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J. Phys. Chem. 1992, 96, 2938-2949
FEATURE ARTICLE Photofragment Translational Spectroscopy Michael N. R. Ashfold,* Ian R. Lambert, David H. Mordaunt, Gregory P. Morley, and Colin M. Western School of Chemistry, University of Bristol, Bristol BS8 ITS, U.K. (Received: October 28, 1991)
Some of the most detailed insight into the dynamics of molecular photofragmentation processes is provided by measurements of the translational energy distributions of the recoiling fragments. In this article we survey recent progress in the extraction of such fragment kinetic energy distributions from careful measurement and analysis of (a) their Doppler broadened spectral line shapes and/or (b) their time-of-flight spectra.
I. Introduction Continued advances in the availability and the capability of laser sources has resulted in the development of ever more sophisticated spectroscopic techniques. Among the more important of the recent advances in laser performance we would list improvements in their tunability, their irradiance (brightness), and their frequency and temporal resolution. Such developments have ensured a steady increase in both the rewards, and the challenges, available to those working in the field of molecular photodissociation dynamics. References 1-17 list a number of reviews which can lead the interested reader through many of these developments. Reasons for interest in this subject area are manifold, but one of the most important is surely the fact that careful studies of the way in which an isolated excited molecule fragments can, in turn, provide experimentalists and theoreticians with a clearer insight of the factors demanding consideration when attempting to describe the intimate details of a full bimolecular collision process. At the microscopic level any complete description of a bimolecular collision requires definition of (i) the internal quantum states of the reagents (defined in both the molecular and laboratory frame), (ii) their relative velocity and their distance of closest approach, and (iii) the corresponding quantities in the reaction products. For experimentalists at least, complete control of the reagent properties remains a distant (impossible?) goal. Hence (1) Zare, R. N.; Herschbach, D. R. Proc. IEEE 1963, 51, 173. (2) Wilson, K. R. In Excited State Chemistry; Pitts, J. N., Ed.; Gordon and Breach: New York, 1970. (3) Zare, R. N. Mol. Photochem. 1972, 4 , 1. (4) Simons,J. P. In Specialist Periodical Report: Gas Kinetics and Energy Transfer; Ashmore, P. G., Donovan, R. J., Eds.: Royal Society of Chemistry: London, 1977; Vol. 2, p 58. ( 5 ) Gelbart, W. M. Annu. Rev. Phys. Chem. 1977, 28, 323. (6) Leone, S. R. In Dynamics of the Excited State; Lawley, K. P., Ed.; Adv. Chem. Phys.; Wiley: New York, 1982; Vol. 50, p 255. (7) Simons, J. P. J . Phys. Chem. 1984, 88. 1287. (8) Simons, J. P. J . Phys. Chem. 1987, 91, 5378. (9) Houston, P. L. J . Phys. Chem. 1987, 91, 5388. (10) Bersohn, R. In Molecular Photodissociation Dynamics; Ashfold, M. N. R., Baggott, J . E., Eds.; Royal Society of Chemistry: London, 1987; p 1. (1 1) Wodtke, A. M.; Lee, Y. T. In Molecular Photodissociation Dynamics; Ashfold, M . N. R., Baggott, J . E., Eds.; Royal Society of Chemistry: London, 1987; p 31. (1 2) Andresen, P.; Schinke, R. In Molecular Photodissociation Dynamics; Ashfold, M. N. R., Baggott, J. E., Eds.; Royal Society of Chemistry: London, 1987; p 61. (13) Docker, M . P.; Hodgson, A,; Simons, J. P. In Molecular Photodissociation Dynamics; Ashfold, M . N . R., Baggott, J. E., Eds.; Royal Society of Chemistry: London, 1987; p 1 1 5 . (14) Schinke, R. Annu. Reu. Phys. Chem. 1988, 39, 39. (15) Hall, G. E.; Houston, P. L. Annu. Reu. Phys. Chem. 1989, 40, 375. (16) Houston, P. L. Acc. Chem. Res. 1989, 22, 309. (17) Dixon, R. N. Acc. Chem. Res. 1991, 24, 16.
0022-3654/92/2096-2938$03.00/0
the conceptual appeal of molecular photodissociations as examples of the so-called “half-collision” process in which products emerge from (what can be) a reasonably well defined “transition state” (the excited-state molecule prepared by the photoabsorption event). How well can we characterize this half-collision process? That is, what are the quantities amenable to experimental determination? In answering this question it may prove helpful to picture a molecular photofragmentation in terms of (i) preparation of the excited state by photon absorption and (ii) the subsequent evolution of these excited-state molecules to (iii) the final asymptotic products. Compared with the time scale for nuclear motions, the electronic excitation (i) may be viewed as an instantaneous process. Consequently our molecule is “born” in the excited state with a geometry identical with that it had in the initial (ground) state immediately prior to photoabsorption. This is merely a statement of the Franck-Condon principle. Thus in the case of a direct dissociation (i.e., a fragmentation process in which the prevailing forces immediately cause the excited molecules to begin distorting, irreversibly, along the dissociation coordinate) of expansion cooled molecules (Le., molecules with rotational angular momentum J 0) brought about as a result of a linearly polarized photoexcitation, the starting conditions (Le., the properties of the “transition state”) are pretty well defined. However, the majority of polyatomic molecules do not dissociate directly. They predissociate over an extended time scale. The dissociation coordinate for such a molecule is of course just one of its several vibrational degrees of freedom; rapid intramolecular vibrational redistribution (IVR) may mean that the nuclear motions prevailing in the excited molecule as it begins its ultimate fragmentation have evolved considerably from those operating immediately after photoexcitation. Spectroscopic studies of the parent molecule can provide some insight into these motions in cases where the excited-state predissociation occurs sufficiently slowly for the parent absorption spectrum to show resolved structure (i.e., on a time scale sufficiently long that uncertainty broadening does not wash out all of the spectral structure). More often, however, the combination of spectral congestion (due to the large number of rovibronic transitions contributing to the electronic spectrum of a polyatomic molecule) and spectral broadening (reflecting the short lifetime of the predissociating excited state) precludes a unique characterization of the starting transition state for the fragmentation process. Strategies for improving upon this rather unsatisfactory state of affairs include (i) seeding the molecule of interest in a supersonic expansion of rare gas atoms (thereby ensuring that all of the population is collapsed into a few low J rotational states) and (ii) using double resonance techniques to ensure selection of one rovibronic level (or a narrow range of rovibronic levels) in
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0 1992 American Chemical Society
Feature Article the intermediate state, and thus to impose some (at least in principle, user selectable) definition on the eventual J quantum number for the predissociating molecules. There have as yet been few direct measurements of molecules in the act of dissociating. This is hardly surprising given the time scales involved. Consider the simplest case of an electronically excited molecule dissociating via a simple bond rupture to two fragments. Irrespective of whether the fragmentation process is direct, or whether it occurs after a finite time during which there has been substantial nuclear motion (i.e., a predissociation), the actual time it takes for the fragmenting molecule to evolve sufficiently far along the dissociation coordinate (a few angstroms only) for the asymptotic products to be established is too brief for direct observation except when using the very shortest laser pulses. Zewail et al.183’9have used state-of-the-art femtosecond pumpprobe techniques to make a few such measurements, e.g., of the CN(X) product arising in the near-ultraviolet (UV) photodissociation of ICN. Kinsey, Imre, and have pioneered a complementary experimental strategy, now often referred to as resonance Raman emission spectroscopy, for viewing molecules in the act of dissociation. This type of spectrum (which may equally well be viewed as a wavelength-dispersed spectrum of the weak emission from molecules traversing the dissociation coordinate) may reveal vibrational modes active in the dissociation process, though detailed spectral interpretation will generally require a sound knowledge of the form of the potential energy surface(s) traversed by the dissociating molecules (including, particularly, any surface intersections in the channel leading to the asymptotic products), of the potential energy surface of the lower state reached by the Raman emission process, and of the way in which the transition moment connecting these states varies with nuclear geometry. Thus it remains the case that most of what we know about molecular photodissociation processes has come from experiments which probe the final products. Fortunately, it is possible to deduce much about the forces acting during the dissociation process from measurements of some of the fragment scalar (e.g., their internal and/or translational energy distributions) and vector properties. Included among the latter are the recoil anisotropy of the photofragments (Le., the distribution of the product velocity vectors v relative to Cph,,,, the electric vector of the linearly polarized photolysis laser radiation, and thus to p, the transition dipole moment in the parent m o l e c ~ l e ) ,their ~ ~ ~alignment * ~ ~ ~ ~(Le., ~ the distribution of the fragment J vectors relative to tpbt and thus p)?5 and, lastly, the mutual correlation between their v and J vectors (the so-called v-J correlation).262s These vector properties are now amenable to investigation through careful measurements of the Doppler broadened line shapes of individual rovibronic transitions in the excitation spectrum of the resulting fragments, and of the ways in which these lineshapes vary as a function of (i) the relative polarizations of the photolysis and fragment probing laser beams, (ii) the precise geometry of the excitation and detection scheme employed, and (iii) the particular branch being probed (Le., whether the excitation of the fragment involves a AJ = 0 or fl change in quantum number). The potential of such methods is well illustrated by the results shown in Figure 1, which displays (18) Rosker, M. J.; Dantus, M.; Zewail, A. H. J . Chem. Phys. 1988.89, 6113. Dantus, M.; Rosker, M. J.; Zewail, A. H. J . Chem. Phys. 1988, 89, 6128. (19) Khundkar, L. R.; Zewail, A. H. Annu. Reu. Phys. Chem. 1990, 41, 15.
(20) Imre, D.; Kinsey, J. L.; Sinha, A,; Krenos, J. J . Phys. Chem. 1984, 88, 3956.
(21) Johnson, B. R.; Kinsey, J. L. J . Chem. Phys. 1987,87, 1525. (22) Sension, R. J.; Brudzynski, R. J.; Hudson, B. S.; Zhang, J.; Imre, D. G. Chem. Phys. 1990, 141, 393. (23) Solomon, J. J . Chem. Phys. 1967, 47, 889. (24) Busch, G. E.; Wilson, K. R. J . Chem. Phys. 1972, 56, 3626, 3638. (25) Greene, C. H.; Zare, R. N. Annu. Reu. Phys. Chem. 1982,33, 119; J . Chem. Phys. 1983, 78, 6741. (26) Dixon, R. N. J . Chem. Phys. 1986.85, 1866. (27) Hall, G. E.; Sivakumar, N.; Houston, P. L.; Burak, I. Phys. Reu. Left. 1986,56, 1671. (28) Dubs, M.; Briihlmann, U.; Huber, J. R. J . Chem. Phys. 1986, 84, 3106.
The Journal of Physical Chemistry, Vol. 96, No. 7, 1992 2939 @MT
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Figure 1. Illustration of the potential of Doppler spectroscopy for revealing vector correlations in diatomic molecular photofragments. This figure shows the way in which the Doppler profiles of OH(X2113,2)u-oJv.14 fragments formed in the 248-nm photolysis of H202vary as a function of photolysis (kphot.tphot)-probe(kprok,tprok)laser beam geometry, and with the particular branch (AJ = 0 or *l) chosen for probing. This latter dependence (the variation in the line shape that arises simply due to whether we choose to probe on a P or Q transition) is especially striking. It reveals the correlation between the fragment recoil velocity v and rotation J vectors; the particular variations observed here can be understood if there is a preference for J to lie parallel to v. Reprinted with permission from ref 29. Copyright 1986 Royal Society of Chemistry.
Doppler line profiles for OH(X) fragments formed in the 211s,2, u” = 0, N” = 14 state following 248-nm photolysis of Hz02.29
Some of the various factors responsible for the wide variations among these observed line profiles are surveyed in the next section. Suffice to say at this stage that the analysis of these line shapes reveals that the OH(X) fragments are formed with a near-monoenergetic velocity distribution ((uOH) 4 X lo3 m d),that they prefer to recoil along directions perpendicular to epho, (and thus perpendicular to the transition dipole moment p in the parent H202molecule) and, lastly, from a comparison of the P and Q line profiles, that there is a preference for J to lie parallel to v (Le., for the nuclear framework to rotate in a plane perpendicular to v).13,29 The deduction that the OH(X) fragments are formed with a recoil energy approaching the maximum permitted by energy conservation, with little vibrational excitation and with “propeller”-like rotational motion, has been interpreted in terms of an essentially direct dissociation in which 0-0 bond rupture in the photoexcited state is accompanied, a t its outset, by simultaneous changes in the parent torsional angle. T h e torsional forces arise because the parent photoexcitation process involves promotion of an electron from one of the doubly occupied 0 atom lone pair orbitals (the occupancy of which are responsible for the skewed equilibrium geometry of ground state H2O2)to an orbital that is 0-0antibonding. As a result the potential energy surface
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(29) Docker, M . P.; Hodgson, A,; Simons, J. P. Faraday Discuss. Chem. SOC.1986, 82, 36.
2940 The Journal of Physical Chemistry, Vol. 96, No. 7, 1992 for the excited state reached in the photoexcitation has a minimum at (trans-) planar geometries. The resulting torque is responsible for the, at first sight surprising, observation of a positive (Le., v 11 J) correlation between v and J in the OH(X) products. Regrettably, the derivation of such detailed information in this manner is restricted to those relatively small number of systems that happen to yield a photofragment that is not only comparatively light (and therefore likely to be moving fast enough to show an appreciable Doppler shift) but also amenable to probing with a narrow-bandwidth tunable dye laser (e.g., dissociations yielding OH, NH, CN, NO, or CO fragments). Further, as we discuss in more detail below, the measured line shapes inevitably are a convolution of the true Doppler broadened absorption profile and contributions arising from the spread of parent molecule velocities and the finite resolution of the probing laser radiation. To derive the sought after product velocity distribution it is customary first to guess some plausible (model) distribution and to calculate its associated Doppler broadened line shape, then convolute in the two additional sources of line broadening indicated above, then include the effects of any recoil anisotropy and/or v,J correlations in the fragments, and then refine the initial guess until one obtains a reasonable match with the experimentally observed line contour. Not surprisingly, except in the somewhat trivial situation that the recoiling partner fragment is an atom or in cases (such as the near-UV photolysis of H202)where the molecular fragments are formed with a near-&function distribution of recoil velocities, it is sometimes difficult to be certain that any translational energy distribution deduced through these procedures is unique. In what follows we summarize some of the recent progress in the extraction of photofragment translational energy distributions from the analysis of Doppler broadened spectral line shapes. We then proceed to highlight some of the very impressive advances that have occurred recently in the measurement of high-resolution photofragment translational energy distributions via time-of-flight (TOF) methods. Given knowledge of this distribution for one state-selected photofragment (here labeled A, though this should not necessarily be taken to imply that the fragment is atomic) then, through energy and momentum conservation, we automatically know something about the (often unobserved) partner fragment (B) arising in the photodissociation of our prototypical molecule AB. This follows because Le., the photon energy plus any internal energy residing in the parent molecule of interest must be balanced by the sum of the dissociation energy of the fragmenting bond, the total recoil energy of the fragments, and their respective internal energies. 11. Developments in Doppler Spectroscopy The frequency, u, of light absorbed by an object moving with velocity u, relative to a probing light source will differ from that absorbed by the same object if stationary by an amount Y
= uo( 1 -
:)
where uo is the absorption frequency of the system at rest. Thus, if we wish to excite a transition in a molecule moving toward the laser, it will be necessary to tune the laser to a slightly lower frequency than if the same molecule was moving in the opposite direction. Clearly, therefore, if we have an ensemble of molecules (or photofragments for example) the spread of absorption frequencies they exhibit will be related to their velocity distribution. How well can we determine this relationship? The answer to some extent depends on the form of the velocity distribution. An ensemble of gas-phase molecules characterized by a Maxwellian speed distribution will give rise to a Gaussian line shape, the full width half-maximum (fwhm) of which scales with where T is the sample temperature. Another (mathematically simple, though perhaps improbable) limiting case we might envisage is that of a spatially isotropic, monoenergetic distribution of fragment velocities, u. As Figure 2 shows, the associated line shape would
Ashfold et al.
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Figure 2. Doppler profiles predicted for a photofragment recoiling with a single speed, v, but different degrees of spatial anisotropy characterized by, respectively, 0 = 2,0, and -1 (see eq 3). In this particular illustrative example, we assume an orthogonal photolysis-probe beam geometry (Le., kplobc perpendicular to kphot)and that the e vector of the photolysis beam
lies in the plane of propagation of the pump and probe laser beams. Under these circumstances,the products of a fragmentation characterized by an anisotropy parameter, (3, of +2 (consistent with a direct dissociation following excitation via a parallel transition) will preferentially fly toward or away from the probe laser, leading to the symmetrically split, forward-backward peaking Doppler profile shown. Conversely, a dissociation characterized by /3 = 0 will yield an isotropic spatial distribution of recoiling fragments (and a flat-topped Doppler profile), while the fragments from a dissociation with = -1 (Le., where v is at right angles to p (and thus cpb)) will tend to recoil in a plane perpendicular to kpmbc and thus give rise to a symmetrical Doppler profile peaked at the line center frequency. be very different with a sharp cutoff at frequencies u = yo( 1 f (v/c)) and uniform absorbance between these limits. However, the most general photodissociation process will give rise to two molecular fragments each with an arbitrary (though correlated) spread of recoil velocities which, quite possibly, will be spatially anisotropic. Here we begin to perceive some of the limitations of conventional Doppler spectroscopy. All the experimentalist can realistically hope to measure in a single experiment with a single probe laser is the onedimensional projection, along the laser propagation axis, of the full three-dimensional fragment velocity distribution. Clearly, given an isotropic distribution of recoiling fragments, their mean translational energy can be derived directly from the second moment (u;) of the distribution. More generally however, as in the H202example outlined previously, the fragments rising from a molecular photodissociation process will show an anisotropic distribution of fragment recoil velocities. Some knowledge of this recoil anisotropy will be essential for any sensible analysis of the observed Doppler line shapes. To appreciate the source of this anisotropy we need only recall that the probability of an electric dipole allowed excitation process is proportional to lr(rI2. Thus, though the original sample of parent molecules will in all probability be randomly aligned in space, the incident radiation will selectively interact with those molecules that happen to be oriented such that their transition dipole moment lies parallel to tphot: the photoexcited molecules will be aligned in the laboratory frame with a distribution of alignments proportional to cosz @,where @ is the angle between c1. and fphot. If these photoexcited molecules dissociate rapidly (Le., in a time that is short in comparison to their period of rotation) then this alignment must be reflected in an anisotropic distribution of recoiling fragments. The angular distribution function will have the general form (3)
where 6 is the anisotropy parameter. This parameter takes the limiting values of +2 in the case that the fragment recoil velocity vector v lies parallel to fi (Le., I ( x ) shows a cos2 x distribution) and -1 when v and p are perpendicular to one another (Le., Z(x)
Feature Article Qc sinZ x ) . j3 = 0 corresponds to an isotropic distribution of recoiling fragments. To see how recoil anisotropy affects the Doppler line shapes of fragments formed via molecular photodissociation brought about using a linearly polarized light source and monitored using a single probe laser, it is simplest to visualize the direct (Le., prompt) dissociation of a simple linear molecule. The transition dipole moment ~c for such a molecule must lie either along, or perpendicular to, its principal axis. Consider the example of a molecular dissociation that occurs as a result of a parallel transition in the parent molecule (i.e., a photoexcitation for which ~.rlies parallel to the linear molecule axis). The forces acting during a collinear fragmentation operate along the molecular axis. The resulting fragments must therefore be formed with their velocity vectors v directed along this axis. Given the proviso that the dissociation occurs promptly, Le., before the photoexcited molecule has time to make significant rotation in space, it then follows that v will be preferentially aligned with (phot. To detect this anisotropy it is customary to monitor the fragments using a probe laser beam that propagates along an axis either parallel or perpendicular to the electric vector of the photolysis laser radiation. Figure 2 illustrates one way of achieving the former situation. In this particular example we have chosen c hot to be parallel to kprobc, and the propagation axes of the photofysis and probe laser beams are arranged to be mutually perpendicular to one another. We continue to focus on the case of prompt dissociation following photoexcitation via a parallel transition. A moment’s reflection should suffice to convince the reader that, in the particular situation described, many more fragments will recoil toward or away from the probe laser beam rather than perpendicular to it; Le., the absorption line shape will be relatively more intense in the wings than near its center. Hence the split Doppler profile shown in the left-hand panel of Figure 2. In complete contrast, in the alternative case of a perpendicular photoexcitation, the same logic leads to the conclusion that the bulk of the fragments will be ejected along axes at right angles to c and thus at right angles to kprok. Such fragments will exhig!?zero Doppler shift with respect to the probe laser, and thus the line profile observed for fragments resulting from this kind of dissociation (prompt fragmentation following a perpendicular photoexcitation in the parent molecule), given the specified photolysis laser-probe laser configuration, will exhibit a peak at line center and only very weak absorption at its extremities (Figure 2, right-hand panel). Rotation of the photoexcited molecule, prior to the fragmentation event, will lead to a reduced anisotropy. In the limit that all anisotropy is lost, a “flat-topped” Doppler line shape of the form shown in the center panel of Figure 2 would result. Recoil anisotropy is not the only factor requiring consideration when attempting to derive fragment velocity distributions from their Doppler line shapes. It is also necessary to explore whether there is any correlation between the rotational and translational motion of the fragment since this, too, will affect the observed line shapes.2629 One form of v,J correlation-the correlation between their magnitudes-is obvious: Given that the total available energy over and above that required to cleave the breaking bond is a fixed quantity (eq 1) then, at least in the limiting case that the partner species recoiling from our molecular fragment of interest is an atom in a uniquely defined electronic state, simple energy conservation dictates that fragments formed with higher rotational angular momentum (and thus higher rotational energy) must possess less translational energy and thus exhibit a narrower Doppler line profile. However, there is also a more subtle v,J correlation, which depends on the relative directions of v and J. This reveals itself through the fact that the line shape observed for fragments formed in a particular J state, probed under otherwise identical conditions, will differ according to whether the probe transition involves a AJ = 0 or AJ = f l excitation. This correlation has been investigated in some detail by Dixonz6 and by Hall et al.z7 Here we content ourselves with a simple physical picture as to how a correlation between v and J can arise. Consider the fragmentation of a nonrotating bent triatomic molecule into an
The Journal of Physical Chemistry, Vol. 96, No. 7, 1992 2941
(J>M,
> -J)
J
(4 = o ) Figure 3. Illustration of the way in which the population of the fragment M J states varies as a function of Doppler shift in the case that v is constrained to be perpendicular to J. Fragments observed with maximum Doppler shift have v parallel to kprobcbut, since we have defined v to be perpendicular to J, can only have one value of M J (M,= 0) for the projection of J along this probe axis. In contrast, the J vector of a fragment recoiling perpendicular to kpk can point anywhere in the plane perpendicular to v and still satisfy our initial constraint; thus the full M J distribution (J 2 M, 2 -J, space quantized with respect to the probe axis) can contribute to the absorption of probe laser radiation at the transition line center.
atom and a diatomic product. All of the forces acting during such a fragmentation are restricted to lie in the plane of the molecule. Thus the fragments recoil with their v vectors in this plane, and the J vector of the rotating diatomic product will (in the absence of other, electronic, contributions to its total angular momentum) be perpendicular to this plane. Already it is evident that, at least in this simple case, v and J should be correlated. why does this correlation affect the line profile of any transitions used to probe the diatomic fragment? It affects the line profile because it influences the MJ distribution of the fragments (Le., their alignment); this affects the relative probability of any particular fragment interacting with the probe laser radiation. We can see this from the schematic illustration shown in Figure 3. Fragments recoiling directly toward or away from the probe laser radiation (i.e., those with maximum Doppler shift) have v parallel to kp,ok but, because of the dynamics of the particular dissociation highlighted here, have J perpendicular to v (and thus kprok)and thus can have only one value of MJ (MJ = 0) for the projection of J along the probe direction (kp+ here, for simplicity, is taken as equivalent to the lab fixed z-axis). In contrast, the J vectors for fragments moving perpendicular to the probe laser beam lie parallel to kprobc.In this case the projection of J onto kprokcan take all values ranging from J IMJ 2 -J. Thus we see that the fragment MJ distribution, and thus the probe transition probability (which depends on the magnitude of MJ2),varies with Doppler shift! Finally, we turn to the question of how this correlation will affect the Doppler line profiles observed when the fragment of interest is probed via a Q, or a P (or R) branch transition. This can be answered, qualitatively, as follows. Let us continue to focus on the particular case that v and J in the fragment are perpendicular to one another. We recognize that the principal difference between Q and P / R probe transitions is the fact that, in the former, the transition dipole prmglies parallel to J (in the classical, high J, limit) while for P/R transitions these vectors are perpendicular to one another. Recalling Figure 3, we see that since the electric vector of the probe radiation must be perpendicular to kprokthen, when probing via a Q branch transition, optimal alignment of ccfrag and tpmkwill occur for fragments recoiling with v parallel to kprobc, Le., for fragments contributing to the wings of the Doppler line shape. Thus Q branch transitions will appear with a central dip in their Doppler profile. Conversely, fragments recoiling perpendicular to kpmkwill show the greatest absorption cross section when they are probed via P or R branch transitions. Consequently, given v I J, P and R branch lines will show a maximum a t line center. For v 11 J the situation is reversed. We have already commented that it is this latter situation that prevails in the case of the OH(X) fragments arising in the near-UV photodissociation of HzOz;a comparison of the various P and Q branch line shapes displayed in Figure 1 should convince the reader that such is indeed the case.
2942 The Journal of Physical Chemistry, Vol. 96, No. 7, 1992
H2S + h v (193nm)
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SH Vibrational S t a t e Figure 4. Spectra of the low-frequency half of the Doppler profile of H atoms resulting from photolysis of H2S at 193.3 nm. Both spectra were recorded using counterpropagated pump (193.3 nm) and probe (121.6 nm) laser beams. Spectrum (a) was recorded using a comparatively low-resolution probe laser and zero-time delay between the two laser pulses; spectrum (b) was recorded with a higher resolution probe laser and a 210-ns time delay between the photolysis and probe laser pulses. The latter VADS line shape (b) reveals structure attributable to the various SH(X), product states (indicated), though the line shape is further complicated by the fine-structure splitting (Av = 0.366 cm-I) of the H Lyman-@ probe transition. The solid line in each case shows the result of a simulation of the line shape employing best-fit values for the fragment recoil anisotropy and the SH(X) product vibrational state population distribution. Reprinted with permission from ref 30. Copyright 1987, 1989 American Institute of Physics.
Ashfold et al. time delay is increased, and the experiment becomes sensitive only to that diminishing fraction of H photofragments whose recoil velocity vectors point into a narrow cone centered around the probe laser axis. Given knowledge of the line profile expected for a monoenergetic distribution of H fragments (nontrivial because of the fine structure of the Lyman-a transition), the observed line profiles, and their variation with time delay, can be modeled30 to yield values for the anisotropy parameter, j3,and the vibrational state population distribution in the SH(X) fragments that accord well with the results obtained by time-of-flight meas~rements~l-)~ of the fragments arising in this same photodissociation. The velocity distribution of molecular photofragments, namely OH(X) radicals arising from the near-UV photolysis of H20234and HON035have also been investigated with the VADS technique. Using narrow (- 100 MHz) bandwidth radiation derived from a pulse amplified cw dye laser Dixon and c o l l e a g ~ e shave ~ ~ *been ~~ able to measure the Doppler profiles of rovibrational state selected OH(X) fragments with sufficient resolution to enable estimation of the internal energy disposal in the (unobserved) partner OH(X) fragment arising in the H202dissociation and the NO(X) fragments resulting from HONO photolysis. The former study34 is particularly noteworthy in that it provides one of the very first measurements of the pair correlation between the rotational energies of the two partner fragments arising in the photodissociation of a neutral parent molecule. 111. Time-of-Flight Spectroscopy
We have already alluded to some of the limitations of Doppler spectroscopy. Paramount among these is its lack of generality. Many interesting and important molecular fragments are not amenable to probing by laser-induced fluorescence (LIF) or resonance-enhanced multiphoton ionization (REMPI), perhaps because they have no suitable optical transitions, or because the available transition gives rise to a spectrum that is impenetrably complex, or because the detailed transition probabilities (Franck-Condon factors, rotational line strengths) needed in order that we can turn observed line intensities into relative populations are not available. Thus, though lacking the same ultimate state specificity as Doppler spectroscopy, time-of-flight (TOF) spectroscopy, by virtue of its generality, provides an appealing alternative route to the determination of photofragment translational energy distributions. The principle of photodissociating a molecular beam containing the sample molecule of interest and measuring the distribution of times taken for one particular type of fragment to “fly” a well-defined distance to a detector, all in the absence of any collisions, was first demonstrated by Wilson and co-workers in the late 1 9 6 0 ~The ~ intervening two decades have witnessed many technological developments (e.g., in the tunability, the output pulse energies and the repetition rate of the laser photolysis sources, in vacuum technology, in mass spectrometry and in data-transfer rates). As a result, the current generation of photofragment translational spectroscopy experiments, most notably those performed in the group of Y. T. Lee” using an apparatus such as that illustrated in Figure 5 , show much improved efficiency and versatility, but the underlying principles of the experiment are nonetheless little changed. The photolysis laser pulse is arranged to intercept the molecular beam (at the point labeled 5 in Figure 5 ) and induce photodissociation. A small angular fraction of the resulting fragment distribution recoils through the acceptance apertures and traverses a well-determined path length L, prior to entering the ionizer region and electron bombardment and subsequent mass analysis using a quadrupole mass spectrometer. The length AL of the ionizer region is deliberately kept short, since
Thus we see that the careful measurement of Doppler line shapes has the potential to reveal a great deal of information-on the distribution of fragment recoil velocities, on their recoil anisotropy, and on the correlation between v and J in the recoiling fragments-but we also appreciate that the extraction of this information in an unambiguousmanner requires considerable care. The analysis becomes yet more problematic for dissociations yielding two (or more) relatively complex molecular fragments. Is absorption observed near the line center due to slow fragments recoiling along kpmkor to faster fragments recoiling perpendicular to the probe axis? Wittig and c o - w ~ r k e r have s ~ ~ pioneered one technique, velocity aligned Doppler spectroscopy (VADS), which goes some way to answering this question. The method employs counterpropagating photolysis and probe laser beams and depends on the introduction of progressively longer time delays between the photolysis event and the subsequent probe laser pulse. In this way the probing process progressively discriminates against those fragments whose velocity vectors do not point either parallel or antiparallel to bok. A representative set of results, obtained using this method, for the H atom products arising in the 193.3-nm photolysis of H2S are displayed in Figure 4. At zero time delay the probe laser maps out the characteristic split Doppler lineshape of the H atom Lyman-a ( n = 2 n = 1) transition but, even with the highest probe laser resolution then available, the contour shows insufficient ( 3 1 ) van Veen, G . N. A.; Mohamed, K. A.; Baller, T.;de Vries, A. E. detail to enable an unambiguous estimate of the fragment Chem. Phys. 1983, 7 4 , 261. translational energy distribution and thus, by energy conservation, (32) Xie, X.; Schnieder, L.; Wallmeier, H.; Boettner, R.; Welge, K. H.; of the internal energy disposal within the unobserved partner Ashfold, M. N . R. J . Chem. Phys. 1990.92, 1608. SH(X) fragments. However, more structure is revealed as the (33) Continetti, R. E.; Balko, B. A,: Lee, Y. T.Chem. Phys. Len. 1991,
-
-1x2. - - , 4nn.
(30) Xu, Z.; Koplitz, B.; Wittig, C. J . Chem. Phys. 1987, 87, 1062; 1989, 90, 2692.
(34) Dixon, R. N.; Nightingale, J.; Western, C. M.; Yang, X. Chem. Phys. Lett. 1988, 151, 328. (35) Dixon, R. N.; Rieley, H. Chem. Phys. 1989, 137, 307.
Feature Article
II
1
50
I
-C
H
2 4
/
+Co
Acrolein -C 2H3 + CHO 50 m \ \\
Figure 5. Illustration of one of the current generation of apparatuses for high-resolution photofragment translational spectroscopy. Key: (1) rotatable, C W molecular beam source, (2) heating wire, (3) background 'gobbler", (4) focusing lens for incident laser radiation, ( 5 ) molecular beam-laser beam interaction region, ( 6 ) liquid nitrogen cooled panels, ( 7 ) gate valve assembly for detector, (8) retractable slotted chopping wheel, (9 and 10) main- and source-chamber diffusion pumps, respectively, (1 1) Brink's type electron impact ionizer, (1 2) quadrupole mass filter, (1 3) magnetically suspended turbomolecular pump for ionization region, (14) exit ion optics, (15) ion target, (16) scintillator, (17) turbomolecular pumps for differential pumping of detector, (18) photomultiplier tube, and (19) liquid nitrogen reservoirs. Reprinted with permission from ref 11. Copyright 1987 Royal Society of Chemistry.
the velocity resolution, and thus the kinetic energy resolution, will be determined largely by the ratio A L / L . This ratio (ALIL = 0.014 for the apparatus shown in Figure 5 ) implies an achievable translational energy resolution AE/E of -2.8%, Le., -0.056 eV (-450 cm-l) for fragments recoiling with 2 eV kinetic energy. Photofragment translational energy spectra recorded in this way thus have the potential (after suitable lab to center-of-mass frame transformation) to reveal information about the vibrational, though not the detailed rotational, energy disposal within the recoiling fragments. The results displayed in Figures 6 and 7 serve to demonstrate some of the strengths (and limitations) of this form of photofragment translational spectroscopy. Let us concentrate first on some of the many, real, strengths of the technique. Mass spectroscopy is a very general detection method. This is illustrated by Figure 6, which shows the center of mass translational energy distributions of various of the products arising in the 193-nm photolysis of the small unsaturated aldehyde acrolein, H2C=CHCH0.36 This molecule has at least three exoergic fragmentation channels following photoexcitation at 193 nm:
and conventional photofragment translational spectroscopy with mass spectrometric detection reveals that all three occur with comparable e f f i ~ i e n c y .Note ~ ~ that in this type of experiment it will often be possible to monitor the translational energy (and angular) distributions of all of the fragments; energy and momentum conservation considerations will usually then be sufficient to enable identification of the dominant primary decomposition channels and any contributions from secondary fragmentation products. These results serve to emphasize the fact that many (36) Haas, E.-M.; Minton, T. K.; Felder, P.; Huber, J. R. J . Phys. Chem. 1991, 95, 5149.
'\\ 0
Acrolein H2CCH-C0
+H
0 0
10
20
30
40
5C
60
c.m translational energy (kcal/md) Figure 6. Center of mass translational energy distributions P(ET) of fragments resulting from the 193.3-nm photodissociation of acrolein: (a) channel leading to C2H4+ C O molecular fragments, (b) the C2H, H C O radical product channel, and (c) the H atom loss fragmentation pathway. Reprinted with permission from ref 36.
+
fragments not conveniently detected by optical spectroscopy (e.g., the C2H3 or HCO radicals arising in this photolysis) can be monitored by mass spectrometry just as easily as those which are. Implicit in this statement is the assumption that the lifetime of the fragment is long compared with the flight time to the ionization region. Given this proviso, the ionization (detection) efficiency for any particular product species generally will not be sensitively dependent upon the particular quantum state in which it is formed, so (as already indicated) this type of experiment has the potential to provide reliable estimates of the branching ratios into the various thermodynamically allowed product channels. This comment has particular significance when considering a fragment like HCO which is amenable to detection by LIF37238or by REMPI,39*40 in some, but by no means all, of the levels of its ground electronic state. It is also relevant when we turn to consider the TOF spectrum of the H atom products arising in the 193.3-nm photolysis of H2S (Figure 7). The earliest studies of this dissociation, involving LIF probing of the SH(X) fragments, succeeded in identifying these diatomic fragments only i n low rotational levels of their ground vibrational state.4I Yet the later H atom TOF meas~rements,~l-~~ (37) Rumbles, G.; Valentini, J. J.; Stone, B. M.; Lee, E. K. C. J . Phys. Chem. 1989, 93, 1303 and references therein. (38) Sappey, A. D.; Crosley, D. R. J. Chem. Phys. 1990, 93, 7601. (39) Tjossem, P. J. H.; Goodwin, P. M.; Cool, T. A. J . Chem. Phys. 1986, 84, 5334. (40) Tjossem, P. J. H.; Cool, T. A.; Webb, D. A,; Grant, E. R. J. Chem. Phys. 1988, 88, 617.
Ashfold et al.
2944 The Journal of Physical Chemistry, Vol. 96, No. 7, 1992
Figure 8. Schematic illustration of the technique of H Rydberg atom TOF spectroscopy. A skimmed molecular beam containing the precursor of interest (seeded in argon) is crossed by three laser beams: (1) to induce the photodissociation, (2) of wavelength 121.6 nm (formed by
-
frequency tripling the output of a conventional dye laser in krypton gas) to excite the n = 2 n = 1 Lyman-a transition in the nascent H atom photofragments, and (3) of a wavelength around 365 nm to excite these selected H(n=2) atoms to a high n Rydberg state. A small dc field is placed around the interaction region to extract unwanted H+ ions formed as a result of 1t 1 REMPI induced by photons from laser (2) only.
15 20 25 30 35 40
Flight Time, psec Figure 7. (a) T O F spectrum of H atom photofragments ( m / z = 1) resulting from 193.3-nm photolysis of H2S using 12 mJ pulse-’ unpolarized laser pulses. The thresholds for the various H + SH(X), product channels are indicated above. The solid line is the summed fit to the experimental data, with the various components shown as dashed lines. (b) As above, but using a laser output energy of 250 mJ pulse-’. The higher photon flux induces secondary photolysis of the nascent SH(X) photofragments; the thresholds for the various SH(X),,w H + S(3P) fragmentation pathways are indicated, as is the peak of the H S(’D) product channel. Reprinted with permission from ref 33. Copyright 1991 Elsevier.
-+
and the VADS studies30 mentioned earlier, both provide compelling evidence that a significant fraction (some 30%) of the SH(X) products are formed in vibrationally excited levels. This discrepancy may be understood once it is realized that the first excited A%+ state of SH (the excited state whose fluorescence is monitored when attempting to probe ground-state SH radical concentrations by LIF methods) has a fluorescence quantum yield that decreases (because of increased competition from the alternative, nonradiative process of predissociation) with increasing levels of vibrational and rotational excitation.42 One further attribute of conventional photofragment translational spectroscopic techniques merits reiteration a t this stage. Measurement of the recoil anisotropy, and thus (through eq 3) the derivation of some information about the symmetry and/or lifetime of the dissociating excited state of the parent molecule reached (in the above examples) by 193.3-nm photoexcitation, are possible in this type of experiment if the apparatus is designed so that the molecular beam source (or the entire detector assembly) is capable of being rotated about the axis defined by the photolysis laser beam. Properly normalized TOF measurements at a number of laboratory scattering angles, followed by the appropriate lab to center-of-mass frame transformation, will yield the angular distribution function and hence, by fitting, the B parameter. We now turn to review limitations of such TOF methods and t o consider possible ways in which they might be alleviated. The major, and obvious, limitation is the achievable resolution. Consider further the TOF spectrum of the H atoms arising in the 193.3-nm photodissociation of H2S. Conventional photofragment TOF spectroscopy resolves the vibrational structure of the partner SH(X211)fragment quite satisfactorily; the contours of the peaks associated with these different vibrational states indicate that the SH(X) fragments are not formed with massive amounts of rotational excitation, but the prevailing resolution prevents any
unambiguous determination of the spin-orbit branching ratio in these fragments, or the detailed energy disposal into the different rotational states. Welge and c o - ~ o r k e r s ~have ~ , ~demonstrated ~~’ one method for greatly improving both the resolution, and the signal to noise ratio, of such photofragment TOF spectra. The technique as presently constituted is limited to photolyses yielding H(D) atoms as one of the fragments of interest but, as we discuss below, this does not appear to be an inviolable restriction. The essence of the method is summarized in Figure 8. Briefly, a cold molecular beam of the hydride molecule of interest is photolyzed and the nascent H atoms are “tagged” at source, prior to their having escaped the interaction volume. -Tagging”, in the earlier variant of this t e c h n i q ~ e , ~ ~involved * ~ ” ~ two-photon two-color ionization resonance enhanced at the one photon energy by the n = 2 state. The Lyman-a radiation required for the initial n = 2 + n = 1 excitation was obtained by frequency tripling the output of an excimer pumped dye laser in krypton. One fortuitous but attractive property of the H atom is the fact that the n = 2 level lies at an energy that is three-quarters that of the ionization potential (IP). Thus the two-photon two-color ionization could be achieved using a single dye laser, since the subsequent absorption of one of the fundamental dye laser photons provides exactly the energy required for threshold ionization. The key feature to note here is that the translational and angular distributions of the nascent neutral H photofragments are monitored via the ion. No subsequent electron bombardment is necessary. Each laser shot provides a complete TOF spectrum, and the signal to noise is improved simply by collecting data for a larger number of laser shots. The resolution should be much better than in conventional photofragment translational spectroscopy because of the much improved definition of the flight distance L separating the interaction volume from the H+ ion detector. This expectation is borne out in p r a ~ t i c e . ~For ~ .example, ~ ~ ~ ~ the translational energy spectrum of the H atoms resulting from near-UV photodissociation of H2S recorded in this way reveals the spin-orbit structure of the partner SH(X211) fragment (A, = -377 cm-’) quite clearly;j2 cf. Figure 7. That the resolution is not better still is a consequence of space charge. The net effect of the two-photon two-color ionization process is to create a concentration of H+ (43) Krautwald, H. J.; Schnieder, L.; Welge, K. H.; Ashfold, M. N. R. Faraday Discuss. Chem. Soc. 1986,82, 99. (44) Biesner, J.; Schnieder, L.; Schmeer, J.; Ahlers, G.; Xie, X.; Welge, K. H.; Ashfold, M. N. R.; Dixon, R. N. J. Chem. Phys. 1988, 88, 3607. (45) Biesner, J.; Schnieder, L.; Ahlers, G.; Xie, X.;Welge, K. H.; Ashfold, M. N. R.; Dixon, R. N. J . Chem. Phys. 1989, 91, 2901.
(46) Schnieder, L.; Meier, W.; Welge, K. H.; Ashfold, M. N. R.; Western, (41) Hawkins, W. G.; Houston, P. L. J . Chem. Phys. 1980, 73,297; 1982, 76, 729. (42) Ubachs, W.; ter Meulen, J. J. J . Chem. Phys. 1990, 92, 2121 and references therein.
C. M. J . Chem. Phys. 1990, 92, 7027.
(47) Ashfold, M. N. R.; Dixon, R. N.; Irving, S. J.; Koeppe, H.-M.; Meier, W.; Nightingale, J. R.; Schnieder, L.; Welge, K. H. Philos. Trans. R. SOC. (London)A 1990, 332, 375.
The Journal of Physical Chemistry, Vol. 96, No. 7, 1992 2945
Feature Article
fragment translational spectroscopy technique is strikingly selfevident. To be successful this method requires that the lifetimes of these high n Rydberg states of atomic H be long in comparison with the flight time. Were this not the case we might expect the slowest H atoms to escape detection by virtue of the fact that they had decayed, radiatively, to levels too far in energy below the IP for the eventual field ionization to be effective. Even in the field free case the lifetimes of these states of the H atom with high n (but low r) quantum number are in the submillisecond range (for a given I the radiative decay rate scales as l/n3). However, here it is important to note one aspect of the experimental method. The Lyman-a radiation in these experiments is generated by frequency tripling, in krypton, as before. The fundamental dye laser radiation is not separated out, but passes into the interaction region where it will inevitably cause some (now unwanted) ionization, as in the earlier variant of the experiment. A pair of biased electrodes are positioned around the interaction region to extract these H+ ions and ensure that they do not contribute to the measured Rydberg atom signal. The presence of this static electric field (a few tens of volts per centimeter only) offers an additional, and crucial, benefit. 1 ceases to be a good quantum number, and the lifetimes of the H atom Rydberg levels accessed in the presence of the field (states which, in the absence of n mixing, may be characterized by n, m,and a swalled parabolic quantum number) can be deduceds&52to be at least 1 order of magnitude longer even than the 1 = 0 and/or 2 states that would have been populated by a two-photon excitation from the 1s state in the absence of the field. Though still in its infancy, this new technique has already shown itself to be a powerful tool for those interested in studies of molecular photodissociation dynamics. We conclude this section by highlighting three recent examples which serve to illustrate the potential of the method. H2S (D2S) Photodissociation at 121.6 nm. Until very recently there was little quantitative information about the primary photochemical processes operating when HIS was excited at shorter wavelengths, i.e., in the vacuum-ultraviolet (vacuum-UV) spectral region. There are no less than seven exoergic decomposition channels available following H2S photoexcitation at 121.6 nm:
-
( b ) simulation
tl \
O J- l
I I
-I
QL I
I
I
I
I
I
internal energy/eV
Figure 9. (a) Internal energy spectrum of SH(X),,,, fragments resulting from HIS photolysis at 193.3 nm together with (b) a best-fit simulation of this spectrum. The greatly improved resolution achievable using the technique of H Rydberg atom TOF spectroscopy is illustrated by comparing the detail apparent in this spectrum with the first (most intense) peak in the TOF spectrum shown in Figure 7a. The various rotational levels of the two spin-orbit components of the SH(X),., fragments are indicated above the experimental spectrum. Reprinted with permission from ref 49. Copyright Royal Society of Chemistry.
ions in a localized volume at a well-defined instant in time. Coulomb repulsion cannot be eliminated in these experiments. It can only be minimized, e.g., by working at reduced laser powers so as to limit the number of ions formed per shot, with the inevitable consequence that data accumulation times have to be increased. This limitation has been circumvented in a more recent variant of the techniquewherein the nascent H atom photofragments are now excited (again via a two-color two-photon absorption process) to a Rydberg state with high principal quantum number (e.g., n = 90) rather than to the ion. The obvious advantage offered by this change in strategy is that the H fragments fly as neutral particles and are only ionized (by a gentle field ionization) after separation by TOF and immediately prior to detection. Space charge effects are obviated and substantially higher resolution results. This is illustrated clearly in Figure 9, which shows a portion of the translational energy spectrum of the H photofragments arising in the 193.3-nm photolysis of H2S.49 The achieved translational energy resolution AEIE,, in this example is -0.3%. Note that the horizontal scale of this spectrum is actually the internal energy of the SH(X) partner, Le., recalling eq 1, where E,,,,, is the total fragment translational energy (i.e,, the measured H atom translational energy scaled by a factor of 34/33 to allow for the momentum conserving translational energy of the SH partner). The important point to recognize is that this richly structured spectrum, which shows well-resolved features associated with not just the two spin-orbit components but also with various of the rotational levels of the vibrationless SH(X) fragments formed in this dissociation, corresponds to just the fastest, most intense peak in the TOF spectrum obtained by conventional photofragment translational spectroscopy (Figure 7). The improvement in resolution offered by the H Rydberg atom photo(48) Segall, J.; Wen, Y.; Lavi, R.; Singer, R.; Wittig, C. J . Phys. Chem. 1991, 95, 8078.
(49) Ashfold, M. N. R.; Schnieder. L.; Welge, K. H. Faraday Discuss. Chem. SOC.1991, 91, 128.
-
H2S
H
+ SH(X211)
E,,,,, I6.29 eV
(sa)
H
+ SH(AZZ+)
E,,,,, I 2.47 eV
(5b)
+ H + S(3P) H + H + S(lD)
E,,,,, I2.58 eV
(5c)
E,,,,, = 1.43 eV
(5d)
+ S(3P)
E,,,,, 5 7.06 eV
(5e)
H2 + S(lD)
E,,,,, I5.91 eV
(5f)
H
H2
+
H2 + S('S) E,,,,, I4.31 eV (5g) but, prior to the study of Schnieder et al.,46 there were no measurements of the relative quantum yields of any of the channels 5a-5g, let alone detailed measurements of the product energy disposal. One contributory reason for this paucity of data was mentioned earlier in this article, viz., the predissociated nature of the A2Z+ state of SH.42 The consequent low fluorescence quantum yield not only hinders studies of the excited product channel 5b, but also restricts the use of LIF on the A-X transition as a means of probing for the formation of ground-state SH fragments. Figure 10 shows a TOF spectrum of the H atom photoproducts, monitored via the Rydberg atom technique, resulting from 121.6-nm photolysis of H2S.46 Figure 11 displays the associated (50) Hiskes, J. R.; Tarter, C. B.; Moody, D. A. Phys. Rev. 1964,133,424. (51) Schnieder, L.; Seekamp-Rahn, K.; Liedeker, F.; Steuwe, H.; Welge, K. H . Faraday Discuss. Chem. SOC.1991, 91, 259. (52) Mordaunt. D. H. BSc. Thesis, University of Bristol, 1991.
2946 The Jouinal of Physical Chemistry, Vol. 96, No. 7, 1992
Ashfold et al.
+
I
t
20
-
'
50
40
30
Ips1
-lme
Cligh:
50
Figwe 10. H Rydberg atom T O F spectrum resulting from photolysis of jet-cooled H2S at 121.6 nm. The inset displays the early time part of this TOF spectrum on an expanded horizontal scale. Reprinted with permission from ref 46. Copyright 1990 American Institute of Physics.
-
0 N (v=O)
20
30 ~
'1'1
I
o
4 600-
o-
o 1 8000
v
I
H
+
+ H:
I
10000
with the (observed) asymptotic products H SH(A). Given the foregoing assumptions, ground-state SH(SD) fragments could only arise from those dissociating molecules that experience such large angle bending forces that they pass through linearity prior to substantial elongation of the breaking S-H(D) bond, since only at near linear configurations are the nonadiabatic couplings to lower potential energy surfaces (which correlate with the ground-state products) effective. It has been argued46that the centrifugal force associated with such dramatic angular distortion in the excited molecules causes direct three-body dissociation (into dissociation products (5d)) before such molecules reach near-linear configurations. The observed H atom TOF spectrum (Figure lo), and the corresponding fragment translational energy spectrum (Figure 1l ) , are further complicated by H atom products arising from the predissociation of the nascent SH(A) fragments.46 The contrast between this photofragmentation behavior and that observed4: following excitation of the H 2 0 molecule to its corresponding BIA, state is striking. This latter photodissociation was the subject of one of the first demonstrations of the technique of H atom photofragment translational spectroscopy. Ground-state OH(X) fragments carrying little vibrational but massive rotational excitation were shown to-be the dominant prod~ct.4~ The potential energy surface for the BIAl excited state of water shows all the same qualitative features as that for the B state of H2S but, because the H 2 0molecule has a less bent equiliblium configuration, m a t of the H 2 0molecules prepared on the B state surface have the opportunity to bend through the linear configuration prior to dissociating, switch to the lower energy A or X state surfaces and ultimately dissociate to ground state H OH(X) fragments. 3,43 HCN (DCN)Photodissociation at 121.6 nm. High-resolution photofragment translational spectroscopy proved especially valuable in the previous example because the fluorescence from the principal molecular fragment of interest is so weak. In the case of the H 2 0 di~sociation,~~ and in confirming the absence of significant ground state SH(X) fragments in the 121.6-nm photolysis of H2S, it was valuable also because the ground-state products were not amenable to study by laser-induced fluorescence. Neither of these problems applies to this next photofragmentation process, since ground-state CN(X) fragments can easily be detected by LIF, and neither the excited A211nor B22+ states of C N (both of which are energetically allowed products from the 121.6-nm photolysis of HCN) are p r e d i d a t e d . Yet the most recent studies of this dissociation process, carried out in our own laboratory using the H Rydberg atom technique, show that the previous literature contained no reliable estimate of the relative branching into these three electronic states of the C N product. Certainly, spontaneous fluorescence from CN(B) photofragments arising in the collision-free photodissociation of H C N molecules at 121.6 nm or nearby excitation wavelengths has been r e p ~ r t e d , but ~ ~ ,the ~~ quantum yield for this process is very West and Berrys9 reported lasing on the CN(A+X) transition following H C N photolysis at somewhat longer wavelengths, but synchrotron s t ~ d i e s led ~ ~ to v ~an~estimate that the quantum yield for forming CN(A) fragments from H C N photolysis at 121.6 nm was only 10-15%. Thus, by inference, it had been assumed that groundstate CN(X) fragments were the major molecular product. The reality may be deduceds3 from the spectra displayed in Figure 12. These show, unequivocally, that 121.6-nm photolysis of HCN and DCN leads to almat exclusive formation of H + CN(A) state fragments, primarily in their u ' = 0 vibrational level. That the earlier synchrotron experiments so underestimated the cross section for forming this product is surely due to the difficulties associated with detecting the CN(A+X) fluorescence which occurs predominantly in the near-infrared region.
"
I
I
12000
14000
I
16000 Total kinetic energy / cm-
"
1
"
'
I
20000
18000
+
+
Figure 11. Spectra of the total kinetic energy of the H S H (D SD) fragments resulting from photolysis of (a) H2S and (b) D2S at 121.6 nm. The energies coi responding to the various rovibrational levels of SH(SD) fragments in their A2Z+electronic state are indicated above the relevant spectra.
+
spectrum of the total translational energy of the H SH fragments and also the corresponding spectrum for the D SD p r o d " arising in the dissociation of D2S at the same excitation wa~e!eagth.~~ Analysis of these spectra clearly shows that, of those fragmeatation channels that yield H(D) atoms, channels 5b and 5d are dominant. The nascent A22+ state SH(SD) fragments are sem to be formed in a number of vibrational levels; however, the majority are formed in their u = 0 level with a rotational state populetion distribution that spans all possible bound and quasibound rotational level^.^^^^^ These findings, and the notable absence of any significant yield of the ground-state products (channel sa) have been rationalized& by assuming the following: (i) Photoexcitation at this wavelength prepares the H,S(D2S) molecules on the first excited ]Al potential energy surface, either directly or via one or more of the predissociated Rydberg states which are apparent in this region of the respective absorption spectra. (ii) The calculated topology of the potential energy surface for this BIA, state of H2SS4is at least qualitatively correct. (iii) The primary fragmentation processes occur on this diabatic surface which, along the RH-SH dissociation coordinate, correlates
+
(53) Morley, G. P.; Lambert, I . R.; Ashfold, M. N. R.;Rosser, K. N.; Western, C. M., to be published. (54) Flouquet, F. Chem. Phys. 1976, 13, 257.
( 5 5 ) Mele, A.; Okabe, H. J . Chem. Phys. 1969, 51,4798. (56) Ashfold, M. N. R.; Macpherson, M. T.; Simons, J. P. Chem. Phys. Lett. 1978, 55, 84. (57) West, G. A. Ph.D. Thesis, University of Madison, Wisconsin, 1975. (58) Lee, L. C. J . Chem. Phys. 1980, 72, 6414. (59) West, G. A.; Berry, M. J. J . Chem. Phys. 1974, 61, 4700.
The Journal of Physical Chemistry, Vol. 96, No. 7, 1992 2947
Feature Article CN A Z l l V'
150-
DCN uarent
;500-
150 . I
-
.
HCN parent
c)
c
$
A
v'
-
100-
r-T"
0
i
CN B ' f
M
A
l l
A
500 , 0
I
'
I " '
10000
5000
I " " I " " I " " I ~ ' " I
150W PMXK) 25OW CN internal energy / em-'
JOOW
35000
Figure 12. Internal energy spectrum of the C N fragments resulting from photolysis of (a) DCN and (b) H C N at 121.6 nm. Thresholds associated with the various vibrational levels of the electronically excited A211and B22+states of C N are indicated.
NH, Photodissociation at 216.38 nm. Our final example highlights the case of NH3 photodissociation following-photoexcitation into the zero-point level of ip fir$ excited (A) singlet electronic state. Earlier studies of the A X absorption spectrum of both NH3 and ND, had led to the realization that this excited level was predissociated; fragmentation to the ground-state products
-
NH3
-
H
+ NH2(%)
E,,,,, I1.08 eV
represents the only thermodynamically allowed primary decomposition pathway capable of yielding an H p_hoiofragmentat this excitation wavelength. LIF on the NH2(A-X) transition is a recognized method for detecting ground state N H 2 fragments. Indeed, an earlier study of NH, photodissociation at a somewhat shorter excitation wavelength (193.3 nm)60 had succeeded in detecting the nascent NH2(X) fragments by LIF. Unfortunately the spectrum_ so, obtained bore very little relation to the welldocumented A-X-absorption spectrum of a thermally equilibrated sample of NH2(X) fragments and was of sufficient complexity to defy analysis. The explanation for this complexity became apparent once this photolysis was investigated using the technique of H atom photofragment translational ~pectroscopy."*~~~~' Figure 13 shows a spectrum of the N H 2 internal energy obtained using the H Rydberg atom technique. Analysis of the well-resolved rotational structure evident in this spectrum reveals that the majority of the NH2(X) fragments formed in this dissociation are formed vibrationally unexcited, but with high levels of rotational angular momentum specifically distributed about their a-inertial axis.44~45~47 The source of this rotational angular momentum can be traced to the effects of a conical int_ersection, between the potential energy surfaces for the A and X states of NH3, in the dissociation channel leading to loss of one H atom.61 Its effect is to massively amplify any out of plane bending motion in t_he photodissociating parent molecule. In the case of NH3(A) molecules prepared (as here) jet-cooled and in their vibrational origin level, the initial out-of-plane motion of interest is simply the vi zero-point vibrational motion. NH, photo_excitation at shorter wavelengths results in the population of A state levels with progressively higher levels of v i (the "umbrella" bending vibration); this larger amplitude outof-plane parent motion carries through as an inverted population distribution amongst the energetically allowed N" Ka" roiational levels of the NH2 product.45 Electronically excited NH,(A) photofragments are identified among the products as soon as the energy provided by the photolysis photon is sufficient for this dissociation channel to become energetically allowed. The deduced quantum yield for forming NH2(A) fragments in the 193.3-nm
-
%HIinternal energy 1 e\' Figure 13. Internal energy spectra of the N H 2 fragments resulting_from NH, photolysis at 216.38 nm,within the origin band of the NH,(A-%) transition, with the detector set so as to detect H atoms recoiling (a) parallel and (b) perpendic$ar to cphol The dominant progression of peaks may be assigned to NH2(X) fragments in their ground vibrational state and with N" = K/, Le., with essentially all of their rotational angular momentum about the a-inertial axis. Reprinted with permission from ref 47. Copyright 1990 Royal Society.
photodissociation of NH3 (-26 f 4?h47is an order of magnitude larger than that estimated from-earlier studies of the spontaneous fluorescence from these NH2(A) fragmentsS6O This, too, is undentandaye given the difficulties of detecting the near-infrared NH,(A-X) emission with conventional photomultipliers.
IV. A Prospective View The technological and conceptual developments summarized in this article mean that photochemists have the opportunity, as never before, to ask very detailed questions about the dissociation dynamics of a very wide range of molecular species. We end by making some predictions, and suggestions, as to likely future directions for activity in this field of research. The first prediction is simple and made with the utmost confidence. It is that the methods described above will be applied to many more molecular photofragmentation processes, and will reveal a wealth of detailed insight into the way isolated molecules redistribute energy and ultimately fragment. With equal confidence, however, we can be sure that technology will not stand still, so it is worth considering likely improvements in experimental technique. It will be surprising if the VADS technique does not find further use as a means of probing the velocity distribution of molecular fragments. A very recent application of this technique to studies of the dynamics of H2 elimination in the 193.3-nm photodissociation of ethene (C2H4),6' which employed a pulse-amplified ring dye laser and subsequent four-wave mixing to generate the necessary narrow-bandwidth vacuum-W radiation, serves to illustrate the likely potential of such experiments. However, as we have already seen, the principal benefit of the VADS technique (as compared with conventional Doppler spectroscopy) is that it has the potential to provide a clearer image of the fragment velocity distribution along the probe (z) direction. One ingenious alternative development which, in principle at least, should allow determination of a conditional product velocity distribution in two, or even three, dimensions has been proposed by Shafer and B e r ~ o h n . Their ~ ~ proposed technique relies on the use of two probe lasers. To see how it would work, first consider
~
(60) Donnelly, V. M.; Baronavski, A. P.; McDonald, J. R. Chem. Phys. 1979, 43, 27 1. (61) McCarthy, M. I.; Rosmus, P.; Werner, H.-J.; Botschwina, P.; Vaida, V. J. Chem. Phys. 1987,86, 6693.
(62) Stolow, A.; Balko, B. A.; Cromwell, E. F.; Zhang, J.; Lee, Y . T. J . Phoiochem. Photobiol., A: Chem. 1992, 62, 285. (63) Shafer, N.; Bersohn, R. J . Chem. Phys. 1991, 94, 4817.
2948 The Journal of Physical Chemistry, Vol. 96, No. 7, 1992
f
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Figure 14. Simulation of (a) 1-D, (b) 2-D, and (c) 3-D LIF excitation line shapes for H atoms resulting from photodissociation of a jet-cooled sample of H20molecules at 157 nm. In these model calculations it is assumed that excitation to the n = 2 state is brought about using a laser of bandwidth corresponding to uu/c = 2 X lo”, and that the bandwidth of the laser used for the subsequent n = 4 n = 2 excitation corresponds to a frequency u,/c = 8 X 10”. For the ultimate 3-D experiment (c) it is assumed that the fluorescence from the n = 4 level is viewed through an interferometer with transmission bandwidth u,/c = 8 X lod. Reprinted with permission from ref 63. Copyright 1991 American Institute of Physics.
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a standard “pump-probe” experimental arrangement involving two laser beams propagating along mutually orthogonal axes (x and y, respectively) with the resulting fragment LIF viewed along z. Following Shafer and Bersohn we consider the specific example of H 2 0 photodissociation a t 157 nm, which yields an H atom together with ground-state OH(X) fragments.I2@ Scanning the frequency of the probe laser (which is assumed to have a bandwidth far narrower than the Doppler width of the 2p 1s Lyman-a transition of atomic H) at minimal time delay would result in a “normal” Doppler line shape (similar to the upper line profile in Figure 4). However, if this probe laser (probe laser 1) is tuned to the line center of the Lyman-a transition (so that it excites only those H atom products with zero velocity component along the y-axis) and we now introduce a second narrow-bandwidth probe laser beam (probe laser 2) which propagates antiparallel to the photolysis laser beam (i.e., along x) and is tuned so as to excite these H atoms from the 2p level to, say, the 4d state, then the line shape obtained by monitoring the emission from this 4d state while scanning the frequency of the second probe laser provides a measure of the velocity distribution along x of H photofragments formed with uu = 0, i.e., a two-dimensional velocity distribution. Finally, as these authors point out, if it proved possible to wavelength resolve the fluorescence from the 4d level reached via this two-photon double-resonant excitation process (using an interferometer perhaps) then the wavelength resolved line shape obtained following fixed frequency excitation with probe lasers 1 and 2 (both set to their respective lime centers for example) would +
Ashfold et al. provide one view of the full threedimensional velocity distribution. Figure 14 provides illustrations of the increasingly detailed line profiles that could be obtained (a) simply by monitoring resonance fluorescence from the H(2p) level while scanning the frequency of probe laser 1, (b) by monitoring emission from the 4d level as a function of the excitation frequency of probe laser 1 while probe laser 2 was fixed to excite the line center of the 4d 2p transition, and (c) as in (b) but now with the restriction that we only view the line center part of one emission line from the 4d level. What developments can we anticipate in the area of photofragment TOF measurements? Here, as always, we come up against the conflicting aims of trying to further improve the time resolution without losing signal intensity. This is the principal advance offered by the form of H atom photofragment translational spectroscopy pioneered by Welge and c o - w o r k e r ~ It .~~~~ is reasonable to assume that before too long the same idea of tagging the fragment of interest at source, prior to their recoiling from the interaction volume will be applied to other light photofragments (0atoms perhaps, or H2 molecular photofragments). Indeed, a similar principle is already employed in the photofragment imaging technique pioneered by Chandler and colleagues.65”8 A recent reinvestigation of the 266-nm photodissociation of a jet-cooled sample of CDJ molecules67 serves to illustrate the potential of this technique. In these experiments the nascent CD3(X) photofragments are ionized a t source, selectively and with quantum state specificity, by 2+1 REMPI. A pulsed dc extraction field is then applied after a brief (user selectable) time delay. This causes the full 3-D distribution of recoiling ions to be accelerated into a TOF mass spectrometer a t the end of which they impinge on a microchannel plate/ phosphor screen detector; the resulting phosphorescence is viewed with an electronic camera. What is observed, therefore, is a 2-D projection of the full 3-D velocity distribution of the ionized CD3 photofragments. Chandler et al.67 have demonstrated how the true photofragment velocity distributions can be extracted from these raw images using an inverse Abel transform. Thus they were able to further investigate, in a very direct manner, the branching into the two different spin-orbit states of the ground-state I(2PJ) atomic partner in this dissociation process, and the way that this branching ratio varied with the level of vibrational excitation within the CD3 fragment. Further applications and developments of these methods can also be anticipated with some confidence! Paralleling these developments in experimentation we can also anticipate continued advances in the field of a b initio quantum chemistry, the results of which will be crucial to the rationalization of many of the experimental observations. Recent papers by Schinke and c o - w o r k e r ~ ~provide ~ , ’ ~ illustrations of the current “state-of-the-art” in computational studies of molecular photodissociation dynamics. The aim of these studies was to provide a coherent explanation for (i) the observed form of the longwavelength absorption band of H2Sand D2S, both of which are essentially continuous but show some diffuse “vibronic” structure, (ii) the observed internal energy disposal in the ground-state SH(SD) photofragments (Le., the experimental results reported in refs 30-33), and (iii) the form of the resonance Raman emission spectrum reported”,72 for these dissociating H2Smolecules. To this end, Schinke et al. first carried out a large-scale ab initio electronic structure calculation of the form of the multidimensional potential energy surface for both of the singlet excited states that
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(65) Chandler, D. W.; Houston, P. L. J . Chem. Phys. 1987, 87, 1445. (66) Chandler, D. W.; Thoman Jr., J. M.; Janssen, M. H. M.; Parker, D. H. Chem. Phys. Lett. 1989, 156, 151. (67) Chandler, D. W.; Janssen, M. H. M.; Stolte, S.;Strickland, R. N.; Thoman Jr., J. W.; Parker, D. H. J . Phys. Chem. 1990, 94, 4839. (68) Janssen, M. H. M.; Parker, D. H.; Sitz, G. 0.;Stolte, S.;Chandler, D.W . J . Phys. Chem. 1991, 95, 8007. (69) Weide, K.; Staemmler, V.; Schinke, R. J . Chem. Phys. 1990, 93, 861. (70) Schinke, R.; Weide, K.; Heumann, B.; Engel, V. Faraday Discuss. Chem. SOC.1991, 91, 31. ( 7 1 ) Brudzynski, R. J.; Sension, R. J.; Hudson, B. S.Chem. Phys. Lert. 1990, 165, 487.
(64) Andresen, P.; Ondrey, G. S.; Titze, 8.;Rothe, E. J . Chem. Phys. IW, 80, 2548.
(72) Person, M . D.; Lao, K. Q.;Eckholm, B. J.; Butler, L. J. J . Chem.
Phys. 1989, 91, 812.
J . Phys. Chem. 1992, 96, 2949-2952
lie in the energy range of interest. They then investigated the nuclear motion of an H2S molecule photoexcited to these two strongly coupled states by following the time evolution of a two-dimensional wavepacket launched, from the ground-state geometry, on each of these two excited-state surfaces. While not yet at the stage of being able to provide an accurate replication of every aspect of the experimental results, these ~ t u d i e s ~do ~-’~ provide a chastening indication of the level of theory required to properly describe the dissociation even of one of the simplest of polyatomic molecules.
Acknowledgment. M.N.R.A. is enormously grateful to Professor K. H.Welge and his colleagues at Universitat Bielefeld,
2949
most notably Drs. L. Schnieder, H. J. Krautwald, and J. Biesner, for allowing and encouraging his participation in the early attempts a t H atom photofragment translational spectroscopy and in generously providing much helpful advice when we came to set up a similar experiment in Bristol. These collaborations were supported by NATO, grant no. 85/0015. All of the authors are very grateful to Mr. K. N. Rosser, for his crucial help in getting the Bristol version of this experiment up and running. We are also indebted to the Science and Engineering Research Council for equipment funding, for a postdoctoral research assistantship (I.R.L.) and for research studentships (D.H.M. and G.P.M.). C.M.W. is grateful to the Royal Society for the award of a 1983 University Research Fellowship.
ARTICLES Electron Rearrangement and Energy Relaxation Due to a Core Hole Creation in Molecules Yongfeng Zhang,* Yaoqi Zhou, Applied Physics and Chemistry Laboratory, 4066 E Mission Boulevard, Pomona, California 91 766
Zi-ping Luo, Department of Chemistry, California State Polytechnic University, Pomona, California 91 768-4032
and David M. Hanson Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York 1 1 794-3400 (Received: May 21, 1991; In Final Form: November 15, 1991)
A theoretical calculation has been utilized to study core-ionization and core-excitation states for NzO, NOz, CO, HCN, HzO, and O3on the SCF level. The calculation suggests the following three approximate results: (i) For the energy shift rule, the energies of the molecular orbitals (MO) for core hole states (either core ionization or core excitation) are all shifted by approximately the same amount regardless of the MO’s character. (ii) For alternating change of population, compared to the populations of the atomic orbitals in the corresponding M O s of the ground state, the populations of the atomic orbitals in the M O s for the atom with a core hole do not as intuitively expected always increase in order to balance the extra positive charge due to the core hole creation. Instead, these populations increase and decrease in an alternating pattern. (iii) For electrons as spectators, approximately identical core hole state populations are observed regardless of whether a core ionization of core excitation has taken place. Although there are a few exceptions, these rules may be useful for qualitative study of more complicated molecules.
I. Introduction The chemical consequence of core level excitation and relaxation in molecules is attracting more and more attention due to the availability of synchrotron radiation and advances in soft X-ray monochromators. This research is significant because the information obtained is beneficial to microfabrication technology and a variety of disciplines.] Although recently new experimental phenomena in this field have been e x p l ~ r e d ,there ~ , ~ have been
only a few recent theoretical advance^.^ Investigation of the effect on molecular orbitals due to a core hole creation will provide a primitive picture of all remaining electrons to predict and understand further subprocesses. Ab initio configuration interaction (CI) can provide more precise results. However, for the information on the MO level, a study of SCF calculations might be more proper. In this paper, we concentrate our theoretical analysis on the energy and population changes of the molecular orbitals of molecules that are core-ionized or
(l),Hanson, D. M. In Chemistry Induced by Core Electron Excitation; Prigogine, I., Rice, S. A., Eds.;Advances in Chemical Physics 77; John Wiley and Sons: 1990; pp 1-37. (2) Hanson, D. M.; Ma, C. I.; Lee, K.; Lapiano-Smith, D.; Kim, D. Y . J. Chem. Phys. 1990, 93,9200 (L).
(3) Lebrun, T.; Lavollk, M.; Morin, P. Molecular Dynamics Following Inner Shell Excitation. In X-Ray and Inner-Shell Processes; AIP Conference Proceedings 215; Carlson, T. A,, Krause, M. O., Manson, S. T., Eds.; American Institute of Physics: New York, 1990 pp 846-859. (4) Larkins, F. P. J. Electron Spectrosc. Relat. Phenom. 1990, 51, 115.
0022-365419212096-2949$03.00/0
0 1992 American Chemical Society
