally resolved spectra have also been reported by Hayman et al.45for a series of rare gas-OCS clusters and by Klemperer and co-workersgl for systems such as NH3C2Hzand NH,-HCN. In the case of the rare gas-OCS clusters the lower limit on the predissociation lifetime is 1 ns. Let us now consider those systems for which only broad spectra have been observed. The first indication that, in at least some of these cases, the homogeneous contribution to the line width might be dominant came with the observation that, when (C2H4)Z is excited by a high-power, narrow-frequency COz laser, nearly all of the dimers in the beam can be d i s ~ o c i a t e d .This ~ ~ is clearly shown in Figure gS9 where the time-of-flight distribution for (CzH4)z is recorded with the laser on and off. Over 99.9% of the dimers are dissociated by the laser. Since the laser line width is extremely small, the maximum fraction of the molecules that can be dissociated by the laser is essentially given by the ratio of the homogeneous line width to that of the overall width of the spectrum. Clearly, this experimental result indicates that the homogeneous width is approximately equal to that of the observed line width. More recently, two-laser saturation experiments have been carried out on (CzH4)z,59(OCS)z, OCS-Ar,60 (C6H6)2?5and (CH30H),6z which strongly suggest that the homogeneous line width dominates the observed spectra, at least for these systems when excited near 10 km. In these experiments, the molecules in the beam first pass through a high-power COz laser which dissociates some fraction of the molecules in the beam. A second, somewhat lower power COzlaser is then used to dissociate a small fraction of the remaining dimers. The first laser will dissociate only dimers which lie within the homogeneous line width of the laser. Therefore, if the homogeneous width is less than the overall width of the spectrum, it should be possible to detect a hole burned in the spectrum by the first laser by using the second. In all the above cases, the spectrum recorded by the second laser was unaffected by the first laser except that the intensity of the spectrum was reduced when the first laser was on. This is clearly consistent with the fact that a single-frequency laser can dissociate
Miller 'R,(3)
.-c .-C n
CH ,,
: Ar:
960
940
980
I
Frequency (ern-') Figure 7. Infrared spectrum of (C2H& obtained by detecting the depletion of the dimer ion mass peak. Adapted with permission from ref 67.
1.015 0.6 0.4 t
c
? 0.2
I
4
LL
- 100
-50
0
t (nsec)
50
-
I
RPo(J) 2 3
I
I
I
I
4
5
6
7
2061.95 2062.00 2062.05 Frequency (crn-1) Figure 9. Free jet-diode laser spectrum of Ar-OCS near 2060 cm-' showing well-resolved and assigned rotational structure. Adapted with permission from ref 45.
I
I
OCS-Ar
h
He = 7.5:200:800
too
Figure 8. Decay of the ethylene dimer ion signal as a function of the time dealy between pump and probe lasers. The rate of decay of the MPI signal is limited by the time resolution of the lasers. Adapted with permission from ref 64.
all of the molecules in the beam and is rather strong evidence in support of the idea that the observed line width is dominated by homogeneous broadening. Given this, the lifetime of the excited state appears to be in the picosecond range. There has been some concern that in view of the fact that these experiments were carried out using pulsed lasers there may have been substantial power broadening present. However, this explanation seems unlikely in view of similar experiments carried out by Janda and coworkers6' using low-power continuous wave (CW) C02lasers. By making the laser-molecular beam interaction length very long, they have also been able to dissociate essentially all of the dimers using very low power densities where power broadening is definitely absent. Figure 7 shows the Lorentzian-shaped spectrum of (C2H4)2 obtained with the C W C 0 2 laser system. For reasons, as of yet unknown, the spectrum obtained with C W lasers is considerably narrower than that obtained with pulsed lasers. Earlier in this section, it was stated that there are some mysteries associated with the available data. Lets examine these. As indicated above, the two-laser saturation experiments strongly suggest that the lifetimes for (OCS), and OCS-Ar are 1.5 and 5 ps, respectively, when excited near 1054 cm-1.60 On the other hand, when excited near 2060 cm-I, the lifetime of A P O C S ~is~ greater than 1 ns and (CO,), and (N,O),, excited near 3700 have lifetimes in excess of 100 ns. At first sight, it is perhaps surprising that the lifetime increases with increasing photon energy. However, there is some justification for this type of behavior in the atom-diatom systems for which the higher energy vibrations provide more energy which must then be disposed of in the fragments, thus resulting in longer lifetimes. In the cases cited above, however, there is the added complication that the constituent molecules have several vibrational degrees of freedom so that the density of vibrational states increases rather quickly with increasing energy. Because of this, it might be expected that there would be easily accessible, low translational energy channels available at the higher energies (corresponding to vibrationally excited fragments) which would therefore have rather short lifetimes. For the case of Ar-OCS there are some geometrical factors which might justify the longer lifetimes for higher energy
vibrations. Indeed, in the studies carried out at 1054 cm-' the first overtone of the bending vibration was excited while the spectrum recorded at 2060 cm-' is associated with the asymmetric stretching vibration. In view of the fact that OCS-Ar is essentially T-shaped, one might expect that the bending vibration would be more strongly coupled to the van der Waals bond, especially considering the mode-specific lifetimes observed for (HF),. Unfortunately, this argument cannot be used to explain the difference seen for (OCS), and (CO,), since, although the excitation frequencies used in the two experiments are very different, the vibration excited in (CO,), at 3700 cm-' has a large component of the bending vibration due to Fermi resonance. In view of the similarity of these two systems, as well as the modes excited, a difference in lifetime of 5 orders of magnitude seems hard to understand. Gentry and c o - w o r k e r ~recently ~~ pointed out that there are some important differences in the experimental techniques used to obtain these two sets of data, which might explain why the resulting lifetime estimates are so different. First, since the C02 laser used in the 1054-cm-I experiments is only line tunable, relatively few points on the spectrum can be obtained. As a result, sharp features in the spectrum could easily be missed. On the other hand, continuously tunable lasers have been used to obtain the rotationally resolved spectra which indicate long vibrational relaxation lifetimes. In this case fine structure in the spectrum will be detected with higher sensitivity than that of any broad bands. Another difficulty with comparing the two sets of results comes from the fact that without detailed spectroscopic assignments it is dangerous to attribute the features in the spectrum to specific clusters. In principle, the mass spectrometer has the advantage in this area since it possesses some degree of mass selectivity. However, as clearly indicated by the scattering experiments of Buck et al.,92fragmentation of higher clusters can lead to contamination of the dimer ion mass peak. In most cases, this problem must be avoided by considering the source pressure and gas composition dependence of the mass spectrum. Recently, Buck et al. have reported preliminary results using the scattering method to ensure that the observed (C2H4)*spectrum is not contaminated by higher clusters. In the case of bolometer detection there is no mass selectivity. However, this method does have the advantage that, for studies carried out directly on the molecular beam, it has extremely high sensitivity. Combined with a high-resolution continuously tunable laser, it is often possible to obtain well-resolved spectra which provide the necessary information for direct spectroscopic species identification. Indeed, we have recently recorded the complete (CO,), spectrum using a computer controlled F-center laser. Although a complete assignment of the spectrum is still forthcoming, we have been able to eliminate the possibility that the spectrum arises from C 0 2 complexed with the helium carrier gas. At this point, the source of the large differences between the estimated lifetimes obtained from the various method cannot be unequivocally identified and we are still some way from being able to make generalizations concerning the behavior of these systems.
Feature Article
The Journal of Physical Chemistry, Vol. 90, No. 15, 1986 3311
One might well ask the question, Does theory have anything to say that might be of some use in trying to understand these results? For these rather complex systems the problem of carrying out reliable theoretical calculations is formidable. The vast majority of theoretical work that b s been carried out on these polyatomic systems is in the form of classical trajectory or Monte Carlo calculations.""21 Calculations of this type cannot be used to follow the motion much beyond the tens of picoseconds range. In addition, there is reason to be concerned that a classical calculation is missing much of the essence of the problem at hand. Indeed, much of our discussion has centered around the idea of deposition of the excess energy into the available quantum states. If this picture is a good one, then quantization of the motion is clearly an important factor in controlling dynamics. As indicated previously, one rather complete quantum-mechanical study has been carried out for Ne-C2H4 and Ar-CIY4 by Hutson et al.lI5 The lifetimes calculated for the most efficient dissociation channels give homogeneous line widths of 0.02 and 0.11 cm-' for Ne-CzH4 and Ar-C2H4, respectively. This is to be compared with the experimentally observed line widths of 0.5 and 3.0 cm-l, respect i ~ e l y .Although ~~ not quantitative, the agreement is promising, especially if one considers that the experimental widths are not necessarily a measure of the lifetime. In addition to the inhomogeneous contributions to the line width, other sources of broadening may be important, as we will now see. An important point that has not been covered in the above discussion, and which is of critical importance when comparing the lifetimes obtained from frequency domain experiments and theoretical calculations, is the contribution to the line width from intramolecular vibrational relaxation (IVR).I2* Gentry and c ~ - w o r k e r s ~first * , ~ suggested ~ that IVR might be responsible for the broad line widths observed in some of these systems. That is to say that intramolecular vibrational relaxation within the dimer could precede dissociation in which case the width of the spectrum would not give information concerning the predissociation lifetime. Indeed, IVR is now rather well understood for stable molecules11s and is important under conditions where the density of vibration states in the vicinity of the excited state is very high. The result is that a large number of nearby vibrational states couple to the excited state and cause the initial excitation to be lost to the bath of states in the molecule. This relaxation process would not be distinguishable from the djssociation process in the frequency domain experiments discussed above. In view of the low-frequency van der Waals vibrations, it has been suggested that even at low excitation energies the density of vibrational states may be sufficient to make this mechanism an important one for clusters. For a more complete discussion of this idea, the reader is referred to the literature.66 Since the frequency domain experiments do not differentiate between the two vibrational relaxation channels described above, there has been a keen desire to carry out experiments in the time domain by monitoring either the disappearance of the dimer or the appearance of the fragments, in real time following a pulsed dissociation laser. Two experiments, one falling into each of these categories, have recently been reported. As indicated in the previous section, King and c o - ~ o r k e r s "have ~ recently studied the N O dimer system in great detail using a two-laser method. The first laser is used to dissociate the dimer while the second is used to probe the fragments. Not only does this type of experiment give direct information on the internal states of the fragments, but by varying the time delay between the two lasers, it is possible to estimate, within the time resolution of the lasers, the predissociation lifetime. For this system, the dissociation lifetime is found to be less than the 10-ns limit imposed by the pulse duration of the lasers. Recently, Gentry and c o - ~ o r k e r s ~ ~ have also carried out real time experiments on (C2H& using a (119) J . E.Adams, J . Chem. Phys., 78, 1275 (1983). (120) J. R. Reimers and R. 0. Watts, Chem. Phys., 85, 83 (1984). (121) L. L.Gibson and G. C. Schatz, J . Chem. Phys., 83, 3433 (1985). (1 22) See for example Photoselective Chemistry, Section 1, J. Jortner, R. D . Levine, and S . A. Rice, Eds., Wiley, New York, 1981,Adv. Chem. Phys. VOl. 47.
pulsed CO, laser for dissociation and a frequency-tripled Nd:YAG laser to detect the dimer by multiphoton ionization. In this way, they were able to monitor the disappearance in time of the dimer following a C 0 2 laser pulse. Once again the dissociation was found to occur on a time scale which is fast with respect to the time resolution of the experiment. However, these experiments do show that the predissociation lifetime for these systems is shorter than the approximately 10-ns limit imposed by the laser. Clearly, the question of whether the frequency domain experiments are measuring rates for predissociation or IVR remains unanswered at this point. However, the experimental tools to answer this question are available and it only remains to find a system for which several of the existing techniques overlap.
Infrared Spectroscopy U p to now, we have concentrated on the dynamical behavior of a van der Waals molecule that follows its vibrational excitation. In the course of that discussion, we pointed out that in order to obtain a detailed theoretical description of these processes the potential energy surface is required. For example, as shown by Beswick and J ~ r t n e r the , ~ ~predissociation dynamics of 12-He depends on the equilibrium structure of the cluster. These structures are also of considerable interest to the quantum chemists who have long been challenged by the difficult task of predicting the equilibrium geometries of van der Waals molecules. For example, the C02 dimer has been the subject of a number of theoretical investigations. Hashimoto and IsobelZ3used the CNDO/2 method to calculate the equilibrium structure of (CO,), and found that the T-shaped structure was the most stable one. More recently, the theoretical predictions by Walmsley and cow o r k e r ~and ' ~ ~Koide and KiharaIz5suggest that the centrosymmetric parallel configuration is in fact more stable. Indirect experimental evidence e ~ i s t s ' ~ ~in- ' support ~' of both of these structures. In view of the interest in the structure determinations, let us examine for a moment the importance of infrared spectroscopy in this regard. As already pointed out, rotational spectroscopy has been extremely useful in obtaining detailed information concerning the structure of clusters. However, for systems which do not possess a permanent dipole moment, the molecular beam electric resonance method is inappropriate. For the case of (CO,)? for example, the most recent studies using molecular beam electnc resonance show that no refocusing of (CO,), is possible, suggesting that the most stable geometry is nonpolar. On the other hand, by choosing an appropriate vibrational band, one can obtain the infrared spectrum for systems df this type. An additional advantage of the infrared technique is that it can provide not only ground-state constants but also those associated with the vibrationally excited states. Let us now examine in some detail what has already been learned about van der Waals molecular structures and constants from infrared spectroscopy. As indicated in the sections dealing with cluster dynamics, the hydrogen-containing rare gas clusters were among the first studied in any detailed way. These systems were first investigated experimentally by Welsh and co-workers at the University of Toronto.22 Much more detailed work was later reported in the literature by McKellar.22 These systems have several features which make them good candidates for study. First, the widely spaced rotational lines make it possible to resolve rotational structure in the spectrum without the need for very high resolution or extremely low temperatures. In addition, the infrared transitions in the monomer are forbidden so that they do not obscure the region of interest. From the theoretical point of view, these systems are also very important since detailed potential surfaces are available for many of them and the number of channels that need (123) M.Hashimoto and T. Isobe, Bull. Chem. SOC.Jpn., 40,40 (1974). (124) N . Briget, S. Odiot, S. H. Walmsley, and J. L. Whitten, Chem. Phys. Lett., 49, 157 (1977). (125) A. Koide and T. Kihara, Chem. Phys., 5, 34 (1974). (126) S . E. Novick, P. B. Davies, T. R. Dyke, and W. Klemperer, J . Am. Chem. Soc., 95,8547 (1973). (127) A. E.Barton, A. Chablo, and B. J. Howard, Chem. Phys. Lett., 60, 414 (1979).
3312 The Journal of Physical Chemistry, Vol. 90, No. 15, 1986
to be considered is relatively small. As a result, close-coupled calculations have been carried out H2-Ar and HD-Ar.'" Because of the extremely small anisotropy of the intermolecular potentials, the H2-rare gas molecules are best thought of as having the H2 molecule freely rotating within the complex. As a result, the energy levels of the complex are given by the sum of two diatomic molecule energies, one corresponding to the free H2 molecule and the other to the rotation of the overall complex (where H2 is assumed to be a point mass). For even slightly more massive cluster systems, conventional infrared spectrometers do not have the necessary resolution to obtain spectra in which the rotational fine structure is resolved. This is clearly seen in the early papers on systems such as (HF)2,128 Ar-HC1,20 and (C02)2.129Even though considerable structure was seen in the HF dimer spectrum, for example, assignment of the spectrum was not possible. Recently, this problem has been somewhat alleviated by making use of high-resolution infrared lasers in conjunction with a long path length gas cell. Experiments of this type have been carried out in several laboratories using different f r e q u e n ~ yand ~ ~ .F~- ~~ e n t e rlasers. ~~ The power of this method has been beautifully demonstrated by Pine and c o - w ~ r k e r on s ~ ~their recent studies of the H F dimer. The authors obtained completely resolved rotational fine structure in both the v i and v2 bands of (HF),. Fits to these spectra give a structure which is consistent with that obtained from the microwave studies."' In addition, by combining the microwave and infrared results, it was possible to generate more accurate and higher order molecular constants than previously obtained by using only the microwave results. More recently, Pine and co-workers have also investigated the HCl dimer24and HCl-Ar116 in the same detail. Mixed dimers have also been studied by using lasers in conjunction with a long path length gas cell. Bevan and co-workers have reported infrared spectra for HF-C02S and HF-HCN.ZS Although spectral congestion is already rather severe for these systems, such that there is some overlapping of lines, the spectra are consistent in both cases with a linear hydrogen-bonded geometry. For more complicated systems, such as dimers formed from polyatomic molecules, it becomes much more difficult to resolve rotational fine structure. Not only does rotational line congestion increase very rapidly with the size of the monomer unit, but as seen in the previous sections, the relaxation lifetime generally decreases. Eventually, of course, the lifetime will become so short, and the density of rotational states so high, that it becomes impossible to resolve any fine structure. At this point, infrared spectroscopy is no longer useful as a tool for obtaining detailed molecular constants and structures. As indicated in the previous section, the optothermal method has been used to resolve rotational fine structure for (C2H2),, (CO,),, (N20),, and (C3H4)2. In these studies (near 3 pm), the instrumental resolution is approximately 1 MHz. Unfortunately, a detailed study of these systems was hampered by the small continuous tuning range of the F-center laser. At North Carolina, we have recently constructed a new apparatus which makes use of a computerized laser-scanning procedure developed by Kasper et al.lN This has allowed us to obtain very complete and detailed spectra for systems such as ( C 0 J 2 and (HF),. At this point it is not clear just how large a system can be studied in this way. For example, some fine structure has been observed in the 3-pm spectrum of (C3H4)2 and even (C6H6)2131 and yet not in (C2H4),. Although infrared absorption has been used for some years in obtaining spectra of ultracold molecules in a jet, it is only very recently that several groups have been able to improve the sensitivity of this method to the point where it is useful for van der Waals spectroscopy. Hayman et al.45 have recently reported a rotationally resolved spectrum for rare gas-OCS clusters using (128) J. L. Himes and T. A. Wiggins, J . Mol. Spectrosc., 40,418 (1971). (129) L. Mannik, J. C. Stryland, and H. L. Welsh, Can. J . Phys., 49, 3056 (1971). (130) J. V. V. Kasper, C. R. Pollock, R. F. Curl, and F. K. Tittel, Appl. ODf.. 21. 236 (19821. ' (131) R. E:Miller and R. 0 . Watts, unpublished results.
.
Miller a diode laser in conjunction with a pulsed jet source. The resolution obtained by using this method is approximately 150 MHz, which is sufficient to resolve most features in the spectrum. As a result, the authors were able to determine an accurate set of rotational constants for both the ground and excited states. Using pulsed jet absorption, Nesbit and co-workers" have recently obtained somewhat higher resolution. A slit orifice was used in an effort to increase the laser path length in the jet. In this case, a difference frequency laser was used to obtain a spectrum for the v i mode of Ar-HF. Although Ar-HF undergoes a wide-amplitude bending motion, its spectrum is well-characterized by that of a linear molecule. In addition to observing the v, mode, they have also been able to detect transitions corresponding to the vl u2 mode of Ar-HF located 71 cm-' higher in frequency. To date, these results have only been reported in preliminary form. It is clear from all of these results, however, that high-resolution infrared spectroscopy, of both small- and medium-sized van der Waals molecules, is now capable of providing very detailed molecular constants. Before leaving the area of van der Waals spectroscopy, it should be noted that in some cases very useful information can be obtained from spectra that do not show well-resolved rotational fine structure. To begin with, consider our recent results on the H20 dimer.s3 Because of the strong hydrogen bond in this system, the transition frequencies in the dimer are substantially shifted from those in the monomer. This shift is obviously related to the intermolecular potential near the equilibrium geometry, suggesting that one might be able to use this information to probe the nature of the potential. Using a quantum random walk method developed by Anderson,132Coker et aLS3calculated the dimer spectrum using a total potential surface represented by the sum of fitted intramolecular and intermolecular potentials. These calculations were not only very useful in making a vibrational assignment but also showed that spectra of this type are very sensitive to the details of the intermolecular potential. Clearly, any system for which the vibrational frequencies are appreciably shifted upon dimer formation is amenable to this type of study. Another area in which useful spectroscopic information can be obtained from relatively low resolution spectroscopy is in largecluster spectroscopy. We have shown in several systems48-4g-54 that it is possible to observe the more or less continuous shift in transition frequency from the monomer to the solid. In the case of (N20):9 a somewhat simpler calculation than that used for (H20)2,based on the use of a fitted intermolecular plus intramolecular potential, was able to give satisfactory agreement with the experimental infrared spectrum. Although these theoretical methods are in their infancy and have not been exhaustively tested, they do point the way for future developments and clearly show that spectra of this type can be used to obtain information on the potential surface. Another promising new technique is matrix isolation studies using cluster beam techniques. Gough et aLSShave examined in detail the spectroscopy of SF6and CH3F trapped in a large argon cluster. Once again, it is possible to observe the shift in the transition frequencies from the monomer to the matrix value. These and other systems have also been studied recently by Janda and ~ o - w o r k e r s using ' ~ ~ a mass spectrometer. Although the latter experiment is limited to relatively small cluster sizes, it does have the advantage that some degree of size separation can be obtained with the mass spectrometer. Even more exciting are the recent results of Gough et al.55on the spectroscopy of SF6 adsorbed on the surface of large Ar clusters. These spectra show resolvable features which can be
+
(132) J. B. Anderson, J . Chem. Phys., 63, 1499 (1975). (133) F. G. Celii and K. C. Janda, to be submitted for publication. (134) J. C. Drobits, J. M. Skene, and M. I. Lesker, J. Chem. Phys., 84, 2896 (19861. (135) M: Snels, R. Fantoni, M. Zen, S. Stolte, and J. Reuss, Chem. Phys. Lett., 124, 1 (1986). (136) B. A . Wofford, J. W. Bevan, W. B. Olson, and W. J . Lafferty, Chem. Phys. Lett., 124, 579 (1986). (137) B. B. Brady, G. B. Spector, and G. W. Flynn, J . Phys. Chem., 90, 83 (1986).
J. Phys. Chem. 1986,90, 3313-3319 associated with both matrix-isolated sF6 and SF, adsorbed on the surface of the cluster. The results suggest that for small Ar clusters an adsorbed SF6 molecule causes reconstruction of the cluster leading to an SF6 molecule surround by Ar atoms. However, as the cluster size is increased, stable surface sites are observed. This method is very appealing in that it provides a way of carrying out surface spectroscopy on molecular crystals. The problems associated with characterizing the surface of the cluster, to which the molecule is adsorbed, still need to be addressed. Finally, a word of caution is in order. Although there are obviously several areas where low-resolution spectra can be used to obtain useful information, it is the author's opinion that little can be learned from rotational band contour fits to low-resolution spectra unless considerable (although not necessarily completely resolved) rotational structure is present. Since the structure and rotational temperature of these species are not well-known, it is our experience that a fit of this type is not unique. For the case of Ne-C2H4 and Ar-C2H4considerable inhomogeneous structure has been observed by Casassa et al.69 and Liu et ales4 In both cases, convincing rotational contour fits have been reported. As pointed out by Boom et al.,98the far-infrared spectrum of van der Waals molecule probes, in a very direct way, the details of the intermolecular potential surface. Unfortunately, these early studies were not conclusive enough to allow an assignment of the spectium to be made. As indicated previously, two groups have developed techniques for observing far-infared transitions in van der Waals molecules formed under free jet conditions and with
3313
much higher resolution. At Harvard, Klemperer and c o - ~ o r k e r s ~ ~ used a far-infrared laser and stark tuning in conjunction with a molecular beam electric resonance apparatus to observe transitions in Ar-HCl associated with the van der Waals vibration. The same transitions have also been observed by Saykally and co-workersIm at Berkeley using intracavity laser absorption spectroscopy. Since a van der Waals bond tends to be very anharmonic, there is hope that overtone transitions will also be amenable to study so that the shape of the intermolecular potential can be mapped out in detail.
Note Added in Proof. Baldwin and Watts (private communication) have recently observed fine structure in the 950-cm-I band of (C2H4)2 using a waveguide C 0 2 laser in conjunction with mass spectrometric and bolometric detection. Although these features have not been spectroscopically assigned, they do appear to place a lower limit of 10 ns on the lifetime of the dimer. How these results can be reconciled with the two laser saturation experiments is still unclear. With each new experiment, however, there seems to be more evidence for longer predissociation lifetimes, and therefore resolvable rotational structure, and less evidence for uniformly short predissociation lifetimes. Acknowledgment. The author thanks Professors G. Scoles, T. E. Gough, and W. R. Gentry for helpful comments on earlier versions of this manuscript.
SPECTROSCOPY AND STRUCTURE The Electronic and Geometric Structures of the Chromium Cations CrF', CrO', CrN', and CrC' James F. Harrison Department of Chemistry, Michigan State University, East Lansing, Michigan 48824-1 322 (Received: October 24, 1985; In Final Form: March 17, 1986)
The electronic and geometric structures of the title compounds have been studied by using MCSCF and CI techniques. In the following we note the term symbol of the predicted ground state, the calculated bond length (A), and De (kcal/mol): CrC+ (42-,1.74, 33); CrN' (%, 1.60,49); CrO' (411,1.63, 57); C r P (52+,1.76,73). The low-lying excited states of CrF' (511) and CrO' (42-)are estimated to be 14 and 6 kcal/mol, respectively, above the ground state of the molecule. The Mulliken population analysis suggests that the ligands all carry an excess negative charge ranging from 0.2 in CrC' to 0.7 in CrF+. While the bonding in CrN', CrO', and C r P involves various two-electron bonds between the Cr 3d orbitals and the ligand 2p orbitals, the bonding in CrC' involves a traditional double bond in the a system and a delocalized one-electron bond in the u system.
Introduction The experimental study of gas-phase, bimolecular reactions of transition-metal ions with organic and inorganic molecules is an active area of chemistry.' While the ion cyclotron resonance experiments of Foster and Beaucham$ pointed out the potential (1) Recent publications of the group currently active in this area include: (a) Mandich, M. L.; Halle, L. F.; Beauchamp, J. L. J. Am. Chem. Soc. 1984, 106,4403. (b) Peake, D. A.; Gross,M. L.; Ridge, D. P.J . Am. Chem. SOC. 1984,106,4307. (c) Jacobson, D. B.; Frieser, B. D. J. Am. Chem. Soc. 1984, 106, 4623. (d) Huang, S.K.;Allison, J. Organometallics 1983,2, 883. (e) Tolbert, N.; Beauchamp, J. L. J . Am. Chem. Soc. 1984, 106, 8117. (2) Foster, M. S.;Beauchamp, J. L. J . Am. Chem. SOC.1971, 93, 4924; 1975, 97, 4808; 1975, 97, 4814.
of such studies the more recent guided ion beam studies of Beauchamp, Armentrout, and co-workers3 are particularly noteworthy. The analysis of these experiments has resulted in accurate values for the bond energies3 of many species of the type M-R+ (M is a transition element and R is an atom or molecule) and is resulting in unprecedented insight into the gas-phase reaction mechanisms of transition-metal ions with various molecules. Unfortunately these experiments provide little structural (either (3) See for example: (a) Armentrout, P. B.; Beauchamp, J. L. J . Am. Chem. Soc. 1980,102, 1736. (b) Armentrout, P. B.; Halle, L. F.; Beauchamp, J. L. J . Chem. Phys. 1982, 76, 2449. (c) Armentrout, P. B.;Halle, L. F.; Beauchamp, J. L. J. Am. Chem. SOC.1981, 103, 6501.
0022-3654/86/2090-3313%01.50/0 0 1986 American Chemical Society
