The Journal of
Physical Chemistry
0 Copyright, 1987, by the American Chemical Society
VOLUME 91, NUMBER 21 OCTOBER 8,1987
Dynamical Aspects of Stereochemistry R. B. Bernstein,* Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90024
D. R. Herschbach,* Department of Chemistry, Harvard University, Cambridge, Massachusetts 021 38
and R. D. Levine* The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University, Jerusalem 91 904, Israel (Received: May 20, 1987)
The first workshop on an emerging subfield of chemical dynamics, dubbed dynamical stereochemistry,was held in Jerusalem, Israel in November, 1986. Outlined here is the program of the meeting, followed by an overview intended to place the subject of reactive stereochemistry in a wider context and to emphasize the major themes. These include classical stereochemical considerations (ab-initio and "molecular mechanics" force fields calculations of conformations); the concept of the steric effect in chemical reactions and its relation to the angle-dependence of the activation barrier; experiments on the elusive transition state itself; orientation vs. spatial alignment of reagents and products as realized in experimental methods and theoretical descriptions; reagent and product state selection, orientation, and angular momentum alignment descriptions, in both reactive collisions and in half-collisions (Le., photofragmentation); orientation effects in electronically nonadiabatic reactions; polarized laser excitation and product fluorescence polarization analysis, exemplifying vector correlations in dynamical stereochemistry. Finally, prospects for the future are briefly discussed.
1. The Jerusalem Workshop The Jerusalem workshop was held to recognize the coming of age of dynamical stereochemistry. The official occasion was the fifth anniversary of the Fritz Haber Research Center for Molecular Dynamics, and the workshop was held under the auspices of the Institute for Advanced Studies of the Hebrew University. The flavor of the meeting is perhaps best conveyed by the ballad composed by Prof. J. P. Simons for consideration during the final discussion: We journeyed to Jerusalem To see what we could find If we could learn a deeper truth And know the Word-aligned At first, 'twas Wittig and the slithy rotes Did gyre and gymbal in the Habe All mimsy were the correlotes and the lone R a f s outgrabe 0022-3654/87/2091-5365$01.50/0
The days passed by, morn and night Day one of course, produced the light The vectors whirled their dance macabre In the library of Fritz Haber Now the Judgement Day's at hand The Name's called out, from Baert to Band With Dudley standing at the gate Smiling, cheering, Laureate Whispers the word that gets you by When passing through, say methyl? Ay! The intention of the workshop was not only to survey where we are but also to look forward as far as reasonable. Hence This could have been Zare, but Zare was not there!
0 1987 American Chemical Society
Bernstein et al.
5366 The Journal of Physical Chemistry, Vol. 91, No. 21, 1987 considerable time was allotted to discussion of individual presentations as well as to working groups meeting to consider more specialized aspects. The formal program began with the potential, both ab-initio (Prof. S. Peyerimhoff, Bonn) and empirical (Prof. A. Y. Meyer, Jerusalem). It became quickly very clear that progress in quantum chemistry and in empirical force fields is such that it is useful and advantageous to keep the dialogue going. The detailed experimental results and the sophistication of the scattering theoretic computations do warrant the best available potentials. It was also evident that considerable effort will be required to produce these potentials. In the near future state of the art ab initio curves for (nonadiabatic) atom-atom collisions and potential energy surfaces for a few selected systems is all that can be reasonably hoped for. Further developmental work is also required before the tremendous data base set up in molecular mechanics can be adapted for computing barriers to reaction and their orientation dependence. Despite these technical difficulties, there is much scope for further interaction with structural theory. What are the phenomena? First and foremost is reactive asymmetry. Oriented molecule beams (Prof. R. B. Bernstein, UCLA) offer the most direct probe of the steric requirements of chemical reactions. Improved focusing (Prof. S. Stolte, Nijmegen) and the possibility of simultaneous probing of products (Prof. D. H. Parker, UC-Santa Cruz) are already being used and will provide an unprecedented degree of detail. Laser-excited aligned reagents for both inelastic (Prof. A. J. McCaffery, Sussex) and reactive (Prof. H. Loesch, Bielefeld) events require much careful consideration of the role of rotational angular momentum (both magnitude and direction). Spectroscopic probing of the products, both Doppler (Prof. C. Wittig, USC) and polarization (Prof. J. P. Simons, Nottingham) and their orientation (Dr. G. M. McClelland, IBM) is providing complementary information. En route from reagents to products is the transition state (Prof. P. R. Brooks, Rice) and studies of ”half-collisions” through photodissociation of van der Waals adducts (Prof. B. Soep, Orsay) or of stable molecules (Dr. P. Andresen, Gottingen, Prof. P. L. Houston, Cornell) are also providing insights on the stereochemistry in the transition-state region. Here a limited range of orientations has been preselected by choice of the precursor. Both scalars (Le. populations), vectors, and vector correlations in the products can then be probed by spectroscopic techniques. The prospects for extending the experimental studies to larger molecules were discussed. Nonadiabatic effects such as unequal population of A doublets which discern planar from nonplanar motion during dissociation or unequal population of spin-rotation levels also provide information on the stereochemistry in the exit channel. The wealth of observed vector correlations has stimulated an extensive activity on the part of the theorists. Transition-state theory is being reexamined so as to extract state-to-state information (Prof. E. Pollak, Weizmann). Quantum scattering theory and its semiclassical approximations need to explicitly consider both electronic and rotational degrees of freedom (Prof. M. H. Alexander, Maryland) if necessary, in the sudden approximation (Dr. M. Baer, Soreq). Where appropriate, classical trajectories (Prof. A. Lagana, Perugia) and simpler models (Dr. N. Agmon, Jerusalem) are called upon. The theory of photodissociation (Prof. M. Shapiro, Weizmann, Dr. R. Schinke, Gottingen) and products’ emission (Prof. A. Ben-Reuven, Tel-Aviv) is central to the extraction of vector correlations. The dynamical implications of the directional properties of the chemical bonding can also be expressed and studied. Such orbital stereospecificity is being examined for both elastic (Dr. R. Dueren, Gottingen) and inelastic (Prof. V. I. Hertel, Freiburg, Prof. K. L. Kompa, Garching) processes. It can influence the branching into distinct products for reactive processes and can also be explored for products as, e.g., in photodissociation (Prof. Y . Band, Ben-Gurion). Other topics discussed in the workshop included the role of steric considerations in molecule-surface processes, including in the approach to the surface and in desorption. The final discussion (orchestrated by Prof. D. R. Herschbach, Harvard) not only charted the near shores but expressed the hope that others will
Figure 1. Equilibrium conformation for a tetrahedral carbon atom adC-H bond eclipses the double bond.
jacent to a trigonal carbon; the
wish to share and explore further. Hence this collection of both “featurelike” articles and specific contributions by the participants and by additional practitioners.
2. Classical Stereochemistry Geometry governs much of chemistry; in essence, the molecular world reverses the familiar architectural dictum that “form follows function”. This is exemplified in both chemical synthesis and in biochemistry by the development over the past 40 years of the vast field now known as conformational analysis.‘ For molecular dynamicists, it is appropriate to stress that from just a few geometrical facts and notions synthetic chemists can conjure up remarkably elaborate molecules with precise control of stereoselectivity. For instance, in devising a stereospecific synthesis for a large class of polyether antibiotics, Kishi2 made repeated use of the conformational preference of an sp3 carbon adjacent to an sp2 carbon. This has a C-H bond to the tetrahedral carbon eclipsing the adjacent double bond, as shown in Figure 1. The key result came from the microwave spectrum of p r ~ p y l e n ea, ~ molecule negligibly small compared to antibiotics! Guided by a few such geometrical prototypes, Kishi devised routes to still more intricate molecules, recently accomplishing the incredible feat of constructing a neurotoxin molecule with 7 1 asymmetric carbon centers in specified conformations. Thus he obtained in high yield the single biologically active form of a molecule that has 2’’ (Le., lo2’)stereoisomers. May the prospect of aiding such adroit synthetic colleagues inspire dynamicists studying geometrical features of simple reactions involving three or four atoms! Likewise, dynamical stereochemistry has a natural symbiotic link to molecular mechanics calculations. Despite the limitations of empirical force fields, these calculations are now applicable to large molecules and offer a quite practical means to explore mechanistic pathways. For instance, over the past decade Karplus and co-workers have conducted an extensive computational study of protein dynamics. An aspect especially congenial for collision dynamicists is the prevalence of conformational changes involving angular reorientation of side chains or other groups. The prime example occurs in the interaction of an oxygen molecule with hemoglobin, which induces a whole series of coupled conformational changes in the heme group and surrounding moieties. Case and Karplus4 discovered an unanticipated “Venus flytrap” mechanism. As the oxygen molecule approaches, a valine residue and a nearby histidine both rotate by 25-30’ to open up an inviting tunnel leading toward the heme. When the molecule passes through, these groups swing back to close the channel again. In effect, the potential hypersurface has a valve operating like a Maxwell demon! Molecular mechanics calculations now can also elucidate how solvation modifies or transforms reaction dynamics. By means of a custom-designed array processor, Wilson and co-workers5have recently examined in detail one of the classic stereochemically
-
(1) See, for example, Eliel, E. L. Conformational Analysis; Interscience: New York, 1965. Burkert, U.; Allinger, N. L.; Molecular Mechanics; American Chemical Society: Washington, DC, 1982; ACS Monograph No. 177. ( 2 ) Kjshi, Y. Aldrichimica Acta 1980, 13, 23 (antibiotics) and private communication (neurotoxin). (3) Herschbach, D. R.; Krisher, L. C. J . Chem. Phys. 1958, 28, 7 2 8 . (4) Case, D. A.; Karplus, M . J . Mol. Biol. 1979, 132, 343. Karplus, M. Ado. Chem. Phys., in press.
Dynamical Aspects of Stereochemistry
The Journal of Physical Chemistry, Vol. 91, No. 21, 1987 5367
specific reactions, the SN2Walden inversion reaction in aqueous solution
C1-
+ CH3Cl-
ClCH3
+ C1-
Barrier recrossing induced by the solvent caused marked departures from transition-state theory. However, Wilson found that a “spectator solvent” model (which assumes that water molecules are unable to move on the time scale of the barrier crossing) successfully predicts the outcome of each reactive trajectory. Like many kindred results from molecular mechanics calculations, the Venus flytrap and spectator solvent models illustrate nicely how intrepid dynamicists can extract nuggets of simplicity from apparently overwhelming complexity and thereby enrich stereochemistry.
I
2. 5
2.0
I
I
ORIENTATIONAL PROBABILITY DISTRIBUTION FUNCTION FOR SYMMETRIC TOP MOLECULES IN SPECIFIC (J, K, M) STATES
I
I
(2,2, 2) r\
1.5
I
(1, 1, 1)
Q)
07 0
e
Q
1.0
3. Steric Effects in Reactive Collisions The most direct connection between classical stereochemistry and the new approaches being developed in chemical dynamics employs the venerable concept of the steric factor. From the very beginnings chemical kineticists recognized that second only to the energetic requirements for reaction was the need for “proper” mutual orientation of reagents, and that the steric factor in the preexponential of the rate constant had to do with the probability of achieving this proper orientation, given the random nature of the molecular encounters. The SO-year-old Eyring “entropy of activation” makes for a quantitative interpretation of the steric factor. The development of the field of molecular beam chemistry and reaction dynamics in the early 1960s invited direct experimental study of the steric effect. The goal is to control the mutual orientation of the reagents and observe its influence on the reaction probability, Le., the total reaction cross section, or, better yet, the angular distribution of products from the reaction of oriented reagents. An idealized experiment might then measure separately the reaction cross sections, and thus the branching ratio for “both ends” of an atom-heteronuclear diatomic reaction:
+ BC - A B + C A + CB - A C + B A
The direction and magnitude of the steric effect on chemical reactivity thus determined could be compared with expectation based on branching ratios obtained from more conventional experiments with unoriented molecules (which can provide the orientation-averaged branching ratio of products), and, of course, with theory. But in order to carry out the direct reactive asymmetry experiments it would be necessary to produce beams of oriented molecules, Le., molecules oriented (e.g., by an electric field) in the laboratory framework. Then one could measure directly the orientation dependence of the reactivity in an atom-molecule crossed beam experiment in which the angle between the relative velocity vector v (or the corresponding wave vector k) and the molecular axis r (or the molecule’s electric dipole moment p ) could be set parallel or antiparallel to v. Unfortunately, for diatomic molecules one requires extremely high electric fields to achieve even slight net orientation in the lab frame. However, for polar symmetric top molecules the situation is vastly improved, since a certain class of rotational states (such as IJKM) = )222), 1111 ), etc.) will precess in an electric field rather than “tumble”. Thus, substantial net orientation can be achieved, Figure 2. Orientation here refers to that of the direction of the rotational angular momentum (vector), and thus of the molecular axis, with respect to an applied electric field. The degree ( 5 ) Bergsma, J. P.; Gertner, B. J.; Wilson, K. R. J . Chem. Phys. 1987, 86, 1356, 1377.
0. 5
(2, 1, 2) 0. 0
-1.0
-0.5
0.0
0. 5
1.0
cos 8 Figure 2. Calculated orientational probability distributions for the designated JKM states of a symmetric-top molecule, adapted from ref 53. These states are the ones readily obtained nearly “pure” by the hexapole system (see ref 57).
of orientation, say ( p ) , is defined as the average value of the cosine of the angle 0 between the dipole moment p (and thus r) and the orientation field E, Le. (p)
=
(cos 0&) = ( E & )
with ( p ) limited to the range -1 I ( p ) I 1. Perfect (and unattainable) orientation would be characterized by ( p ) = 1 or -1 (parallel or antiparallel orientation of p with respect to E). Random orientation corresponds to ( p ) = 0. Later on we will discuss more of the technical aspects. Here we briefly review the history. Bennewitz et aL6 showed how to achieve rotational state selection and focusing of polar diatomics (via their second-order Stark effect) using an electrostatic quadrupole field. Their work followed that of Friedburg,’ who introduced the general concept and employed a magnetic hexapole to focus a beam of potassium atoms utilizing the magnetic moment of the atom. This led to the introduction of the electric hexapole by Kramer and Bernsteid to focus and state-select polar symmetric top molecules via their first-order Stark effect. Focused molecules with a specified ( p ) are oriented by a weak homogeneous electric field E, and a crossed atomic beam directed such that v is parallel or antiparallel to E, so that the atoms collide with the molecules in either the “heads” or “tails” configuration. In 1966, Brooks and Jonesg and Beuhler et a1.I0 used this method to show that the reactions of alkali atoms with oriented methyl iodide molecules exhibit a pronounced steric effect. Further work has characterized this in quantitative detail]’ and applied the electrical hexapole field technique to other reactions showing
Bennewitz, H. G.; Paul, W.; Schlier, Ch. Z. Phys. 1955, 141, 6. Friedburg, H. Z. Phys. 1951, 130, 493. Kramer, K. H.; Bernstein, R. B. J. Chem. Phys. 1965, 42, 767. (9) Brooks, P. R.; Jones, E. M. J . Chem. Phys. 1966, 45, 3449. (10) Beuhler, R. J.; Bernstein, R. B.; Kramer, K. H. J. A m . Chem. Soc. 1966, 88, 5331. (1 1) For a review, see Bernstein, R. B. In Recent Advances in Molecular Reaction Dynamics, Vetter, R., Vigue, J. Eds.; CNRS: Paris, 1986; p 51.
5368 The Journal of Physical Chemistry, Vol. 91, No. 21, 1987
marked orientation dependence.l2-I4 Another approach to steric requirements for reaction exploits the orientation dependence of the dipole selection rule for electronic excitation. Molecular photodissociation served as the archetype. For the “reaction” of a photon with a diatomic molecule, the transition probability for electronic excitation is just proportional to cos2 a, with a the angle between the electric vector of the light and the transition dipole moment, If the excited state dissociates, it often does so in a time very short compared with the classical rotational period of the molecule. The angular distribution of photofragments thus is anisotropic and can be characterized by simple, general form factors.I5 These are specified by the polarization of the exciting light, by the orientation of the transition dipole within the molecule (parallel or perpendicular to the molecular axis), and by the direction of departure of the product atoms (superposition of axial recoil along initial direction of the molecular axis or transverse recoil perpendicular to it). Over the past 20 years, the method of photofragment spectroscopy based on such form factors has extracted a new lode of information about dissociative excited states and their repulsive potential curves or surfaces.I6 Recent developments, particularly the use of Doppler-resolved laser-induced fluorescence of atomic or molecular photofragments, have made accessible many further directional aspects of photodissociation dynamics. This elegant work is described in reviews by HoustonI7 and SimonsIs and several workshop papers. Finally, real time (picosecond and even femtosecond) observations of molecular photofragmentation by Zewail and co-w~rkers’~ have revealed dissociative lifetimes of excited states. Alignment of reagents for chemical reactions can likewise be achieved by the anisotropy of electronic excitation. This approach was initiated by Zare and co-workers2” in 1978. Here linearly polarized laser radiation is used to selectively excite a diatomic molecule (homonuclear or heteronuclear) to achieve alignment of the rotational angular momentum j with respect to the electric vector E of the light.21 Thus, molecules which are excited have specified j and *mJ quantum numbers. Since the relative population of AmJ states is 1:l there is no net orientation, only alignment. Nevertheless, one can study the dependence of the reactivity of the aligned (excited) molecules (with a collision partner, say, an atom) upon the orientation of the relative velocity vector v with respect to j, e.g., by comparing cross sections for v 11 j vs. v l j . In the classical limit (largej), the rotating diatomic can be likened to a disk, so the cross sections for v 1) j (broadside collisions) are expected to be larger than those for v 1j (edge-on collisions). One advantage of the polarized laser excitation method to produce aligned molecules is that, by virtue of the fact that they are excited (electronically or merely vibrationally), they usually react preferentially (more rapidly) with respect to the ground-state molecules. They often form excited products which fluoresce and from the degree of polarization of the fluorescence one can learn about the correlation between j and j’ (prime refemng to product). As exemplified by the workshop papers, the bulk of the experimental research on stereochemical aspects of dynamics thus far has utilized the polarized laser excitation-polarization analysis methodology. Yet from a chemist’s viewpoint the primary goal is to ascertain the role of the reagents’ molecular orientation (rather than alignment) in determining chemical reactivity. (12) Parker, D.H.; Jalink, H.; Stolte, S. J. Phys. Chem. 1987, 91, 5427. (13) Brooks, P. R. Science 1976, 193, 1 1 . (14) Stolte, S. Ber. Bunsen-Ges. Phys. Chem. 1982, 86, 413. (15) Zare, R. N.; Herschbach, D . R. Proc. ZEEE 1963, 5 1 , 173. Zare, R. N. Mol. Photochem. 1972, 4, 1 . (16) For reviews, see Riley, S. J.; Wilson, K. R. Faraday Discuss. Chem. Soc. 1972, 53, 132. Lin, S . H.; Bersohn, R. Adv. Chem. Phys. 1969, 16, 67. (17) Houston, P. L. J. Phys. Chem. 1987, 91, 5388. (18) Simons, J. P. J . Phys. Chem. 1984, 88, 1287. Ibid. 1987, 91, 5378. (19) Knee, J. L.; Khundkar, L. R.; Zewail, A. H. J. Chem. Phys. 1985, 83, 1996. Scherer, N . F.; Knee, J. L.; Smith, D. D.;Zewail, A. H. J. Phys. Chem. 1985.89.5141. Khundkar, L. R.; Knee, J. L.; Zewail, A. H. J. Chem. Phys. 1987,87,77. Scherer, N. F.; Zewail, A. H . J. Chem. Phys. 1987.87, 97. (20) Karny, Z.; Estler, R. C.; Zare, R. N. J. Chem. Phys. 1978, 69, 5199. (21) Zare, R. N. Ber. Bunsen-Ges. Phys. Chem. 1982, 86, 422.
Bernstein et al.
4. Anisotropic Reactive Scattering Although less directly linked to classical stereochemistry than the steric factor, which concerns preferred orientation in space, product angular distributions reveal whether there is any preferred direction relating the reagent and product relative velocity vectors.22 This is an intrinsic aspect of dynamical stereochemistry and often provides at least qualitative information about steric effects. It is the simplest example of vector correlations, of which we shall have more to say in section 6. Markedly anisotropic distributions of product relative velocity vectors have been found in practically all reactive scattering experiments (unless rendered unobservable by unfavorable kinematic features). Several prototype modes of reaction dynamics for A BC AB C are typically characterized by these distributions.22 Processes involving abrupt, impulsive bond exchange or formation of a persistent complex comprise the two major categories. In the impulsive regime, many systems exhibit rebound behavior, in which AB recoils into the “backward” hemisphere and C is ejected forward (Le., in the direction of the incoming A atom). The original example, vintage 1961, is the K + CH,I reaction;23another is the H + C12 reaction.24 Other systems display stripping behavior, in which AB recoils forward and C backward. For others, the products are emitted sideways, giving a conical angular distribution about the initial relative velocity vector. In some cases, the cone angle varies with product translational energy in a fashion resembling the rainbow features familiar in elastic ~ c a t t e r i n g . ~Comparison ~ with classical trajectory calculations or models designed to simulate impulsive dynamics indicates that often the preferred direction of product emission reflects the optimal reaction geometry, especially when the products’ relative translational velocity is high. For instance, the product angular distributionsz4give evidence that the optimal reactive configuration is collinear for H-C1-C1 but substantially bent for H-Br-Br and strongly bent for H-1-1. This trend is qualitatively consistent with the role of electronegativity in Walsh’s rules for bond anglesz6 and has recently been confirmed by ab initio electronic structure calculation^.^^ In the persistent complex regime, attractive interactions allow the A-B-C complex to hang together for many vibrational periods and at least a few rotational periods. The product distributions then typically display forward-backward symmetry with respect to the initial relative velocity28 (although a long lifetime for the complex is not strictly sufficient to guarantee this symmetry29). The distributions also typically show strong “glory” peaks at 0’ and 180’. These arise because the products emerge with equal probability a t all azimuthal angles about the total angular momentum vector of the complex, like water from a rotating lawn sprinkler, and all orientations of the sprinkler about the initial relative velocity vector are equally likely. The two uniform averages give a product distribution with low intensity in the equatorial regions and high intensity in the polar regions, if the complex is prolate in the critical configuration for dissociation. At wide angles the nonreactive scattering likewise shows a glory peak arising from breakup of the complex to re-form the reagents rather than proceed to products.!’” According to a transition-state model (akin to the liquid drop model for nuclear fission), the shape
+
-
+
(22) Levine, R. D.; Bernstein, R. B. Molecular Reaction Dynamics and Chemical Reactivity; Oxford University: New York, 1987. (23) Kwei, G . H.; Norris, J. A,; Herschbach, D. R. J. Chem. Phys. 1961, 34, 1842. 1970,52, 1317. Kinsey, J. L.; Kwei, G . H.; Herschbach, D. R. Ibid. 1976, 64, 2133. (24) McDonald, J. D.; LeBreton, P. R.; Lee, Y . T.; Herschbach, D. R. J . Chem. Phys. 1972,56, 769. (25) Riley, S. J.; Siska, P. E.; Herschbach, D. R. Faraday Discuss. Chem. Soc. 1979, 67, 27. (26) Walsh, A. D. J. Chem. Soc. 1953, 2288. (27) Eades, R. A,; Dunning, T. H.; Dixon, D. A. J. Phys. Chem., t o be submitted. (28) Miller, W. B.; Safron, S. A.; Herschbach, D. R. Faraday Discuss. Chem. Soc. 1967, 44, 108. (29) McClelland, G . M.; Herschbach, D. R. J . Phys. Chem. 1979, 83, 1445. (30) Ham, D.0.;Kinsey, J. L.; Klein, F. S. Faraday Discuss. Chem. Soc. 1967, 44, 174. J . Chem. Phys. 1968, 48, 939. 1970, 53, 285.
The Journal of Physical Chemistry, Vol. 91, No. 21, 1987 5369
Dynamical Aspects of Stereochemistry of these glory peaks reveals the relative contribution of centrifugal motion of the complex and rotational tumbling of the reagent and product molecules.28 Centrifugal motion is usually dominant and the glory peaks sharp because in the critical configuration the complex is stretched out, Le., decidedly prolate. However, a few examples of oblate complexes have been f o ~ n d . ~ These ~ - ~ ~do not give glory scattering but rather the product distributions peak at 90°. For instance, reactions of alkali atoms with SnC14appear to have two distinct decay modes,34one forming alkali chloride and the other alkali chlorostannite, MSnCl,. For the Li case, the latter channel appears dominant and the complex oblate, as indicated by a broad sideways peaked product di~tribution.~~ For larger alkali atoms, the chlorostannite channel becomes less prominent and involves a prolate complex, as indicated by forward and backward glory peaks. Formation of the chlorostannite might proceed via a trigonal bipyramidal transition state M
+
CI3SnCI
r“‘ i- c I M+---s~----cI
M+SnCI3
+
Orientation
field
/I, I *
Oriented
CH3 I
-
beam
CI
CI
in which the alkali atom approaches a tetrahedral face of the reactant molecule and the pyramidal halogen triad undergoes inversion. With Li, such a transition state is an oblate rotor for reasonable assumed structures, whereas with heavier alkali atoms it becomes a prolate rotor. This example again illustrates how dynamical stereochemistry can augment classical views. It also offers a rare instance of a product that is a strongly nonlinear molecule and hence suitable for analysis by the electric hexapole technique. In both the impulsive and persistent complex regimes, when two or more product channels are open, the prevalent one is often not that expected on energetic or purely statistical grounds. Thus, reactions of H, Br, 0, and CH, with IC1 all form chiefly or solely iodides, even though the exoergicity to form chlorides is considerably higher. This stereochemical preference has been attributed24 to orbital asymmetry. As a consequence of the electronegativity difference, in IC1 both the highest occupied orbital (T*) and the lowest unoccupied orbital (a*) are predominantly I atom orbitals. Thus, an attacking radical prefers to deal with the I end, whether the radical wants to donate or to extract (partial) electron charge. Such considerations led to the unorthodox predi~tion,~ that the 0 + F2 reaction should have a relatively high activation energy, despite its large exoergicity and the notoriously aggressive reagents. Since oxygen is less electronegative than fluorine, the preferred order of atoms should be F-0-F rather than 0-F-F. Thus sideways insertion rather than end-on attack might be expected. Subsequent experiments indeed found36that this reaction is inhibited by a large activation energy. Such “insertion” mechanisms have been suggested for other reactions37 (e.g.,38 O(lD) + H2) while in others (e.g.,3e42H 0,) the barrier to insertion appears to be lowest for a sideways approach. These barriers can be overcome using translationally hot atom^.^,.^^ There is indeed some e ~ i d e n c e that ~ ~ .such ~ ~ fast atoms can explore alternative,
+
(31) Parrish, D. D.; Herm, R. R. J. Chem. Phys. 1969,51, 5467. 1971, 54, 2518. (32) Entemann, E. A.; Kwei, G. H. J. Chem. Phys. 1971, 55, 4879. (33) Parson, J. M.; Shobotake, K.; Lee, Y.T.; Rice, S. A. Faraday Discuss. Chem. SOC.1973, 55, 344. (34) Riley, S. J.; Herschbach, D. R. J. Chem. Phys. 1973, 58, 27. (35) Parrish, D. D.; Herschbach, D. R. J. Am. Chem. SOC.1973,95,7889. (36) Krech, R. H.; Diebold, G. J.; McFadden, D. L. J. Am. Chem. SOC. 1977, 99,4605. (37) Tsukiyama, K.; Katz, B.; Bersohn, R. J. Chem. Phys. 1985,83, 2889. (38) Jorsich, G. M.; Wiesenfeld, J. R. Chem. Phys. Lett. 1985, 119, 511. Luntz, A. C.; Schinke, R.; Lester, Jr., W. A.; Gunthard, H. H. J. Chem. Phys. 1979,70,5908. Whitlock, P. A.; Muckerman, J. T.; Fischer, E. R. Ibid. 1982, 76, 4468. (39) Melius, C. F.; Blint, R. J. Chem. Phys. Lett. 1979, 64, 183. (40) Miller, J. A. J. Chem. Phys. 1981, 74, 5120. Kleinermans, K.; Schinke, R. Ibid. 1984, 80, 1440. (41) Kleinermans, K.; Wolfrum, J. J. Chem. Phys. 1984, 80, 1446. Kleinermans, K.; Linnebach, E. Ibid. 1985, 82, 5012. (42) Schechter, I.; Levine, R. D.; Bernstein, R. B. J. Phys. Chem. 1987, 91, 5466.
Figure 3. Cartoon of the arrangements2 for polarized laser photofragmentation of oriented (JKM state-selected) molecules of CH31. The I and I* atoms, as well as the CH3 radicals, can be detected by resonance-enhanced multiphoton ionization mass spectrometry (REMPIMS).
steric approaches which are not accessible for thermal reagents. Another instructive episode involving a “wrong end” preference appeared in exchange reactions of alkali atoms with alkali hali d e ~ the , ~ prototype ~ persistent complex system.28 A statistical transition-state model gave good agreement with the angle and translational energy distributions but overestimated the ratio of reactive to nonreactive decay of the collision complex, often by a factor of 3 to 5 or more. Potential energy surfaces4’ suggest this reflects a geometric c o n ~ t r a i n t . ~The ~ preferred direction of approach is collinear, with the incoming alkali atom attacking the “alkali end” of the salt molecule as a consequence of the unusual stability of a dialkali ion. However, since most complexes are formed in collisions with large impact parameters, the centrifugal momentum often restrains the roughly collinear initial configurations from bending into the triangular configurations required for reaction. Trajectory s t ~ d i e have s ~ ~given ~ ~ particularly ~ striking evidence confirming such “centrifugally enhanced stereochemistry”. The examples cited in this section illustrate how even fairly unsophisticated beam scattering experiments that merely define a reference axis or plane associated with the collision process can reveal stereochemical properties when supplemented by chemical arguments or model calculations. Current developments, as displayed a t the workshop, employ more powerful physical techniques but often might likewise be enhanced by typical chemical stratagems such as electronic structure correlations.
5. Reagent Preparation: Stereoselectivity The goal here is to probe, the dependence of the reactivity on the initial “orientation” of the reagents. There are still relatively few direct studies of stereoselectivity so that new experimental techniques are important and existing techniques need be further refined and more extensively applied. The theoretical framework for the interpretation of such experiments also needs further (43) Flynn, G. W.; Weston, R. E. Annu. Rev. Phys. Chem. 1986,37,551. (44) Johnston, G. W.; Katz, B:; Tsukiyama, K.; Bersohn, R. J. Phys. Chem. 1987, 91, 5445. (45) Schechter, I.; Kosloff, R.; Levine, R. D. J. Phys. Chem. 1986,90,977. (46) Stolte, S.; Proctor, A. E.; Bernstein, R. B. J. Chem. Phys. 1976,65, 4990. (47) Roach, A. C.; Child, M. S. Mol. Phys. 1968, 14, 1 . Struve, W. S. Ibid. 1973, 25, 777. (48) Tamir, M.; Levine, R. D. Chem. Phys. 1976, 18, 125. (49) Brumer, P.; Karplus, M. Faraday Discuss. Chem. SOC.1973,55, 80. (50) Rynefors, K.; Nordholm, S . Chem. Phys. 1985,95, 345. Markovic, N.; Nordholm, S.; Rynefors, K. Ibid. 1986, 108, 287.
5310
Bernstein et al.
The Journal of Physical Chemistry, Vol. 91, No. 21, 1987
attention and more computational studies are required. Even our intuition needs to be better acquainted with the new kinds of differential cross sections which are usually “integrated over”. Indeed, it is the very need to understand the configuration of the system at the point of reaction, which is required for interpreting stereoselectivity, which places this emerging field at the center of molecular reaction dynamics. Polar symmetric top molecules can be most readily oriented with respect to the relative velocity axis. As noted in section 3, this was the route to the first direct demonstrations of the dependecce of the reactivity on the “angle of attack”, ?, where cos y = i.R with i a unit vector in the direction of the dipole moment. Intense, state-selected beams can now be prepared5’ and used for reactive scattering experiments. Photofragmentation experiments to demonstrate the laboratory orientation of the molecules in such a beam are in progress.52 State-selected CH31molecules in the rotational state IJKM) = 111 1 ) are photodissociated with the laser radiation polarized along the orienting field direction, Figure 3. From the observed spatial anisotropy of the ejected 1(2P,j2) photofragment, it is possible to detect the laboratory orientation of the CH31molecules and compare results with theoretical expectation~.~~,~~ There have been, thus far, only a few studies of reactive scattering using oriented molecules. The following constitutes the complete set: Rb CH31 (Bernstein group)
+
K
+ CH31, CF31, CF3Br NO + 0,, Ba + N 2 0
(Brooks group) (Stoke group)
Limitations of the hexapole orientation method due to the complexity of instrumentation are, however, being overcome,55and there is progress toward extending its applicability of the technique to other reactions. The major restriction of this method is that it requires not only polar molecules, but molecules with angular momentum around the axis, Le., the existence of a first-order Stark effect. A new development is that one can take advantage of the first-order Stark effect arising from the I-doubling in the vibrationally excited bending mode of linear triatomics (such as N 2 0 and OCS) to achieve o r i e n t a t i ~ n . ’ ~ ~ ~ ’ ~ ~ ~ Translational energy dependence of the orientation effect has already been measured.I2 In the near future it should be possible to measure detailed orientation-dependent reaction cross sections by working with selected (vibrational such as uR(O,Etr,Enb,J,K,M) and) rotational states.57 Such data should ultimately lead to a much-improved knowledge of the angle dependence of the activation barrier, V ( T ) . ~ * The highest level of sophistication thus far achieved with the oriented molecule beam technique was the experiment of Jalink et al.59 The study dealt with the question: How does the mutual orientation of the reagents determine the alignment of the products? The reaction examineds9 was Ba
+
N 2 0 ( J / M= I I I )
-
BaO(A‘ZC)
+
N,
ihv BaO(X’z+)
The polarization of the chemiluminescence (CL) of the nascent BaO was measured for three (average) orientations of the N20: (51) Gandhi, S.R.;Xu, Q.-X.; Curtiss, T. J.; Bernstein, R. B. J . Phys. Chem. 1987, 91, 5437. (52) Gandhi, S.R.; Curtiss, T. J.; Bernstein, R. B., work in progress. (53) Choi, S.E.;Bernstein, R. B. J . Chem. Phys. 1986, 85, 150. (54) Brumer, P.; Shapiro, M. Faraday Discuss. Chem. SOC.1986,82, 177. (55) Stolte, S. In Atomic and Molecular Beam Methods, Scoles, G., Buck, U., Eds.; Oxford University: New York, 1987. (56) Jalink, H.; Harren, F.; van den Ende, D.; Stolte, S . Chem. Phys. 1986, 108, 391. (57) Gandhi, S.R.; Curtiss, T. J.; Xu, Q.-X; Choi, S. E.; Bernstein, R. B. Chem. Phys. Lett. 1986, 132, 6. (58) See, e.g., Levine, R. D.; Bernstein, R. B. Chem. Phys. Lett. 1986, 132, 11. (59) Jalink, H.; Parker, D. H.; Stoke, S. J . Chem. Phys. 1986, 85, 5372.
( p ) = +OS, 0, -0.5; the cross sections ucL were also measured59 and showed a marked dependence on ( p ) . For the “heads” orientation, strong in-plane polarization of the BaO was found. On extrapolating to perfect “tails” orientation the polarization (and ucL) goes to zero. A promising new technique for studying reagent orientation dependence takes advantage of the inherent mutual orientation of the molecules in the van der Waals adduct.Mt62 Thus photolysis of hydrogen halide in an adduct such as BrH-OCO initiates a “local” hot hydrogen atom attack reaction. A case studied was60
BrH-aOCO photolysis of HX favorably oriented in vdW molecule
-
BrH hot H atom attack, near-collinear due to precursor geometry
hw
‘93nm
-+
-0CO
-
+
+
Br OH(u’J’) CO formation of excited O H product; state analysis by LIF
Because there is a broad range of initial angles of attack (of the hot atom on the target molecule) due to the high-amplitude bending motion of the (weak) van der Waals bond the experimental results require some deconvolution to be fully interpreted. This technique, Le., the study of “precursor geometry-limited’’ bimolecular reactions (initiated by photolysis, not of the van der Waals bond but of the hot atom donor molecule) should be quite general and should provide useful data on steric effects in bimolecular reactions. In particular, by varying the photodissociation wavelength, the initial kinetic energy of the attacking atom can be varied. Interesting systems to explore include N20-.HF, SCO-HX, or N02.-C0. Even larger adducts can be prepared63 which will truly provide a bridge with traditional organic stereochemistry. With two-color experiments, the range of interesting experiments is even wider: One laser can excite one moiety in the adduct while another laser generates the attacking atom by photodissociation of the other moiety. Electronic excitation can also be considered6’and will be mentioned when we discuss orbital stereochemistry. Steric information can also be extracted from collision experiments involving aligned (rather than oriented) reagents. The simplest case is that of a diatomic molecule with its angular momentum vector j aligned with respect to the relative velocity ~ ~exact65quantum mechanical vector v. Both a p p r ~ x i m a t eand computations show a marked dependence of the reactivity on the initial helicity. To interpret such results consider, for simplicity, the diatomic molecule in t h e j = 1 rotational state. To describe the alignment of j , let us use the three p orbitals made familiar by general chemistry, using v as the z axis. When the molecule is preferentially in the pi state, it will encounter the attacking atom preferentially head-on. At the complementary alignment (when the molecule is preferentially in the px or pu state), the collision is primarily broadside. When the barrier to reaction depends (as it usually will) on the direction of a t t a ~ k , ~ *alignment , ~ ~ - ~ ~can influence reactivity. Indeed, using a simple quantitative version of the concept of an orientation dependent barrier, one can70 semiquantitatively account for the exactly computed65helicity dependence of the reactivity. Of course, if the molecule could be oriented and not merely aligned one could distinguish between the two “ends” of the molecule. Even so, alignment is a valuable (60) Buelow, S.;Noble, M.; Radhakrishnan, G.; Reisler, H.; Wittig, C.; Hancock, G. J . Phys. Chem. 1986, 90, 1015. (61) Jouvet, C.; Boivineau, M.; Duval, M. C.; Soep, B. J . Phys. Chem. 1987, 91, 5416. (62) Buelow, S . ; Radhakrishnan, G.; Wittig, C. J . Phys. Chem. 1987, 91, 5409. (63) Jortner, J.; Levine, R. D.; Rice, S . A. Adu. Chem. Phys. 1987, 70, 1. (64) Kafri, A,; Kosloff, R.; Levine, R. D.; Alexander, S. Chem. Phys. 1976, 1 3 , 323. (65) Schatz, G.C.;Kuppermann, A. J . Chem. Phys. 1976, 65, 4688. (66) Smith, I. W. M . J . Chem. Educ. 1982, 59, 9. (67) Jellinek, J.; Pollak, E. J . Chem. Phys. 1983, 78, 3014. (68) Levine, R. D.;Bernstein, R. B. Chem. Phys. Lett. 1984, 105, 467. (69) Loesch, H.Chem. Phys. 1986, 104, 213. (70) Kuppermann, A,; Levine, R. D. J . Chem. Phys. 1985, 83, 1671.
Dynamical Aspects of Stereochemistry
The Journal of Physical Chemistry, Vol. 91, No. 21, I987
+
tool and the pioneering experiments on Sr aligned HF are likely to be extended, using IR pumping with linearly polarized laser radiatione2’ Alignment of hydrogen halides is both experimentally feasible7’ and of considerable theoretical interest because of the availability of optimized semiempirical potentials and, more recently, of ab-initio ones. In the future the alignment of triatomic reagents (e.g., COz, N,O, HCN) will also be explored. A high degree of alignment can also be achieved by a complementary procedure. Photodissociation using a high-power polarized laser will effectively remove those diatomic molecules favorably aligned with respect to the field. The remaining population has a preferential plane of rotation. In the reaction of IBr with electronically excited Xe it was found72 that reaction is enhanced when the approach is coplanar. From the very beginning, the experimental work in this field has been accompanied by a corresponding theoretical effort.73 The recent surge of activity is also reflected in a higher level of theoretical publications which specifically address the issues of dy~ ~expected, ~ ~ ~ ~ ~ ~classical ~ - ~ ~ tranamical s t e r e o c h e m i ~ t r y . ~ As jectory computations have played a dominant role. These however are somewhat like experiment in that the results will benefit from further interpretation, using more naive but more specific models of the dynamics. One of the key problems here is that our intuitive concept of “orientation”, governed, in the simplest case, by the angle of attack y,is not “conserved” during the approach motion. There are two reasons for this. One is that even in the absence of intermolecular forces the free, unperturbed rotation of the molecules can lead to changes in y. This can be overcome by using another variable, e.g., the angle between j and k, to define “orientation” but the price is the absence of direct contact with intuitive ideas of steric hindrance. Alternatively, one can accept an approximate picture where, due to the slow rotation of most molecules, the difference between the initial angle of attack and its value “at impact” cannot be large. Trajectory calculation^^^^^^ show that, for all but the lowest energy regime, this “sudden” approximation is quite reasonable unless strong anisotropy is present in the entrance channeLS8 Another reason for the variation of the angle of attack during the approach motion of the reagents is the anisotropic character of the potential energy in the entrance valley. At low collision energies one can expect such forces to impose a different orientation than that selected for the reagents. For collinearly dominated reactions one can then assume that the transition state is (71) Hoffmeister, M.; Schleysing, R.; Loesch, H. J . Phys. Chem. 1987, 91, 5441. (72) de Vries, M. S.; Srdanov, V. I.; Hanrahan, C. P.; Martin, R. M. J . Chem. Phys. 1983, 78, 5582. (73) Karplus, M.; Godfrey, M. J . Am. Chem. SOC.1966, 88, 5332. (74) Case, D. A,; Herschbach, D. R. J . Chem. Phys. 1978, 69, 150. (75) Hijazi, N. H.; Polanyi, J. C. Chem. Phys. 1975, 11, 1. (76) Lagana, A,; Garcia, E. J . Mol. Struct. 1984, 107, 91. (77) Blais, N. C.; Bernstein, R. B.; Levine, R. D. J . Chem. Phys. 1985, 89, 10. (78) Schechter, I.; Kosloff, R.; Levine, R. D. Chem. Phys. Lett. 1985, 121, 297. (79) Schechter, I.; Levine, R. D. Intl. J . Chem. Kinet. 1986, 18, 1023. (80) Wyatt, R. E. J . Chem. Phys. 1969,51, 3489. Connor, J. N. L.; Child, M. S . Mol. Phys. 1970, 18, 653. For the bending-corrected linear model see Hayes, E. F.; Walker, R. B. J . Phys. Chem. 1984.88, 3318, and references therein. (81) Agmon, N. Chem. Phys. 1981, 61, 189. Agmon, N. Intl. J . Chem. Kiner. 1986, 18, 1047. ( 8 2 ) Pattengill, M. D.; Zare, R. N.; Jaffe, R. L. J . Phys. Chem. 1987, 91, 5489. (83) Schechter, 1.; Prisant, M. B.; Levine, R. D. J . Phys. Chem. 1987, 91, 5472. (84) Alvarino, J.; Lagana’, A. J . Phys. Chem. 1987, 91, 5487. (85) Kornweitz, H.; Persky, A.; Levine, R. D. Chem. Phys. Lett. 1986, 128, 443. (86) Loesch, H. Chem. Phys. 1987, 112, 8 5 . (87) Alvarino, J. M.; Basterrechea, F. J.; Hernandez, M. L.; Lagana, A. Mol. Phys. 1986, 59, 559. (88) Persky, A.; Kornweitz, H. J . Phys. Chem. 1987, 91, 5496. (89) Jansen op de Haar, B. M. D. D.; Baht-Kurti, G. G. J . Chem. Phys. 1986, 85, 2614.
5371
linear irrespective of the initial conditions.80 It is however still possible to account for the initial orientation dependence of the reactivity by allowing for variable bending excitation of the linear triatomic.” An approach which seeks to combine the best features of both points of view has recently been described.89 Intermediate between a simple one-dimensional picture and a full trajectory computation are the model^^^^^^ which allow both the relative separation and the angle of attack to vary during the approach motion. Such a simpler, two-dimensional picture of the dynamics in the entrance valley is derived by confining the motion The question to a plane (Le., a “j, conserving appro~imation”~~). is how to choose that invariant plane. Experience from inelastic scattering9’ would suggest that a body-fixed (rather than a laboratory-fixed) system of coordinates with R along the z axis is preferable. Such a choicess also has the advantage that it can be implemented at finite values of the impact parameter. The orientation-dependent barrier to reaction determines (in the sudden limit) the range of attack angles that can lead to reaction, Figure 4. The magnitude of the reactivity at any given orientation depends on the range of impact parameters b that lead to reaction. The relation between the initial angle of attack as determined by the experimenter and its value at the barrier is also b dependent. Even assuming no intermolecular forces, it is only for near zero impact parameters that the two angles are the same. For reactive collisions with large impact parameters (Le., collisions leading to forward scattering of the products) the difference between the two angles can be quite large and hence erode much of the reactive asymmetry. Experimental results on Rb CH3192 as well as trajectory computations on the H + D27’ and K CH3193systems confirm this picture. A trajectory studyg4which isolated out the anisotropic forces via a rigid-ellipsoid modeled system also demonstrates the impact parameter effect. Understanding the reorientation during the collision is necessary both for the quantitative extraction of the angle dependence of the barrier from the measured reactive asymmetry and for the qualitative interpretation of the experiments and computations. The issue is not fully resolved, yet is at the heart of our topic. More effort is required. An important new class of experiments aimed at steric control of reagents takes advantage of orbital alignment of atomic reagents achieved by polarized laser excitation. An exampleg5of an inelastic atom-molecule collision involving orbital alignment is the study by the Hertel group of
+
Na(3p)
+ H2(u=O)
-
Na(3s)
+
+ H2(o=1,2,3)
The alignment of the Na p orbital with respect to the relative velocity vector is found to influence the outcome of the collision. Somewhat more relevant to the chemical domain is the extension of this technique to reactive encounters, made by Rettner and Zare,96as exemplified by the reaction Ca(’P,)
+ HCl
-
CaC1(B2Zt,A211) + H
Here the perpendicular ( T ) alignment of the Ca p orbital, which most favors CaCl A 2 n formation, is least effective in forming B2Zt product; the parallel ( c r ) alignment favors the formation of the B2Ef state and is least effective for producing the A211 state. Recently, Lee and co-workers have done crossed-beam studies for reactions of aligned alkali atoms with hydrogen chloride, oxygen, and nitrogen d i ~ x i d e . ~ ’With the alkali valence electron in the (90) See, for example, Kouri, D. J. In Atom-Molecule Collision Theory, Bernstein, R. B., Ed.; Plenum: New York, 1979. (91) See, for example, Mulloney, T.; Schatz, G. C. Chem. Phys. 1980,45, 213. Pack, R. T. Chem. Phys. Lett. 1984, 108, 333. (92) Parker, D. H.; Chakravorty, K. K.; Bernstein, R. B. Chem. Phys. Lett. 1982, 82, 113.
(93) Blais, N. C.; Bernstein, R. B. J . Chem. Phys. 1986, 85, 7030. (94) Janssen, M.; Stoke, S. J . Phys. Chem. 1987, 91, 5480. (95) Reitland, W.; Tittes, H. U.; Hertel, 1. V. Phys. Rev. Lett. 1982, 46, 1389. Botschwina, P.; Meyer, W.; Hertel, I. V.; Reitland, W. J . Chem. Phys. 1981, 75, 5438. (96) Rettner, C. T.; Zare, R. N. J . Chem. Phys. 1982, 77, 2416. (97) Vernon, M. F.; Schmidt, H.; Weiss, P. S.;Covinsky, M. H.; Lee, Y . T. J . Chem. Phys. 1986, 84, 5580.
Bernstein et al.
5372 The Journal of Physical Chemistry, VoL 91, No. 21, 1987
Kinematic Model
Classical Trajeclories
E, = .6 eV
.3 1
.?ll
P I
\ \ O . 2 .
.o
I
-1
-.5
0
cos(a)
J
.8
c m.
0 H+HD+H2+D 0
Classical Trajectories ..?
Kinematic Model
H+HD+HD+H
E, = .795 eV
1
1
cos(a)
cos(a)
,2L 0 H+HD-+H2+D 0
0-1
-5
H+HD+HD+H
0
CO\(:/)
Figure 4. The variation of the reaction cross section with the approach angle for the reaction of H atoms with either end,of HD a t two translational energies. Computed by using exact classical trajectories with the angles defined at the barrier (left side panels) and by using a models3 where reaction occurs for those (straight line) trajectories with enough energy to surmount the barrier (right side panels). The advantage of using the angle CY (see figure) is that the height of the barrier vs. CY is the same for both ends of the molecule. To within statistical noise, the kinematic results show no isotope effect. This is largely true also for the exact trajectories. This scaling of the exact dynamics provides an “internal” demonstration of the utility of the angle-dependent barrier to reaction. With the angle y defined with respect to the center of mass, the cone of acceptance about the D atom is wider79 for purely kinematical reasons. (Schecter, I.; Levine, R. D., to be published.)
3p, 4d, or 5s orbital, the product angular and velocity distributions k i n g orbital alignment is the issue of “orbital following”, Le., the varied markedly with the collision energy, the symmetry of the extent to which the initially selected alignment (in the lab frame) atomic state, and the alignment of the excited orbital. persists as the colliding particles approach close to one another. Involved in the interpretation of all such e x p e r i m e n t ~uti~~,~~ (98) Hertel, V. I.; Schmidt, H.; Bahring, A,; Meyer, E. Rep. Prog. Phys. 1985, 48, 375.
(99) Bahrine. A.: Hertel. I. V.: Mever. E.: Schmidt. H. 2.Phvs. 1983. A3j2,‘293. H h , M. D.; Hertel, V. 1.: Leow, S . R. Phys. Reu. Lilt. 1984, 53, 2296.
The Journal of Physical Chemistry, Vol. 91, No. 21, 1987 5313
Dynamical Aspects of Stereochemistry Under certain circumstances (strong long-range forces, low relative velocities, etc.) one can expect "orbital following", which could destroy "memory" of the prepared (precollision) alignment. The analogue of orbital following in collisions of oriented molecules, termed the "reorientation effect", has already been discussed. By preparing a Ca-HCl van der Waals adduct via a supersonic expansion one may be able to avoid some of the problems of interpretation, by eliminating the high-b collisions when Ca is electronically excited. Another important issue is that of spin-orbit effects.lW In the next section we consider the complementary aspect, the stereospecific disposition of the reaction products. It is necessary, however, to emphasize that just as studies of specificity of energy disposal can yield the selectivity of energy requirements of the reverse reaction, the same holds true for orientation."' The application of microscopic reversibility toward the extraction of steric information should enhance our knowledge of steric requirements in the entrance valley.
6. Product Analysis: Stereospecificity Beyond the angular distribution of products, the most accessible stereodynamic property is the spatial distribution of rotational angular momentum. Efforts to observe product rotational alignment by use of electric deflecting fields began early in the alkali age of reaction dynamics,lo2but success was long delayed by problems involving "reprojection" due to nonadiabatic changes in the quantization axis.lo3 The reactions first examined, such as K + HBr, produce alkali halides with quite high angular momenta, typically 100h. At feasible field strengths, the deflections produced by the second-order Stark effect thus are small, typically -0.2 mm. A dipole deflecting field (electric analogue of the StemGerlach field) hence was used rather than a multipole field, since small deflections can more readily be observed with respect to a plane than an axis. Comparison of deflection profiles obtained with the field oriented parallel (+ = 0') and perpendicular (+ = 90') to the plane of the reagent beams revealed the alignment of rotational angular momentum of the alkali halide product molecules. An intermediate profile (at = 55') corresponds to isotropic rotation. A funnel-shaped buffer field extending from the reaction zone to the deflecting field served to preserve any angular momentum alignment produced by the reaction.lo4 Reduced profiles obtained from differences and ratios of data with the buffer field on and off were shown to be insensitive to all experimental parameters except the leading coefficients in a Legendre expansion of the alignment angle distribution p(c0s x) = 1 + a2Pz(cos x) + a,P,(cos x) + ... (2) where x is the angle between the rotational angular_Tomentum and the initial relative velocity vector (Le., cos x = j'sk). In this way Hsu" et al. determined the a2 coefficient and in some cases the a4 coefficient for reactions of K or Cs with several halogen compounds. The observed rotational alignment is large for the HBr and H I reactions, substantial for Brz, CHJ, and CFJ, but very small for CC14, SF4,and SF,. In all cases, a, is negative and a4 positive, indicating the preferred alignment of j' is perpendicular to k. For the hydrogen halide reactions, strong alignment in this sense is required by essentially kinematic constraints, almost independent of dynamical properties. The main constraint is the light mass of the H atom, which prevents it from carrying much angular 1, the initial orbital momentum. Thus, for these reactions j' angular momentum associated with the approach of the reage n t ~ . ' For ~ ~ the other reactions, such kinematic constraints are
-
+
-
m u c h w e a k e r o r negligible. (100) Dagdigian, P. J.; Campbell, M. L. Chem. Reu. 1987, 87, 1. (101) Engel, Y. M.; Levine, R. D. Chem. Phys. 1984, 91, 167. (102) Herm, R. R.; Herschbach, D. R. J . Chem. Phys. 1965, 43, 2139. (103) Maltz, C.; Weinstein, N . D.; Herschbach, D. R. Mol. Phys. 1972, 24, 133. (104) Hsu, D. S. Y.; Weinstein, N. D.; Herschbach, D. R. Faraday Discuss. Chem. Sac. 1973, 55, 116. Mol. Phys. 1975, 29, 257. (105) Noda, C.; McKillop, J. S.; Johnson, M. A,; Waldeck, J. R.; Zare, R. N . J . Chem. Phys. 1986, 85, 856.
I
I
0"
30" Alignment angle,
I
I
60"
IO
x or 7
Figure 5. Distributions of rotational alignment for KBr from the K + HBr reaction. Solid curve for angle x between product rotational angulas momentum vector j'and reagent relative velocity vector k. Dashed curve for angle TJ between product internuclear axis r' and k, after uniform average over rotation about .'j Dotted curves from statistical model. All are symmetric about 90'. (Adapted from ref 104 and 106.)
Thus far we have discussed the alignment of the products' rotational angular momentum. One can also consider the alignment of the molecular axis itself. For this purpose note that the rotational alignment coefficients a, and a4 also specify the Legendre moments for the angle 7 between the internuclear axis r' of the product molecule and the initial relative velocity vector. Integrating over the molecular rotation gives (P,(COS 7)) = p m (P,(COS
x))
(3)
where the P,,(O) factor occurs because r' and j' are perpendicular. Thus the Legendre expansion for the molecular axis alignment is given by
COS 7) = 1 - y2a2P2(cos7) + 3/8a4P4(~os 7) + ...
(4)
The alignment of r' is of course poorer than that of j'. This is illustrated in Figure 5 , where we plot for the K HBr reaction the approximate distributions of cos x and cos 7 obtained from the a, and a4 coefficients. Also shown are curves derived from a statistical phase space model.lo6 Three other methods to determine these rotational alignment coefficients are now available, but not yet widely applied. For very low rotational momenta, the individual space-quantization states can be observed by electric resonance spectroscopy; this has been donelo' for the reactions of Li and Cs with SF,. For reactions producing an electronically excited molecule, the rotational alignment becomes observable in the fluorescence spectrum (provided t h e angular distribution of t h e emitting product is also anisotropic, as it usually is). For reactions giving a product molecule amenable to laser-induced fluorescence, the same holds.
+
(106) Case, D. A.; Herschbach, D. R. Mol. Phys. 1975, 30, 1537. J . Chem. Phys. 1976, 64, 4212. (107) Freund, S. M.; Fisk, G. A.; Herschbach, D. R.; Klemperer, W. J . Chem. Phys. 1971, 54, 2510. Bennewitz, H. G.; Haerten, R.; Muller, G. Chem. Phys. Lett. 1971, 12, 335. Mariella, R. P.; Herschbach, D. R.; Klemperer, W. J . Chem. Phys. 1973, 58, 3785.
5374
The Journal of Physical Chemistry, Vol. 91, No. 21, 1987
Fluorescence is surely the method of choice, since it can provide alignment data as a function of the vibrational and rotational excitation of the product molecule. The review by Simonsls discusses several nice examples from his own work and that of Zare. Thus far, Ca F2 is the only reaction for which rotational alignment has been measured for resolved product vibrational states;lo8 the alignment proved to be most pronounced for the highest vibrational levels, which correspond to the smallest release of energy into product relative translation. For reactions of excited Xe* atoms with hydrogen halides, halogens, CHJ and CC14,the product rotational alignment has been measured over a wide range of collision energy in an elegant experiment using a magnetically levitated rotor to generate accelerated molecular beams.Io9 As expected, the alignment at thermal energies is similar to that found for the analogous Cs atom reactions but it increases markedly with increase in the collision en erg^.'^^,^^^ In the future we should also expect electrostatic focusing of polyatomic products using their first-order Stark effect.”’ This procedure, which is similar to that used to orient reagents but is now being used to probe the products, will directly determine the orientation, cf. eq 1, with respect to the laboratory axis. Just as with reagent preparation, electronic orbital alignment is now accessible in product analysis. As yet such analysis has not been performed for product atoms, but a sizable body of data has been obtained for certain product diatomic molecules (mostly NO and O H with data for C H and N H probably forthcoming) which have electronic states of II symmetry. For these the rotational levels are split into A-doublet components with wave functions either symmetric or antisymmetric to reflection in the plane of rotation. Typically, the A-doublets are unequally populated and thereby offer information on the spatial distribution of electron density. In the classical limit, one can think of the two states as corresponding to the unpaired electron in a p orbital perpendicular to or coplanar with the plane of molecular rotation. (Hence the method is limited to systems with weak spin-orbit coupling.) While the information about the spatial distribution of the charge cloud pertains to the plane of rotation, it can be related to the relative velocity vectors k and k’ via the rotational alignment. The O H producing reactions of 0 + H2,@H + 02$1 and H + NO2Il2are typical examples. The latter is of particular interest because the same set of products results from the photodissociation of HONO.lI3 In general, product analysis in photodi~sociation’~ has often been spectroscopic114(with NO, as in ref 1 15, being a favorite molecule). The prime example has suggesting a coplanar been the photodissociation of H20,116,117 process. The A-doublet population asymmetry has become a very active topic, also reviewed by Simons.18 As yet, rotational alignment has been interpreted chiefly by comparison with simple reference models of impulsive118or statistica11”6character. Doubtless alignment will soon be accorded its rightful place among standard properties evaluated in classical trajectory calculations, but at present only few exploratory studies are a ~ a i l a b l e . ~Here ~ ~ *we ~ cite three cases to illustrate how the alignment complements other dynamical properties. ( 1 ) For direct interaction models which prescribe a repulsive force between the products AB C, the scattering angle and
+
+
(108) Prisant, M. G.; Rettner, C. T.; Zare, R. N. Chem. Phys. Left. 1982, 88, 271. J . Chem. Phys. 1984, 81, 2699. (109) Johnson, K.; Simons, J. P.; Smith, P. A,; Washington, L.; Kvaran, A. Mol. Phys. 1986, 57, 255. (110) de Vries, M. S.; Tyndall, G. W.; Cobb, C. I,.; Martin, R. M . J . Chem. Phys. 1986, 84, 3 1 5 3 . (1 1 1) Novakoski, L.; McClelland, G. M. Phys. Rec. Lett., in press. ( 1 12) Kinsey, J. L. J . Chem. Phys. 1984,81, 6410. Murphy, E. J.; Brophy, J. H.; Arnold, G. S.; Dimpfl, W. L.; Kinsey, J. L. Ibid. 1981, 74, 324. ( 1 13) Vasudev, R.; Zare, R. N.; Dixon, R. N . J . Chem. Phys. 1984, 80, 4863. (1 14) Greene, C. H.; Zare, R. N. Annu. Rec. Phys. Chem. 1982, 33, 119. (1 1 5 ) Lavi, R.; Schwartz-Lavi, D.; Bar, I.; Rosenwaks, S. J . Phys. Chem. 1987,91,5398. Briihlmann, U.; Dubs, M.; Huber,J. R. J . Chem. Phys. 1987, 86, 1249. ( 1 16) Andresen, P.; Ondrey, G. S.; Titze, B.; Rothe, E. W. J . Chem. Phys. 1984, 80, 2543. (117) Andresen, P.; Rothe, E. W. J . Chem. Phys. 1985, 82, 3634. (1 18) McClelland, G. M.; Herschbach, D. R. J . Phys. Chem. 1987, 91. 5509.
Bernstein et al. velocity can be calculated by specifying just the total repulsive energy released, whereas the rotational angular momentum requires in addition the repulsive force as a function of separation distance. For instance, this is readily shown for variants of the DIPR model formulated originally by Kuntz and P01anyi.l’~ If the exit AB + C interaction is weak, as in the spectator stripping model (or the mass of C is very small), such models give I j’ and thus j’ is strongly aligned perpendicular to k. This holds too for high collision energy. Accordingly, impulsive models appear consistent with the relatively strong alignment observed for the Ca + F2 case for low final translational energy and for the Xe* reactions at high collision energies. This result, which is essentially unchanged on varying the repulsive energy or introducing various forms for the orientation dependence of the reaction, arises from a Jacobian factor. The ”dart board” distribution of initial impact parameters must be projected onto a sphere of radius Rx centered on the BC molecule. A Jacobian weighting proportional to k.Rx is thereby introduced and this anisotropic factor produces the residual rotational alignment obtained at low collision energies. For the trajectory calculations currently available,75product repulsion has at least qualitatively the same role as in the DIPR model. Evidently other models or potential surface features need be invoked to account for the rotational alignment and its energy dependence. ( 2 ) The electron-jump model for alkali reactions offers another instructive case. This involves attraction between transient At and B- ions as well as repulsion of the outgoing C atom. The incipient rotation of A% then tends to be converted into orbital motion of C, since the impact parameter for approach of A+ and B- is thereby reduced.lZ0 The final product rotational alignment is thus expected to be smaller than in the conventional DIPR model, but quantitative calculations are required to evaluate this “coulomb torque” effect. (3) For statistical complex models, including both transitionstate and phase space theory, CaseIo6has given a comprehensive treatment of directional properties for an A + BC reaction. All such properties involving an angle between any pair of vectors chosen among j,j’,k,k’,r,r‘ are determined by only two dimensionless scalar parameters A = ( 1 / ( 1 + j ) ) and A’ = (l’/(l’+j’)) (5)
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which specify the mean fraction of the total angular momentum associated with relative orbital motion of the reagents and products, respectively. Since typical attractive forces make large impact 1 and then all these directional parameters dominant, often A properties are governed just by the A‘ parameter. In this regime, angular distribution and rotational alignment measurements thus become practically equivalent. For instance, the Cs H I reaction 1 and A’ 0 so the statistical model makes the angular has A distribution nearly isotropic while the rotational alignment becomes very sharp, nearly a 6 function about x = 90’. The Cs RbCl reaction has A 1 and A’ 1, so the angular distribution becomes very strongly peaked, approaching l/sin 8, whereas the rotational alignment becomes isotropic. The directional properties of the final state were also extensively studied for inelastic collisions.121 For such transitions which occur at a fairly well-defined relative distance R, one can argue that Aj is essentially perpendicular to Ak. Such would be the case when the intermolecular potential is steeply repulsive in the region where the torque is imparted. The quantitative argument is a simple one. Conservation of total angular momentum implies that for an A + BC collision Aj = -AI. With I = R X p R and assuming a localized transition 41 N R X PAR or
-
-
-
+
-
Aj = -R X p A R
+
(6)
In the model of an orientation-dependent barrier to reaction, the “transition” from reactants to products is also well localized and ( I 19) Kuntz, P. J.; Mok, M. H.; Polanyi, J. C. J . Chem. Phys. 1969, 50, 4623. (120) Birely, J. H.; Herschbach, D. R. J . Chem. Phys. 1966, 44, 1690. (121) McCaffery, A. J.; Proctor, M. J.; Whitaker, B. J. Annu. Rec. Phys. Chem. 1986, 37, 223.
Dynamical Aspects of Stereochemistry
The Journal of Physical Chemistry, Vol. 91, No. 21 1987 5375 ~
0 + HClCj) + OH + C1
I
m
I 1
I !&= 1.0 eV
-1
0
I -1
l
(AJ,Ak)
(Aj.Ak)
Figure 6. Results frcm-a kinematic model (as discussed in ref 83) for the distribution of Aj-Ak for the 0 HCIU) reaction. The preference for Aj to be orthogonal to Ak is evident. For this mass combination, AjeAk a j.R. At low ET,only collinear low-impact parameter collisions are reactive, hence R-j u 0. At higher ET,the cone of acceptance opens up so that reactive trajectories are possible at higher I’s with the result that k need not be directed along the HCI axis and hence trajectories with-j-t # 0 can be reactive. The increasing width of the distribution of Aj-Ak with increasing ET is thus a direct reflection of the increasing cone of acceptance. (Schecter, I.; Levine, R. D., to be published.)
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one can compute both AR and at the barrier.83 The case most similar to an inelastic collision is a light atom transfer where AR 0 and 1.1 1.1’ so that MAR Ak. Kinematic model computations of Aj-Ak for the 0 HCI reaction are shown in Figure 6 . The alignment of Aj with respect to the Ak axis is clear. Model calculations have also pointed to more incisive probes of product stereodynamics that can be obtained by simultaneous measurement of two or more angles. The prototype of such probes is the triple vector correlation (k,k’,j’), which involves both the scattering angle 0 and the rotational alignment angle x. In principle, this vector correlation offers a means to undo the “dart board” averaging over the random azimuthal orientations of initial impact parameters. The distributions of both k’ and j’ must have azimuthal symmetry about k, but when a subset is selected of k’ vectors with particular j’ (or vice versa), this subset in general will not have azimuthal symmetry about k. The three-vector correlation has been evaluated for both the impulsive DIPR model”* and the statistical phase space theory.lo6 Both give pronounced azimuthal asymmetry with the same sense: j’ prefers to be perpendicular to the k,k’ plane. This preference which can be understood on the basis of kinematic consideration^^^ has also appeared in classical trajectory75and quantum scattering calcul a t i o n ~ .In ~ ~an electric deflection study of the Cs + CHJ reaction,+ even quite crude resolution of the scattering angle was found sufficient to reveal the azimuthal asymmetry.122 In-addition to the rotational alignment coefficient, equivalent to ( (’j’-k)2), this experiment gave just one more parameter, a rotational projection coefficient equivalent to ( (j‘-kxk’)2). The impulsive and statistical models predict much different values for both these quantities. The observed alignment is much larger than the impulsive result but close to the statistical value; the projection is close to the impulsive result and much larger than the statistical value. Another prototype is the Ba + oriented N 2 0 chemiluminescence experimentsg which likewise gives two moments for the (r,k,j’) correlation. Far more information is in prospect from crossed-beam experiments using laser-induced fluorescence detection. A theoretical
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‘Note that the password suggested by John Simons at the end of his ballad is only approximate. As evident particularly from the original angular distribution, reactive asymmetry, and three-vector correlation experiments, the correct password is methyl iodide! (122) Hsu, D. S. Y.; McClelland, G. M.; Herschbach, D. R. J . Chem. Phys. 1974, 61, 4927.
analysis’23has shown that data for several choices of quantization axis and polarization modes can be combined to determine 12 independent moments involving Cartesian components of j’ up to rank four; 8 are even and 4 odd with respect to reflection in the k,k’ plane. That is an encouraging prospect, even if obtaining all 12 moments might bear comparison with the fabled labors of Hercules! In summary, we are blessed with such a profusion of stereodynamical parameters that a systematic approach has become essential. The theory of “angular correlations” as developed in particular by the nuclear theorists’24and further elaborated upon in atomic p h y s i ~ s ’ ~is~particularly ,’~~ suitable for our needs. It enables the results from many types of experiments to be treated in the same way. For instance, a measurement of the polarization direction for an emitted photon may be treated as analogous to a measurement of the flight direction of a product particle. All collision experiments in which only two vectors are observed then belong to the same class, termed direction-direction or simply two-vector correlations. These are each governed by a single, invariantly defined angle between the two vectors; all other angles are unobserved or random and are averaged over. Legendre polynomials provide natural expansion functions and various experimental situations are classified according to which Legendre moments can be determined. All experiments in which three vectors are observed belong to a higher class, termed triple-angle or three-vector correlations. For these an unambiguous prescription requires two polar angles and one dihedral angle, and suitable expansion functions are constructed from rotationally invariant combinations of spherical harm0ni~s.l~~ The general formalism becomes simplest when all vectors, quantized or not, are considered classical, and statistical theory is employed to average over unobserved angles and magnitudes in computing moments of the correlations. This approach has been worked out for an A BC reaction up to and including the four-vector correlation (j,k,k’J’), in optimistic anticipation.128 This correlation of course contains even more information than found in the six two-vector and four three-vector correlations involving pairs or triads of the four vectors. Such information includes the azimuthal asymmetry with respect to both k and k’, the preferred rotational orientation of both the reagent and product molecules with respect to the k,k’ plane, and even the relative sense of rotation (parallel or contrary). Several averages implicit in lower order correlations are thus “undone”. It no longer seems far-fetched to suppose that at least some moments of a four-vector correlation will soon be measured.
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7. Perspectives The Jerusalem workshop on dynamical aspects of stereochemistry ushered in a new era of chemical dynamics, in which the emphasis is on spatial requirements for reactive reagents and spatial relationships among nascent products. However, the balance of attention at the workshop was heavily weighted toward the second of these, namely vector correlations involving products of halfcollisions. There has been considerable activity in the area of polarized laser photofragmentation with polarized laser-induced fluorescence detection (for product angular momentum alignment measurement).’* In the future, the use of circularly polarized laser light for the pumping of reagents to produce orientation (not (123) Case, D. A,; McClelland, G. M.; Herschbach, D. R. Mol. Phys. 1978, 35, 541.
(124) Biedenharn, L. C.; Rose, M. E. Rev. Mod. Phys. 1953, 25, 729. Biedenharn, L. C . In Nuclear Spectroscopy, Ajzenberg-Selove, F., Ed.; Academic: New York, 1960; part B, p 732. (125) Fano, U.; Macek, J. H . Reu. Mod. Phys. 1973, 45, 533. (126) Fano, U.; Rau, A. R. P. Atomic Collisions and Spectra; Academic: New York, 1986. Kleinpoppen, H., Williams, J. F., Eds., Coherence and Correlation in Atomic Collisions; Plenum: New York, 1980. (127) Yutsis, A,; Levinson, I . B.; Vanagas, V. V. Theory of Angular Momentum; Israel Program for Scientific Translarions: Jerusalem, 1962; p 31. (128) Barnwell, J. D.; Loeser, J. G.; Herschbach, D. R. J . Phys. Chem. 1983, 87, 2781.
5376 The Journal of Physical Chemistry, Vol. 91, No. 21, 1987
just alignment) is likely to make laser “pump and probe” bulk experiments a rich source of stereodynamical information. We can also expect much more emphasis on real-time (picosecond and femtosecond) e x p e r i m e n t ~ lin~ ,which ~ ~ ~ the excited, aligned molecules are studied while in the process of dissociation to yield spatially and temporally correlated products. But such controlled experiments have rarely been carried out for full collisions, Le., bimolecular reactions of oriented molenew development in this direction is the c u l e ~ . ~An* ~important ~~ technique of “precursor geometry-limited” (PGL) photoinitiated bimolecular reactions.mz Very recently Wittig and wworkersIN were able to detect and characterize both O D and S D nascent products from the PGL reaction of D OCS (from the BrD-0CS precursor van der Waals molecule). It appears that orientation effects in many bimolecular hot-atom reactions can be readily studied by this PGL technique. A bridge from unimolecular to bimolecular stereodynamics can now be built through the use of such van der Waals complexes as precursor molecules providing a restricted range of initial configurations for the bimolecular hot-atom reactions. The first example comes from the work of Zewail and co-worker~.’~’Using a picosecond laser pulse to photodissociate the H I in a beam of IH-.OCO molecules and a delayed picosecond laser probe of the OH product, they were able to clock the formation and decay of the HOCO reaction complex in the reaction H + C 0 2 HOCO OH CO. The first pulse establishes the zero of time for the bimolecular reaction, and then real-time evolution of correlated products can be observed. Thus we are rapidly approaching the “ideal” experiment in which one makes use of prepared states of oriented reagents and measures the time development of the asymptotic product state (and orientational) distribution. Another bridge, from gas-gas collisions to gas-surface dynamics, has been constructed and is now being traversed. The directionality of forces in the scattering of an atom or molecule from a metal surface is being probed by measurements of the angular d i s t r i b u t i ~ n and l ~ ~ both the rotational alignment133and the ~ r i e n t a t i o n ’of~ ~the scattered molecules. What about the theoretical and computational approaches to stereodynamics? Thus far, most of the computational studies have used the quasi-classical trajectory method with Monte Carlo selection of initial conditions. Very many trajectories must then be run to generate the detailed distributions of interest. When it comes to three- or four-vector correlations, the Monte Carlo sampling error soon becomes prohibitive, requiring an ever-increasing number of initial conditions to reduce the statistical uncertainty to acceptable limits. In the future we can expect this problem to be overcome using one of several alternatives. For example, importance sampling135will replace the random Monte Carlo selection so as to reduce the total number of trajectories required for a given statistical accuracy. Nor is it necessary to generate the actual distribution. Theory should mimic experiment and compute directly the parameters of interest, such as the alignment coefficients in eq 2. We should also recognize the possibility that a quantum mechanical treatment can now be computationally attractive. In the short run, perturbation t h e ~ r y ~or~ sudden-type13’ ,’~~ approximations will prove useful. Both have the advantage that their results can be readily factored into purely kinematic and dynamical contributions. The importance of the entrance and exit “cones” in governing the stereodynamics implies that exact and approx-
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(129) Dantus, M.; Rosker, M. J.; Zewail, A. H. J . Chem. Phys. 1987,87, 2395. (130) Hausler, D.; Rice, J.; Wittig, C., to be published. (131) Scherer, N. F.; Khundkar, L. R.; Bernstein, R. B.; Zewail, A. H. J . Chem. Phys. 1987, 87, 1451. (132) Barker, J . A.; Auerbach, D. J. Surf. Sci. 1984, 4 , 1 . (133) Kleyn, A . W.; Luntz, A. C.; Auerbach, D. J. Surf. Sci. 1985, 152/153, 99. (134) Sitz, G. 0.;Kummel, A. C.; Zare, R. N. J . Chem. Phys., in press. (135) Faist, M. B.; Muckerman, J. T.; Schubert, F. E. J . Chem. Phys. 1978, 69, 4087. (136) Schatz, G . C.; Amaee, B.; Connor, J. N. L. Chem. Phys. Letr. 1986, 132, 1. (137) Baer, M.; Nakamura, H. J . Phys. Chem. 1987, 91, 5503.
Bernstein et al. imate dynamics, based on reaction-path H a m i l t o n i a n ~ , ’ ~will ~.’~~ prove particularly useful. This will also pave the way for a dynamical approach to larger systems. Theory will also continue to have a role in the design of experiments. The selection of initial states using laser pumping2] and the laser probing of final states all require proper analysis.’* The exuberant proliferation in stereodynamic processes and parameters now becoming accessible calls for a comprehensive quantitative viewpoint that brings out common features. For this purpose, the angular correlation formalism offers a welcome paradigm, literally suited to discussing all angles of stereodynamics. Underlying the theory of angular correlations is a density matrix f o r m a 1 i ~ m . I ~In~principle, the relevant parameters can be computed from a dynamical theory. In such an approach, only that which is not “averaged-over” need be computed. Ultimately, this should be the method of choice for dealing with high-resolution experiments. Coherent rotational statesl4I will provide for a time-dependent wave-packet descriptionk4*of stereodynamics. Equally important is the goal of understanding dynamical stereochemistry, i.e., explaining the main observed effects and predicting new ones. In the absence of extensive ab initio mapping of the potential energy surface, we must learn to take full advantage of the force fields provided by molecular mechanicsk and of a limited map of the surface in the neighborhood of the reaction coordinate as provided by gradient methods, whether ab initio or semiempirical. For these larger systems, simple extensions beyond transition-state theory proper may be all that is required. (In strict TST, there is no reagent state selection; one can, however, relax this condition.) More generally, the reaction-path Hamiltonian139can be used. The stochastic Langevin type of equations used’43to mimic the influence of the solid or liquid (the “bath”) will also prove useful for approximately incorporating the “rest” of the molecule when limiting attention to a few degrees of freedom that are strongly coupled during the reaction. Alternatively, and as in nuclear physics, time-dependent self-consistent field theory’44 can be used. (In particular, S C F techniques can be used to compute directly the parameters in a density matrix approach.) We must both provide a framework for thinking about new experiments and quantifying their results and, most important, forge a link with the traditional ideas on the role of steric effects in chemical reactivity. In pursuing dynamical aspects of stereochemistry, the kinship of scientist and artist becomes especially evident. Not only are we working with spatial relationships (which often almost elude our visualization!), but we must likewise explore general phenomena by treating particular instances. This fosters profuse variety in technique, style, and cultural context, as amply displayed at the Jerusalem workshop. In commenting on future perspectives, we emphasize that a field so broad and eclectic as stereodynamics must be approached from every feasible angle! Yet we stress also that this field needs and provokes creative tension at the intersection of chemistry and physics. (Also exhibited in some lively Jerusalem discussions.) The chemist wants above all to understand why one substance behaves differently from another; the physicist wants to find disembodied principles that transcent the specific substances. Both these cultural outlooks are essential for reaction dynamics. The experimental repertoire has now widened enough to provide chemical scope for stereodynamics. This calls for more vigorous pursuit of electronic structure studies, qualitative as well as quantitative. In structural chemistry, ab initio calculations typ-
(138) Hofacker, G. L. 2. Naturforsch. 1963, 189, 607. Marcus, R. A . J . Chem. Phys. 1966, 45, 4493, 4500. Hofacker, G.L.; Levine, R. D.Chem. Phys. Lett. 1971, 9, 617. (139) Miller, W. H. J . Phys. Chem. 1983, 87, 381 I . (140) Devon, S.; Goldfarb, L. J. B. Encyclopedia of Physics, Vol. XLII; Springer-Verlag: Berlin, 1975; p 362. (141) Kais, S.; Levine, R. D. J . Phys. Chem. 1987, 91, 5462. (142) Heller, E. J. Acc. Chem. Res. 1981, 14, 368. (143) Adelman, S. A . Adu. Chem. Phys. 1980, 44, 143. Tully, J. C.Acc. Chem. Res. 1981, 14, 188. (144) Ratner, M. A,; Gerber, R. B. J . Phys. Chem. 1986, 90,20.
The Journal of Physical Chemistry, Vol. 91, No. 21. 1987 5311
Dynamical Aspects of Stereochemistry
1
Figure 7. "The Poplars", by Claude Monet ( 1 890). upper panel (slightly truncated on right side). Lower panel shows detail at close range (ca. 5% coverage).
ically are more reliable for geometric than for energetic aspects; this may well hold also for some dynamical properties. But we must overcome the prevalent tendency to "wait for our quantum chemist friends to do better". Qualitative electronic structure ideas have proven extremely fruitful in the study of many stereochemical questions, as exemplified especially by the work of Woodward and H ~ f f m a n n . ' ~Particularly ~ inviting are new possibilities to exploit orbital alignment tests of propensity rules for reaction. The contrast in sophistication between an elegant experiment and a lowbrow electronic structure interpretation of it may seem incongruous. Such interpretations deserve more attention from dynamicists, however, since electronic structure offers the surest (145) Woodward, R. B.; Hoffmann, R. The Conservation of Orbital Symmetry; Verlag-Chemie: Weinheim, 1970.
guide to chemical correlations or predictions. Because directionality is an almost universal property of chemical interactions, we can expect that many stereodynamical features elucidated in the single-collision domain will appear also for, reactions in condensed phases or at interfaces or even at the active sites of enzymes. If this prospect seems visionary, we point again to conformational analysis,'*2 which exemplifies the remarkable scope of geometrical constraints in synthetic chemistry and biochemistry. Surface science already offers compelling new opportunities. These include an analog of the "precursor geometry-limited" technique, in which photochemically induced surface reactions are studied with reagents prealigned by crystal forces.'& This can exploit recent advances that enable the geometrical configuration of adsorbed molecules to be determined by means of the polarization dependence of near-edge X-ray ~cattering.'~' Other far-reaching new capabilities are emerging from the scanning tunneling microscope,'48particularly a version that makes it possible to measure interatomic forces dire~t1y.I~~ This device is now being used to study the molecular dynamics of friction, with subatomic resolution in both magnitude and direction of the forces, as a tungsten probe is dragged across a graphite surface.'50 Beyond enlarging the scope of dynamical stereochemistry, such enterprising new methods provide means to pursue a further, distant goal of chemical science: the ability to predict, tailor, and control the reaction rate as well as the yield. Like the kindred quest of the ancient alchemists, this may be unattainable; yet only a modest enhancement in control could have profound consequences. The Jerusalem meeting closed with a metaphorical comment, which we illustrate here with Figure 7. Chemistry is like an impressionistic painting. If we view it from too close, all we see is puzzling detail in myriad dabs of paint. If we look from too far, all we see is a shimmering blur. (Some physicists tend to stand too close, some biologists too far away.) At the right distance, wondrous and lovely things appear. We can strive to make that happen as we abstract from a host of experiments and calculations some basic facts and insights about dynamical stereochemistry.
Acknowledgment. We thank the Academic Council (Chairman: Prof. M. Yaari) and staff of the Institute for Advanced Studies of the Hebrew University (Director: Dr. S. Gairon) and the Scientific Council (Chairman: Prof. E. W. Schlag, Munich) and staff of the Fritz Haber Research Center for Molecular Dynamics (Director: Dr. I. Schechter) for their many contributions toward making this workshop possible. Acknowledgment is also due to the U.S.-Israel Binational Science Foundation (BSF), Jerusalem, Israel for travel support for some of the American participants. The Fritz Haber Research Center is supported by the Minerva Gesellschaft fur die Forschung, mbH, Munich, BRD. R.B.B. and D.R.H. gratefully acknowledge research support from the National Science Foundation (Grant No. CHE-86- 15286 and 86-04382, respectively). (146) Polanyi, J. C. Science 1987, 236, 680. (147) Stohr, J.; Jaeger, R. Phys. Rev. 1982,B26,4111. Friend, C. M. Acc. Chem. Res., in press. (148) Binnig, G.; Quate, C. F.; Gerber, Ch. Phys. Rev. Lett. 1986,56,930. (149) McClelland, G. M.;Erlandsson, R.; Chiang, S. Rev. Prog. Quant. Non-Destruct. Eval. 1987, 6B, 1207. (1 50) Mate, M.; Erlandsson, R.; McClelland, G. M.; Chiang, S. Phys. Rev. Lett., submitted for publication.
