The chemical shape of molecules: an introduction to dynamic

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J. Phys. Chem. 1990. 94, 8872-8880

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FEATURE ARTICLE The Chemical Shape of Molecules: An Introduction to Dynamlcal Stereochemistry R. D. Levine The Fritz Haber Research Center f o r Molecular Dynamics. The Hebrew University, Jerusalem 91 904, Israel, and Department of Chemistry and Biochemistry, University of California, Los Angeles, Los Angeles, California 90024-1569 (Received: June 5, 1990)

The steric requirements of activated atom exchange reactions are examined in light of the detailed information becoming available from experiments and simulations. The results are interpreted in terms of the physical shape of the molecule, which governs the ability of the reagents to reach the barrier, and the chemical shape, Le., the barrier location as a function of distance and orientation. These two shapes can be probed by varying the initial conditions and/or via isotope effects. The discussion begins with the simplest model, where both shapes are equivalent and spherical, which suffices to discuss the main feature, namely, the orientation dependence of the reactivity. Refinements are then introduced to account for orientation/disorientation of the reagents en route to the barrier, the enhancement/decline of the cross section upon rotational and/or vibrational excitation and branching ratios.

I. Introduction Dynamical stereochemistry seeks to determine the chemical shape of molecules. That is, how does its reactivity depend on the direction of approach and distance of the other reagent. As is only to be expected, the chemical shape depends not only on the molecule itself but also on the other reagent, a C12 molecule presents a different shape to an H vs a CI atom. Molecules have also a more “physical” shape, being that of a hard sphere in the zeroth approximation. Beyond that it can be regarded as a “hard elipsoid” or even a “space filling’’ model. At the end of our road we shall have to conclude that the physical and chemical shapes need to be distinguished and that it is the interplay between the two that accounts for much of the detail provided by experiments and computational studies. In the beginning, however, we shall not attempt to make this distinction. Our zeroth approximation will thus regard the molecule as a hard sphere, where only a region on the surface is reactive, defining the “cone of reaction”. We begin therefore with the idea of a steric hindrance: A bulky atom or group is “in the way“ so that there are directions of approach that are nonreactive. The first experiments that provided a direct demonstration of this idea were carried out quite some time ago.ls2 These involved the CH31 molecule oriented by using an inhomogeneous electric field.3 The reactivity upon collision with Rb was markedly lower for an unfavorable orientation when the alkali-metal atom approaches the CH3 group. It required further experiments and improved data analysis to conclude that much more detail can be p r o ~ i d e d . ~For . ~ example, for the Rb + CH31 reaction, while there is a “cone of no reaction” about the CH3 group, Figure 1 ,6 the reactivity within the cone for reaction does depend on the approach angle. This review provides the essentials of our understanding of such phenomena. Two recent conference proceedings7~*provide much additional material. In particular, the important role of lasers (pointed out early on9) both for the preparation of the initial state and for the ( I ) Beuhler, R. J.; Bernstein, R. B.; Kramer, K . H. J . A m . Chem. SOC. 1966, 88. 533 1 ,

( 2 ) Brooks, R. P.; Jones, E. M . J . Chem. Phys. 1966, 45, 3449. (3) Bernstein, R . B. Chemical dynamics via molecular beam and laser techniques; Clarendon Press: Oxford University, New York, 1983. (4) Parker, D. H.; Bernstein, R . B. Ann. Reo. Phys. Chem. 1989, 40, 561. ( 5 ) Stolte, S. Ber. Bunsen-Ges. Phys. Chem. 1982, 86, 413. (6) Parker, D.H.; Chakravorty, K. K.; Bernstein, R. B. J . Phys. Chem. 1981, 85, 466. ( 7 ) Dynamical Stereochemistry. J . Phys. Chem. 1987, 9 / , (21). (8) Orientation and Polarization Effects in Reactive Collisions. J . Chem. Soc.. Faraday Trans. 2 1989, 85, (8). (9) Zare. R. N . Ber. Bunsen-Ges. Phys. Chem. 1982, 86, 422

0022-3654/90/2094-8872$02.50/0

probing of the final state is well documented therein. We shall therefore consider in some detail the stereochemical information provided by studies of the role of reagent rotational and vibrational excitation, for not necessarily aligned molecules. In particular, we shall agree with the early indicationsl*12 that varying reagent rotation is an important diagnostic tool. Before we get down to details it is worthwhile perhaps to comment on the quite recent growth of interest in dynamical stereochemistry. There has been, of course, a considerable and systematic improvement in our understanding of the dynamics of chemical reactions.I3-l6 Much of that earlier work has, however, been influenced by the way a physicist would approach the problem. That is, attention has been centered on such variables (initially, the direction and later the magnitude of the linear momentum of relative motion,I3J4internal quantum numbers;15 more recently, internal vector quantities”*’*)that will be conserved in the absence of the collision. Dynamical stereochemistry, together with a number of other new initiatives, asks more chemical type of questions. In particular, and as will be discussed in some detail below, dynamical stereochemistry can provide useful insights and even quantitative estimates of the shape of the potential energy surface. On the other hand, it is necessary to relate those variables that are of direct chemical interest (e.g., the angle of attack) to the physicists’ type variables that the scattering experimentalist can control. Indeed, as will be discussed, much of the current efforts in this field is directed toward the understanding of the relation. An important development has been the class of exp e r i m e n t ~ ’where ~ * ~ ~the approach geometry is constrained via the preparation of a van der Waals precursor. Such experiments use the anisotropy of the longer range forces, a source of complication in the scattering experiments, to limit the initial geometry. (10) Dispert, H. H.; Geis, M. W.; Brooks, P. R. J . Chem. Phys. 1979,70, 53 17. ( 1 I ) Muckerman, J . T. In Theorerical Chemistry, Theory of Scattering: Papers in Honor of Henry Eyring, Henderson, D., Ed.; Academic Press: New York, 1981. (12) Hodgson, B. A.; Polanyi, J . C. J . Chem. Phys. 1971, 55, 4645. ( I 3) Herschbach, D. R. Angew. Chem., Inr. Ed. Engl. 1987, 26, 1221. ( I 4) Lee, Y . T.Science 1987, 236, 793. ( I 5 ) Polanyi, J . C . Science 1987, 236, 680. (16) Levine, R. D.; Bernstein, R. B. Molecular Reaction Dynamics and Chemical Reactivity; Oxford University Press: N e w York, 1989. (17) Houston, P. L. J . Phys. Chem. 1987, 91, 5388. (18) Simons, J. P. J . Phys. Chem. 1987, 9 / , 5378. (19) Hausler. D.; Rice, J.; Wittig, C. J . Phys. Chem. 1987, 9 / , 5409. Shin, S. K.; Chen, Y.; Oh, D.; Wittig, C . Philos. Trans. R. SOC.London, A. (20) Jouvet, C.; Boivineau, M.; Soep, B. J . Phys. Chem. 1987, 91, 5416.

0 1990 American Chemical Society

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The Journal of Physical Chemistry, Vol. 94, No. 26, 1990 8813

150,

180-

Figure 2. Polar plot of the (relaxed; cf. ref 33) H + H2potential energy surface. Each point represents the potential for an H atom at a given distance and angle of attack (with respect to the center of mass) with respect to an H2 molecule. In such a relaxed plot the H2 distance is allowed to vary so that the molecule can adjust its bond length to the presence of the nearby H atom.

I'C"

/

I20

"1-

90

60

Figure 1. Polar plot presentation of the probability for the R b + CHJ reaction for backscattered products vs the angle of attack with respect to the center of mass. Adapted from ref 38. Note the cone of no reaction about the CH,group and the variation of the measured reactivity (dots) with the angle of attack.

In this article we center attention on the approach motion to the chemical barrier to reaction. It follows, however, from microscopic reversibility that an equally useful source of stereochemical information is available by probing (e.g., the polarization of) the products as they recede from the barrier.17 This is particularly so for "half-collision" experiment^^^,^'-^^ which photodissociate a stable molecule. Here the initial unbound state has a Franck-Condon limited geometry. It would be particularly interesting to pursue such experiments with the stable molecule (or ion23)not in its ground vibrotational states2*This can provide much additional needed information on the stereochemical role of internal excitation. 11. The Angle-Dependent Barrier to Reaction Simple considerations of electronic structure suggest and detailed computations verify that the height of the potential energy barrier to reaction can depend on the approach angle.'6*24-27As an example, consider the H H2 exchange reaction. The lowest barrier is for a collinear approach. That does not, however, imply that reaction is not possible for an off-collinear geometry. It only means that the barrier to reaction is higher for such collisions. A polar plot of the H H2 potential is shown in Figure 2.28 The rise of the barrier with the approach angle is evident. One can also think of this increase as the potential energy for the bending motion H3 (with the interatomic distances of the saddle point on the potential energy surface). Much of the interpretation is based on the following simple idea: reaction occurs whenever the trajectory can cross this angle-dependent barrier. This criterion has long been used in collision t h e ~ r y 'and ~ , ~can ~ be used in a transition-state theory context.30 What this means is that the reactivity for different orientations is a direct measure of the angle-dependent barrier to r e a ~ t i o n . ~ ' Note, however, that we are talking of the orientation at the barrier,

+

+

(21) Zewail, A. H. J. Chem. Soc., Faraday Trans. 2 1989, 85, 1221. (22) Qian, C.; Reisler, H. In Advances in Molecular Vibrations and Collision Dynamics; Bowman, J. M., Ed.; JAI Press: London, 1990. (23) Goursaud, S.;Sizun, M.; Fiquet-Fayard, F. J . Chem. Phys. 1976,65, 5453. (24) McDonald, J . D.; Le Breton, P. R.; Lee, Y. T.; Herschbach, D. R. J . Chem. Phys. 1972, 56. 769. (25) Carter, C. F.; Levy, M. R,; Grice, R. Faraday Discuss. 1973,55,357. (26) Mahan, B. H. Arc. Chem. Res. 1975, 8, 5 5 . (27) Proserpio, D. M.; Hoffman, R.; Levine, R. D. J. Am. Chem. Soc., in press. (28) Schechter, 1.; Kosloff, R.; Levine, R. D. Chem. Phys. Letr. 1985, 121,

-_

797. .

(29) Smith, 1. W. M. Kinerics and dynamics of elementary gas reactions; Butterworths: London, 1980. (30) Jellinek, J.; Pollak, E. J. Chem. Phys. 1983, 78, 3014. (31) Levine, R. D.; Bernstein, R. B. Chem. Phys. Leu. 1984, 105, 467.

which need not be the same as that of the initially prepared reagents. As is to be expected on physical grounds,32the assumption that trajectories that cross the angle-dependent barrier to reaction do not recross back to the reactants region is quite accurate at lower collision energies. At energies significantly above the barrier we find that some recrossing occurs.33 However, for many applications no recrossing is a realistic first approximation, which will fail at lower energies for exoergic reactions with an earlier barrier (e.g., F + H234),where the trajectories reach the inner hard core (cf. Figure 2) at higher than their initial collision energy. model^^^.^^ that consider the motion along the reaction coordinate can, of course, avoid making the assumption of no recrossing. To compute a reaction cross section for use in scattering experiments, we need to relate the distribution of approach angles at the barrier to its form for the well-separated reagents. It is here that complications of two kinds arise. The first type can be exactly overcome, but it does complicate the interpretation. Consider, for simplicity, the collision of an atom with a diatomic molecule. The orientation of the molecule is specified in terms of the angle it makes with the z axis. Say the initial relative velocity is along the z axis and for simplicity let us even neglect the intermolecular potential en route to the barrier so that the physical shape is that of a hard sphere. Up to the barrier the relative motion is then a straight line. At zero impact parameter ( b = 0), the atom meets the molecule at its initial orientation angle. Not so, however, for finite impact parameters. Since the azimuthal angle of the molecule (for rotation around the z axis) is random, at any finite b there is an entire range of attack angles that correspond to a given initial orientation angle. The higher the impact parameter, the wider is the range of attack angles sampled for a given initial orientation angle. Computing the cross section as a function of the distribution of angles at the barrier (cf. eq 2) is therefore simpler than computing the cross sections vs the experimental angle of orientation. Semiquantitatively, we expect for direct reactions a correlation between the scattering angle of the products and the initial impact parameter. While the relation is not one-to-one, forward scattering is usually associated with larger impact parameters. Our considerations above suggest that experimentally the effects of initial reagent orientation will be most evident for backward-scattered products and will diminish for more forward ~ c a t t e r i n g . This ~~ purely kinematic and strictly apparent loss of stereoselectivity has indeed been observed.38 The kinematic relation between the experimental angle of orientation and the theoretically useful concept of angle of attack can be analytically worked out.39 In practice, we often use a (32) Pechukas, P. Ann. Rev. Phys. Chem. 1981, 32, 159. (33) Schechter, 1.; Levine, R. D. Int. J . Chem. Kiner. 1986, 18, 1023. (34) Pollak, E.; Levine, R. D. J . Phys. Chem. 1982, 86, 493. (35) Miller, W. H. J . Phys. Chem. 1983, 87, 3811. (36) Mayne, H. R. Chem. Phys. Lett. 1986. 130, 1249. Harrison, J. A.; Isakson, L. J.; Mayne, H. R. J . Chem. Phys. 1989, 91, 6906. (37) Schechter, 1.; Levine, R. D. Chem. Phys. Lett. 1988, 153, 527. (38) Parker, D. H.; Chakravorty, K.K.;Bernstein, R. B. Chem. Phys. Lett. 1982, 68, I .

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The Journal of Physical Chemistry, Vol. 94, No. 26, 1990 10

El = O 5 5 e v

Figure 3. Construction showing that for a spherical barrier of radius d,

the component of the initial velocity that is perpendicular to the barrier is L' sin 9,where cos 9 = ( b / d ) .

Monte Carlo sampling of initial conditions40to generate the required distribution of attack angles at the barrier. Suitable averaging is also required when the physical shape of the molecule is approximated not as a hard sphere but, more realistically, as a hard e l i p ~ o i dand, ~ ~of~ course, ~ when the exact location of the barrier is used.40 The rather sudden onset of chemical forces is evident in Figure 2 and serves to justify the neglect of the potential en route to the barrier. In this approximation it is only kinematic transformations which relate the initial, experimental, distribution of reactants to their distribution at the barrier (which determines the reactivity). This simple (albeit useful) approximation is no longer quite valid when we recognize that molecules also have a physical shape that need not be isotropic. The second complication is correlating the initial orientation and the distribution at the barrier is the anisotropic nature of the potential en route to the chemical barrier. This applies to both the intermediate- (i.e., chemical) and long-range (Le., physical) intermolecular potential. Such anisotropy will tend to dynamically reorient the reactants during the approach motion to the barrier. Under many conditions of practical interest, the motion to the barrier is quite sudden with respect to the rotation and hence, in a zeroth approximation, this reorientation can be neglected. It cannot be overlooked if either one (or more than one) of the following is the case: (i) very slow approach to the barrier (i.e., for energies just above threshold); (ii) a faster than usual rotation (Le., for rotationally excited reactants); (iii) for intermolecular potentials that are markedly anisotropic in the region en route to the barrier (and such can also be the case due to mass effects as is discussed below). In the extreme limit of strong anisotropic forces (as, e.g., for ion-molecule collisions) and particularly so at low collision velocities44 an adiabatic approximation is more realistic. Here, at every separation R , the reactants fully adjust their orientation to the ansitropy of the potential. The dynamical approach of section IV includes both the sudden and the adiabatic approximations as limiting cases. 111. Kinematic Models The steric requirements of an activated chemical reaction are determined by the orientation dependence of the barrier to reaction. In the absence of recrossing of the barrier, computing the cross section as a function of this orientation is quite simple.16 Kinematic models relate this differential cross section, da/d cos 7,to the differential cross section in terms of the precollision

COS(y) Figure 4. Cross section vs the angle y of crossing the barrier for the H

+

D, reaction at two collision energies. Adapted from ref 33. Each plot shows the cross section for crossing the barrier (label C) irrespective of whether the trajectories do or do not proceed to form products and the (smaller) cross section for crossing the barrier and exiting as a product. The location of the barrier is a t the crest seen in Figure 2. distribution of reactants by neglecting the potential enroute to the barrier. This is not unreasonable for nonpolar reagents due to the short range of the chemical forces outside the barrier, Figure 2. The simplest model in this class is when the location of the barrier can be approximated as a sphere around the reactants. This is just the 1918 vintage hard-spheres line-of-centers model with one, ca. 1932, m ~ d i f i c a t i o n :The ~ ~ height of the barrier is allowed to depend on the attack angle y. The kinetic energy for motion perpendicular to the barrier is (cf. Figure 3) ET(1 - b*/&). Here ET is the initial kinetic energy, b is the impact parameter, and d is the radius of the barrier. Reaction is possible for all impact parameters such that ET(1 - b 2 / & )

(1)

where E o ( y ) is the barrier height for the attack angle y. If b,(y) is the maximal impact parameter for reaction (Le., the value of b for which equality obtains in ( I ) ) , then the corresponding reaction cross section is, for ET 1 E o ( y )

The dependence of the cross section on the attack angle as given by (2) has been verified by a number of trajectory computations (e.g., ref 33). A more detailed implication of (1) is that at every impact parameter b, the reaction probability P(b) (the so-called opacity function) satisfies P(b) =

- cos ? ( b ) )

f/2(1

where16 T(b) is that angle for which an equality holds in eq I . Some computational studies46 of this more detailed result have found it not quantitative. This is due, in part, to reorientation en route to the barrier. By taking y to be the angle at the barrier, as it is meant to be, we found the result valid provided P ( b ) is interpreted as the probability for crossing the barrier. At higher energies, where recrossing is possible, the reaction probability is indeed lower.33 Recrossing is particularly important for those orientations, (collinear for H + H2), where the translational energy across the barrier is maximal, Figure 4. Next we consider, as a particular example, the reaction

(39) Grote. M.; Hoffmeister. M.; Schleysing, R.; Zerhau-Dreihofer. H.: Loesch, H. J . In Selectivity in Chemical Reactions: Whitehead, J. C . , Ed.; Reidel: Dordrecht, 1988, p. 25. (40) Schechter, 1.; Prisant, M.: Levine, R. D. J . Phys. Chem. 1987, 91. 5472. (41) Evans. G . T.:She, R. S . C.; Bernstein, R. B. J . Chem. Phys. 1986, 84, 2204. (42) Janssen, M. H. M.: Stolte, S . J . Phys. Chem. 1987, 91, 5480. (43) Evans. G . T.: She. R . S. C.; Bernstein. R. B. J . Chem. Phys. 1985, 82. 2258. (44) Clary, D.C Mol. Phys. 1984, 53. I .

EO(7)

IXH+

X+HD-xXD+H ~

~

~~~~~~~~~~~~~~~~~~

~~~~~

(45) Connor, J. N. L.; Jakubetz, W .In Selectiuity in Chemical Reactions; Whitehead, J . C . , Ed.: Kluwer: Dordrecht, 1987. Aoiz, F. J.; Candela, V.;

Herrero, V. J.; Saez Rabanos, V. Chem. Phys. Lett., in press. (46) Pelzer, H.; Wigner, E. 2.Phys. Chem. 1932, ISB, 445. Johnson, H. S. Gas Phase Reaction Rate Theory; Ronald Press: New York, 1966.

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The Journal of Physical Chemistry, Vol. 94, No. 26, 1990 8875 Kincmxic Male1

Classical Trajectories

"1

cos(a)

P H t HD + H z + D H +HD+HD+ H

Figure 5. Dependence of the reaction cross section on the attack angle (at the barrier) for the reaction of H atoms with either end of H D a t ET = 0.6 eV. Computed by using exact classical trajectories (left side panels) and by using the kinematic model where reaction occurs for those (straight line) trajectories with enough energy to surmount the barrier (right side panels). The advantage of using the bond angle a (see figure) is that the height of the barrier vs a is the same for both ends of the molecule. To within statistical noise, the results show no isotope effect. With the angle y defined with respect to the center of mass, the cone of acceptance about the D atom is widerJ3 for purely kinematical reason^.'^

where X can be any one of a number of possible atoms (e.g., H,17 0,'" F,11*48 Cl,49*50 etc.). We have already drawn attention3' to the implications of the energetic factor in ( 2 ) regarding this class of reactions. For H D the potential as seen by the X atom must be symmetric with respect to the center-of-charge (Le., the geometrical center) of HD. Hence, if a is the attack angle measured in a symmetric fashion,).(a must be the same for both ends. Trajectory computations, Figure 5, verify that this is the case and thereby provide an absolute (Le., computation-free) test of the model. Yet, for a nonrotating H D molecule, the overall (Le., integral over y) reaction cross section is larger for attack on the D end of the molecule. To treat the two ends on a common basis we define the angle of attack y with respect to the center-of-mass of the molecule. This is nearer to the D atom, with the result that the cone of acceptance is wider about the D end, Figure 5. We shall discuss the rotating HD molecule in section V and the general question of the mass effect in section VII. The simplest kinematic model can be refined by taking the radial dependence of the location of the barrier to be ellipsoidal rather than ~ p h e r i c a l . ~We ' ~ ~have ~ preferred to improve on the spherical barrier approximation by taking the location of the barrier as determined by a realistic potential energy function. It is then not possible to obtain analytic results, but the Monte Carlo averaging over initial conditions4' can at the same time handle the general barrier location. Kinematic models have another advantage that we shall not discuss in detail. it is that one can also use them to discuss the stereospecificity of the products of the reaction. In particular, many of the observations on the polarization of reaction products Can be readily rationalized on purely kinematic grounds.s3 0+,51952

IV. Dynamics of Reorientation The reorientation of the reagents, due to their anisotropic interaction, en route to the barrier cannot always be neglected. (47) Tsukiyama, K.; Katz, B.; Bersohn, R. J . Chem. Phys. 1985,83, 2889. (48) Mayne, H. R. J . Phys. Chem. 1988, 92, 6289. (49) Persky, A.; Klein, F. S.J . Chem. Phys. 1967, 44, 3617. ( 5 0 ) Persky, A.; Rubin, R.; Broida, M. J . Chem. Phys. 1983, 79, 3279. (51) Sunderlin, L. S.;Armentrout, P. B. Chem. Phys. Leu. 1990, 167, 188. (52) Dateo, C. E.; Clary, D. C. J . Chem. SOC.,Faraday, Trans. 2 1989, 85, 1685. (53) Schechter, 1.; Levine, R. D. Faraday Discuss. Chem. SOC.1987.84, 250; J . Chem. Soc., Faraday Trans. 2 1989, 2, 1287.

While this effect can enhance the reactive asymmetry of the moleculess4 and not necessarily spoil an initially selected orientation, it is still desirable to have a simple understanding of its importance. A particular aspect under this heading is the effect of the radial dependence of the location of the barrier to reaction. Realistic potential energy surfaces show that for different attack angles, the radial location of the saddle point can change, sometimes quite significantly so. As a result, just before the barrier, the potential can be quite anisotropic and may either focus or defocus the incoming trajectories into the cone of acceptance. Of course, reorientation is fully accounted for (at the level of classical mechanics) in any 3-D trajectory computation. Our purpose here is to discuss a simpler, albeit approximate, approach to the problem. In the simple kinematic model the approach motion is uncoupled from all other degrees of freedom. Mathematically it is a onedimensional model. In the present section we consider a mathematical two-dimensional model where the two coupled variables are the relative separation R and the approach angle (with respect to the center of mass) y. We eliminate the other degrees of freedom by (i) constraining the diatomic molecule to a given interatomic distance and (ii) confining the motion to a plane so that in addition to R itself only the angle y between R and molecular axis r is allowed to vary. The angular momentum j of the diatomic molecule can be resolved as j2 = P,2

+ (sin2 y)-lP;

(3)

where 4 is the azimuthal angle (with respect to the z axis being along R). By construction of the model, P+, which is the z component of j, is conserved. This is equivalent to thej,-conserving approximation of inelastic collision theory.5s It is used here, however, for the motion en route to the barrier. For the b = 0 case these assumptions are equivalent to those introduced by Loesch.s6 The general b # 0 case is discussed in refs 57-59. Many practical aspects as well as a mathematical three-dimensional model where the BC bond length is allowed to vary are discussed in ref 60. Using mass scaled coordinates for the A + BC collision r = a-lrBc

where a = (+-BC/pBC)'/4 and the Hamiltonian ass7

R = aRA-Bc p

(4)

= (pA-BC~BC)1/2, we can write

Here, due to the use of mass scaled coordinates, the reduced mass is the same and re is the fixed BC distance. The potential energy, which is in general a function of R , r, and y, is r independent since r is held constant. The centrifugal term (2pR2)-'f2 is added, as usual, to V(R,y)to give an effective, impact-parameter dependent, potential V,rr(R,y). It is also sometimes useful to replace the angle coordinate y by a radial coordinate ?, The equation of motion, taking into account that P+, cf. (3), is conserved, is derived from the Hamiltonian p

H = (2p)-'(PR2+ Pie2)+ Verr(R,y)+ (sin2 (?Ja))-IP;

(6)

The z component of j, which contributes the last term, can be expressed in terms of the initial j since P# j , = j cos x, where x is the angle between j and the z axis. The last term of ( 6 ) can thus be written in E R cos2 X/sin2 (?,/a) and can be included as (54) Bernstein, R. B.; Levine, R. D. J . Phys. Chem. 1989, 93, 1687. ( 5 5 ) Mulloney, T.; Schatz, G. C. Chem. Phys. 1980. 45, 213. (56) Loesch, H. J. Chem. Phys. 1986, 104, 213. ( 5 7 ) Kornweitz, H.; Persky, A.; Levine, R. D. Chem. Phys. Len.1986,128, 443. ( 5 8 ) Muga, J. G.; Levine, R. D. Chem. Phys. Left. 1989, 162, 7. (59) Kornweitz, H.;Persky, A.; Schechter, 1.; Levine, R. D. Chem. Phys. Lett. 1990, 169, 489. (60) Muga, J. G.;Levine, R. D. J . Chem. Soc.. Faraday Trans. 1990.86, 1669.

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8876 The Journal of Physical Chemistry, Vol. 94, No. 26, 1990

+

TABLE I: Cross k t i o n s (A2)ComputedHfor F HD ( Y = 0, j ) at Various Collision Energies, ET,Oby the Method of Section IV E , = 4.5 E, = 6.05 E T = 8.3 HF DF H F DF DF j HF 1.483 2.664 2.381 1.213 0 0.905 1.810 1.420 1.270 1.930 2.551 I 0.905 1.483 1

3 4 5

6 a

1.081 0.930 0.861 1.188 1.194

0.855 0.478 0.214 0.163 0.113

1.276 1.181 1.206 1.426 1.678

1.514 1.024 0.666 0.434 0.440

1.464 1.489 1.477 1.690 1.916

2.136 1.715 1.451 1.238 0.955

I n kcal mol-'.

gamma (deg)

an additional contribution in Verr The Hamiltonian ( 6 ) yields equations of motion aR/at = p R i p a R / a t = -av,,/aR ai,/at = P ~ J ~ aP,e/at = P,2(cot ?/sin2 y ) / g - aver&

(7)

which can be solved (numerically) for R and y as a function of time. Starting with a given value of y,b and R,R large, each trajectory is integrated in either until it reaches the location of the barrier (which is a curve in the R - i, plane) or until it turns back and r is large again. If the initial y is not zero, x # 0 and a Monte Carlo (or a systematic) averaging over all possible x values (7 is initially uniformly distributed,@ cos 7 sin y = cos x) is performed. Note that in the Hamiltonian ( 5 ) or (6) and equations of motion (7), R and i, are Cartesian coordinates, where ?, = r,y. The potential function needs therefore to be plotted not in a polar form as in Figure 2 but in a Cartesian form as in Figure 6. It must be emphasized that as in section 111 the equations of motion (7) describe only the approach motion of the reagents, up to the barrier to reaction. They are not intended to account for the formation of products. The location of the barrier to reaction is a curve in the R-Fe plane specified by the coordinates of the saddle point on the potential energy surface. If the computed trajectory reaches that curve, reaction is said to have taken place. Note that here, no energetic criterion is required since this is built inherently into the equations of motion. A trajectory in the R-i, plane can reach the barrier if it has enough energy. Whether the trajectory will or will not reach the barrier depends, inter alia, on its initial b value. Since b is conserved, its only role is to add the (repulsive) term E T b 2 / R 2 (21R)-'12to V ( R , y ) . This is a y-independent potential which in the R-y plane has contours parallel to the y axis. The advantage of the present approach over that of section 111 is that here a reorientation of the molecule due to the potential is allowed. This is reflected in the trajectory not being a straight line in the R-i, plane. If we neglect the -aVerr/ayterm in (7), the equations of motion decouple and reorientation is not possible. We discuss the role of -aV/dy in section V. For rotating reagents, further discussed in section VI, we need to average over the distribution of initial P , values. An extensive discussion of this point is given in ref 60. We have applied this approach to a variety of systems in order to examine the steric requirements in the entrance channel. Results for H + H2 collision are discussed in refs 58 and 60. Results for the F + H D ( v = 0, j ) reaction at various collision These are in good agreement with energies are given in Table exact trajectory computations.Il We defer the discussion of the results f o r j # 0 to section VI. V. Intermezzo on the Shape of a Molecule We are now ready to discuss the shape of a molecule with a realistic degree of detail. The technical tools are the equations of motion (7) and the potential V ( R , y )shown in Figure 6. The (61) Kornweitz, H., unpublished results.

Figure 6. Two possible LEPS type potentials for the 0 + HBr collision. Adapted from ref 73. Trajectory computations on these surfaces are reported in refs 69 and 75. Shown are equipotential contours OF V ( R , y ) spaced 2 kcal mol-' apart in a Cartesian R, y plot. (Recall that in the Hamiltonian (6), y appears as a radial and not as an angular coordinate.) The preferred direction of approach is collinear, shown as a dashed line at y = 0. The location of the barrier to reaction is the solid hemispherical

line that clearly crosses the equipotential contours as y varies. The solid arrows indicate the direction of the force, -aV/8y, on the y motion. This force tends to orient trajectories toward the collinear for the oblate surface I1 and away from the collinear for the prolate surface 1. equations and the potential govern the "physical" shape of the molecule as seen by the approaching atom. Each equipotential contour of the V(R,y) plot in Figure 6 shows how close the atom, at a given collision energy E, can get to the molecule. From certain directions, a closer approach is possible. We shall refer to the ABC molecule as oblate if from the y = 180' direction, A can get nearer to BC as compared to the y = 90' direction, and prolate if the opposite is true. The chemical shape is determined by the location of the barrier to reaction in the R - y plane. It is shown as a thick line in Figure 6. The location of the barrier is not a potential energy contour for the reason discussed in section 11: the barrier height varies with y . Only in the simplest of all models, the so-called painted sphere limit,62are the physical and chemical shapes equivalent (being both spheres of the same radius). In this model, the barrier height does not vary with approach angle. All indications, whether based on ab initio computed or semiempirical potentials63 or upon inversion of experimental data64-65are that the barrier height does depend on angle and therefore that the chemical shape is distinct from the physical one. Once we accept the conclusion that the height of the barrier to reaction will depend on the orientation, it follows inevitably that the chemical shape of the molecule is not the same as the physical one. The chemical shape, being the location of the barrier, is not a potential energy contour, while the physical shape (being determined by the closest approach at the energy E ) , is. A detailed probe of the differences between the two shapes is provided by rotationally excited reagents, section VI. Before we turn to it, we comment on the reorientation effect. Figure 6 contrasts two empirical LEPS-type potentials that have been used to compute trajectories for the 0 + HBr rea~tion.~"' Surface 1 is prolate, while I1 is oblate. Also shown therein is the direction of the force, -dV/ay, on the y motion for trajectories with y = 0. The pictorial correlation can also be justified on analytical grounds. By its very nature, a prolate type potential must have a higher potential at y = 0 than at either side, and vice versa for an oblate potential. Consider how a trajectory where (62) Beuhler, Jr., R. J.; Bernstein, R. B. J . Chem. Phys. 1%9,51, 5305. (63) Schechter, 1.; Levine, R. D.; Bernstein, R. B. J . Phys. Chem. 1987, 91, 5466. (64) Bernstein, R. 8.; J . Chem. Phys. 1985, 82, 3656. (65) Loesch, H. J.; Hoffmeister, M. J . Chem. Soc., Faraday Tram. 2 1989, 85, 1249. (66) McKendrick, K. G.; Rakestraw, D. J.; Zhang, R.; Zare, R. N . J . Phys. Chem. 1988, 92, 5530. (67) Broida, M.; Tamir, M.; Persky. A. Chem. Phys. 1986, I IO, 83.

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The Journal of Physical Chemistry, Vol. 94, No. 26, 1990 8877 I

I

I

I

I

I

t

0

O*HCI-OH-CI

0

o.Dcl--ao.cl :10kcol/mol

SURFACE1

O2

d

O.0

I

'r

--

/ 1 /

I

4

5

8

h

%

I

SURFACE TI

I

Figure 8. Reaction cross section vs j for 0 + HCI (u = 0, j ) and for 0 + DCI ( u = 0, j ) on surfaces I and 11, respectively. Adapted from ref 59. The differences in the initial decline with j on surface I1 can be understood by using eq 9.

In certain situations, the anisotropy of the long-range physical forces may be of a character different from that of the shorter range chemical forces. The SLTH surface for H3is one such example.60 This surface also becomes remarkably oblate upon vibrational excitation of H2.28*60 Under such circumstances, actual integration of eqs 7 must replace the more qualitative interpretation. Even a numerical integration will be physically more transparent than a full classical trajectory simulation.

VI. Role of Reagent Rotation A question intimately related to the steric requirements of reactions is the effect of initial rotation of the reagents on the reactivity. There is a tremendous literature on this subject (e.g., refs 39 and 71 for earlier reviews). It may well be that some of the conflicting conclusions in the literature are due to there being opposite ways in which the initial rotation contributes and that their relative importance depends also on the initial translational (and also on the vibrational) energy. The simplest generalization to be discussed is that at low collision energies on an oblate potential, initial reagent rotation tends to disrupt entry into the cone of acceptance. At higher translation or for a prolate potential, reagent rotation tends to enhance the probability for crossing the barrier. It is interesting to note that for initially rotating reagents, the role of the oblate and prolate surfaces is reversed: An oblate surface tends to accept nonrotating reagents with a wider range of initial orientations, so that the reaction cross section for randomly oriented reagents is larger than for an otherwise equivalent prolate surface. The large cross section for an oblate potential markedly declines with increasing initial j,59*72-76 Figure 8. The interpretation of the role of reagent rotation is complicated because even in the absence of any reorientation effects, j 2 has two components, cf. eq 3 . The component P+ in the direction of the initial relative velocity provides an additional centrifugal barrier, E R cos2 X/sin2 y. The component which changes y, Pi,, is the one acted upon by the anisotropy of the potential. Fur-

(68) Johnson,,G. W.;Kornweitz, H.; Schechter, 1.; Persky, A,; Katz, B.; Bersohn, R.; Levine, R. D. J . Chem. Phys., to be published. (69) Kornweitz, H.; Persky, A. Chem. Phys. 1989, 133, 415. (70) Loesch, H . J.; Remscheid, A., to be published.

(71) Sathyatmurthy, N . Chem. Reu. 1983, 83, 601. (72) Loesch, H . J . Chem. Phys. 1987, 112. 85. (73) Kornweitz, H.; Persky, A.; Levine, R. D. J . Phys. Chem., in press. (74) Broida, M.; Persky, A. J . Chem. Phys. 1984, 81, 4352. (75) Menendez, M.; Baiiares, L.; Gonz2les Ureiia, A,; Whitehead, J. C. J . Chem. SOC.Faraday Trans. 2 1988, 84, 1765. (76)Schechter, 1.; Levine, R. D., to be published.

Levine

8878 The Journal of Physical Chemistry, Vol. 94, No. 26, 1990

-

2.03

0”

gomma (deg)

Figure 9. Potential V(R,.I)in a Cartesian plot for the D end of F + DH. The equipotential contours are spaced 2 kcal mol-! apart. The location of the barrier to reaction is shown as a solid line. Adapted from ref 73.

thermore, the increased rate of molecular rotation as j increases makes reorientation effects more significant. The purely kinematic limit of section Ill is still, however, useful for delineating the main effects. As a first example we consider the trends evident in the results for the F H D ( v = 0, j ) FD + H reaction shown in Table I. Clearly the cross section to produce FD is large for H D ( v = 0. j = 0) but drops with increasing j . At higher collision energies the drop is more moderate; the F + DH FD + H reaction is similar to the 0 + HCI O H + CI reaction as computed on surface 11; cf. Figure 8. This is by far not an accident as both surface 11 and the Muckerman VI1 surface for F DH are strongly oblate,73Figure 9. For the discussion of the role of reagent rotation it is convenient to examine the kinematic limit in the R-y plane of section IV. F o r j = 0 the trajectories are straight lines parallel to the r axis since y = 0. (The value of y at the barrier is thus equal to its precollision value.) For j # 0, the trajectories are no longer parallel to the R axis since y is changing even in the kinematic limit when no reorientation is possible. The value of y at the barrier is then shifted with respect to its initial value.57 Figure 9 shows the region of the potential for an F atom approach to the D end of the HD molecule. This potential (a LEPS type known as Muckerman” V) is remarkably oblate.73 If H D is intially rotating, the P, component, (cf. eq 3) of j carries the trajectory parallel to the y axis. Unless the radial velocity, PR, is high enough, the trajectory will fail to enter the narrow valley leading to the cone of acceptance. Let A y be the angular range of the valley; A y 7/10 for Figure 8. Let A d be the depth in R of the barrier below a spherical potential contour of radius d. Ad 0.4 A for Figure 9. Then unless (d R/d t) / (dPe/dt ) > Ad / reAy (8)

+

-

-

-

+

-

-

reaction is not possible.59 Converting to energy, this requires the ratio of translational to rotational energies to satisfy

(ET/ER)> (PA-BC/~BC)(A~/AT)’ (9) where I is the BC moment of inertia and p A -is~the reduced mass for the A-BC collision. For the present example, the right-hand side of (9) has the value -9. At ET = 4.5 kcal mo1-I (cf. Table I), a rotational excitation in t h e j motion in excess of ca. 175 cm-’ should suffice to fully hinder the reaction. Note that some of the reagent rotational excitation may be not in P, but in P,, cf. eq 3, and so the nominal E , needs to exceed 175 cm-I. Also the rotation near the barrier is far from free, so that one cannot put E R = Bj(j + I ) . Still, the prediction of (9) is certainly consistent with all known trends. These effects are seen also in exact trajectory computations.” We agree with the original interpretation that the effect is due to the center of mass of HD being nearer to the D end. It is true that as a result, when an isolated HD molecule rotates, the radius of gyration of H about the center of mass is twice that of D. However, it is not quite the case that in a rotating HD molecule, the H atom screens the D atom. The reason is that the relevant radius is not from the H or the D atoms to the HD center of mass but from the attacking atom to the HD center of mass. Take as an example a collinear approach. The larger the attacking atom,

the more nearly the same is the radius to the center of mass for attack at either end. The effect of H D rotation should then be most for H + HD and least, say, for CI + HD.49950It is more reasonable, to us, to regard the hindrance as due to the rotation of the repulsive part of the oblate potential, whose range exceeds that of either the D or the H atoms rather than that of the H end of the molecule. An oblate potential, which for nonrotating reagents tends to pull trajectories into the cone of acceptance, tends for rotating reagents to constrict the access to the cone. A prolate potential tends to disorient incoming trajectories and, as we shall now discuss, for rotating reagents is able to use part of the rotational energy to overcome the barrier. To understand the beneficial role of reagent rotation, we return to our starting point: trajectories are reactive when they can cross the barrier. The new feature here is that, as already discussed, the location of the barrier (Le., the chemical shape) is typically not a sphere around the center of mass. (Rather, it much more resembles a sphere about the attacked atom as in a space-filling model; cf. Figures 2, 6, and 9). The velocity normal to the barrier is thus made up of two components, R along the R axis and 4 along the y axis. It is the resultant of these two components that is relevant. The relative weight of the two velocities is determined by the direction of the normal to the barrier. If the normal is only slightly off the direction of R (Le., if the barrier is very nearly a sphere about the center of mass), the role of rotation will only be slight.’6 If the location of the barrier is very much y-dependent, rotation will have a marked effect. The beneficial role of rotation is the norm for all trajectories that enter the cone of acceptance, whether the potential is oblate or prolate. For an oblate potential, as already discussed, reagent rotation can inhibit entry into the cone. To conclude, the dependence of the reaction cross section on reagent rotational excitation probes both the physical and chemical shapes of the molecule. The decline of reactivity with increasing rotation is evidence for an oblate physical shape. The increase of the reactivity with increasing rotation is measured by the anisotropy in the location of the chemical barrier to reaction. VII. The Mass Effect Varying the masses can lead to distinct dynamical features.77 Here we consider the steric requirements in particular and derive a quantitative characterization of oblate and prolate potentials as a byproduct. Let y be, as before, the angle between R and the BC bond so that -1 5 cos y 5 1 and cos y -1 for a collinear attack of A on the B end. An oblate potential is one where the equicontours of the potential occur at lower R values near the B end; cf. Figures 5 and 8. In other words, as cos y decreases toward -1, the potential decreases or dV/d cos y is positive for R values in the entrance to the barrier region and for cos y -1. Or as shown pictorially in Figure 5, -aV/dy is positive for an oblate potential. For a prolate potential, dy/d cos y is negative. If we use the familiar Legendre series expansion for the longer range potentialI6 V ( R , y ) = V,(R) + V,(R)PI(COS7) + VZ(R)P,(COS7) + ...

-

-

then, to leading order, an oblate/prolate potential is one where V , ( R )is positive/negative in the region of entrance to the barrier. The potential V(R,y) is not invariant upon isotopic substitut i ~ n . ’ ~The , ~ ~reason is that R is the distance to the center of mass (cm) of BC and the location of the cm will change when the mass of B is changed. (What is invariant in the Born-Oppenheimer approximation is the potential as a function of the three interatomic distances.) Say that for the A + B’C system the potential is spherical and depends only on R’, the A to B’C cm distance. If we change the mass of B’ to that of B, the cm will move by a distance of 6, ( 6 / r E ) (77) Polanyi, J . C. Furaduy Discuss. 1973, 55, 389. (78) Kreek, H.; LeRoy, R. J . J . Chem. Phys. 1975, 63, 338.

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The Journal of Physical Chemistry, Vol. 94, No. 26, I990 8879

nn

m ((j’-j).(k’-k))

(j’k)

Ob

-0’5

0s

m

m

Ib

cosw

Figure 10. Orientation dependence of the reaction cross section for H

+ D2(u) for u = 0, 1, 2.

Adapted from ref 33.

7.00

-

((j’-j).(k‘-k))

(i’.k)

Figure 12. j’.k and (i’ - j).(k’ - k ) correlations in the H + H2 (u = 0, j ) reaction at ET = 0.9 eV for j = 1, 2 (lower and’upper row). Shown is a histogram of the distribution of the scalar product of the unit vectors in the range -1 to I . Note the preferred direction of j’ is perpendicular to k’ as can be readily understood on purely kinematic grounds“*s3if the reaction occurs at a narrow range of R values. Such and higher correlations provide a sensitive probea6of the dynamics.

5.00

m

z

3.00

tend to produce a more oblate potential ( V I > 0). Indeed, VI can become large enough that a well can be created in the region in front of the barrier, Figure 1 I . This is the same well responsible for the resonances in H H,;cf. refs 58, 60, and 80. The same effect also serves to lower the barrier in the collinear direction so that for vibrationally excited BC (i) at each y a wider range of b values is reactive (cf. eq 1 ) and (ii) the maximal ?r-y for which (1) holds is now higher. It is to be emphasized that the angle y discussed here is for the orientation at the barrier. For the asymptotic angle y, its reactive range will be even higher due to the more oblate character of the potential for stretched BC.

+

1 .w

I

1.0

I

-30.0

I

I

30.0

90.0

’

Gamma(deg)

Figure 11. Cartesian plot of V ( R , y )for H + H2 for a stretched H2 bond. Adapted from ref 67. Note the well in front of the barrier for reaction.

+

= ( M B- MBt)Mc/(MB + M c ) ( M v M c ) , toward the B end. If the A B’C potential is Uo(R’) V ( R , y ) ,then the coefficients in the expansion (1 0) are, to order 6, given by v,(R)= u ~ ( R ) v,(R) = - s a u o / a R v,(R)= o ( I I )

+

Hence if B’ is replaced by a heavier isotope B so that 6 is positive and since en route to the barrier -aVo/aR is positive, A + BC is oblate and vice versa if B is lighter than B’. These conclusions are essentially unchanged to higher order in 6. Similarly, if U is a function not only of R’but also of y, V(R,y) is more oblate than U(R’,y)if B is heavier than B’ and less oblate if it is lighter. VIII. Role of Reagent Vibration Steric considerations provide an explanation for the enhancement effect of reagent vibrational excitation for such (typically, nearly thermoneutral) reactions that do not have a late barrier.28*33*79 The H + H2(v) reaction, with its symmetric barrier, is a typical example. The basic observation, Figure IO, is that the cone of acceptance opens up upon vibrational excitation. There are essentially two effects that can be distinguished and traced to features of the potential energy surface. The first is that the range of orientations that contribute to reaction is higher. The second is that for each orientation the reactivity (Le., du/d cos y) is higher. Both are clearly evident in Figure IO. It might appear that stretching the BC molecule should make the potential more prolate and that a sideways approach would be easier. For large stretches that may well be the case. But excitation of H2 (or HC1,79etc.) from u = 0 to u = 1 or 2 results only in a small fractional elongation of the bond. The discussion of section VI1 therefore applies since I

avi/arBc = l i d COS Y COS

(12)

where roBCis the equilibrium bond distance and a is the ABC angle. At fixed R and y, extending the BC distance lowers the AB distance, but as long as rAB > rBc,the derivative is positive. Hence, en route to the barrier small extensions of the BC distance (79)Schechter, I.; Levine, R. D. J . Pfiys. Cfiem. 1989, 93, 7973.

IX. Concluding Remarks The same potential energy function (regarded as a function of the three interatomic distances) determines both the physical and the chemical characteristics. In the Born-Oppenheimer approximation it is also invariant to mass change. It is the more fundamental concept than that of a shape. A function of even only three variables is already, however, capable of exhibiting a considerable variety of topographical features that our lack of plotting abilities in 4D prevents us from contemplating. It is inevitable therefore to think of special features of this function. Space-filling models do this for the physical shape by restricting the function (Le., the potential) to having two possible values, infinity (inside) and zero (outside). The orientation dependence of the height of the barrier to reaction prevents us from simply painting a “target” area on the space-filling model. The other extreme is to take the shape to be a sphere, a function of only one variable. It is then easy to plot the barrier height as a function of angle. This, however, shortchanges us on the effects of the physical shape (reorientation, hindrance for rotationally excited reagents). The representation of the potential as V ( R , y )provides a suitable midway between these two extremes. In this article we have discussed the main features of this function and of the barrier location superposed on the same plot and the implications for the dynamics. Our technical discussion was limited to the simplest possible case: the steric requirements of a gas-phase atom-exchange reaction between an atom and a diatomic molecule. There are technical points one can improve upon. Our discussion used classical dynamics so that explicit geometrical concepts can be introduced. There can be quantum effects such as tunneling near the rim of the cone of acceptance.*’ These can be taken into account by using the reactive infinite order sudden approximation.82-84 The importance of reorientation suggests that a j , (80) Wu, S. F.; Levine, R. A. Chem. Phys. Leu. 1971, 1 1 , 557. (81) Pollak, E. J . Chem. Phys. 1985,82, 106. ( 8 2 ) Khare, V.; Kouri, D. J.; Baer, M. J . Cfiem. Phys. 1979, 71, 1188. Baer, M.; Kouri, D. J.; Jellinek, J. J . Chem. Pfiys. 1984, 80, 1431. (83)Bowman, J. M.:Lee, K. T. J. J . Cfiem. Pfiys. 1980, 72, 5071.

J. Phys. Chem. 1990, 94, 8880-8885

8880

conserving approximation would do even better and at lower velocities an adiabatic rather than a sudden approach should be employed.8s There are other interesting aspects to stereochemistry.86 For example, the available evidence is that the steric requirements change in a significant fashion upon electronic excitation. Another aspect is the correlation between steric requirements and products' rotational state distributiona7 (scalar j ? , and/or p~larization'~*'~ (vector j ? , or even products' angular distribution88 and, of course, the correlation therefore of.89 Such correlations, inter alia, serve as very useful probes for the shape, Figure 12.53 Larger molecules need also be explored. Measurements in real time2' also add another dimension. Perhaps,

however, the most unexpected results are yet to come when we depart from isolated gas-phase collisions and consider the steric requirements of processes on surface or in solution. We are readily accumulating a wealth of evidence that there is much to be explored in such system^.^^^^ It is in solution or on surfaces that most of the "real" chemistry takes place. By pursuing such questions we therefore have a hope of contributing to the practice of chemistry. Acknowledgment. 1 thank Drs. 1. Schechter, H. Kornweitz, and J. G. Muga for their contributions. The pioneering experiments and insights of Profs. R. B. Bernstein and D. R. Herschbach provided much stimulating input. The Fritz Haber Research Center is supported by the Minerva Gesellschaft fur die Forschung, mbH, Munich, BRD.

(84) Baer. M. Adu. Chem. Phys. 1982, 49, 191. Jellinek, J.; Kouri, D. J. I n Theory of Chemical Reaction Dynamics; Baer, M., Ed.: CRC Press: Boca Raton, FL, 1985; Vol. 11, Chapter I . ( 8 5 ) Clary, D. C.; Henshaw, J. P. In The Theory of Chemical Reaction Dynamics; Clarry, D. C . , Ed.; Reidel: Dordrecht, Holland, 1986. (86) Bernstein, R. B.; Herschbach, D. R.; Levine, R. D. J. Phys. Chem.

Soc., Faraday Trans. 2 1989, 85, 1337.

1987, 91, 5365. (87) Persky, A.; Kornweitz, H. Chem. Phys. 1989, 130, 129. (88) Schechter, I.; Levine, R. D. J. Chem. Soc., Faraday Trans. 2 1989, 85, 1221. (89) Barnwell, J. D.; Loeser, J. G.; Herschbach, D. R. J . Phys. Chem. 1983,87, 278 I .

(91) Jacobs, D. C.; Kolasinski, K. W.: Madix, R. D.; Zare, R. N. J. Chem. Sor.. Faraday Trans. 2 1989, 85, 1325. (92) Mackay, R. S.; Curtiss, T. J.: Bernstein, R. B. Chem. Phys. Left. 1989, 164, 341. (93) Benjamin, 1.; Liu, A.; Wilson, K. R.: Levine, R. D. J. Phys. Chem. 1990, 94, 3937.

(90) Kleyn, A. W.; Kuipers, E. W.; Tenner, M. G.; Stoke, S. J. Chem.

ARTICLES Time-Resolved Resonance Raman Spectroscopic Studies of the Photosensitization of Coiiotdal Titanium Dioxide S. Umapathy, A. M. Cartner,l' A. W. Parker,lband R. E. Hester* Department of Chemistry, University of York, York YOISDD, United Kingdom (Received: December 27, 1989; In Final Form: June 25, 1990)

Resonance Raman and time-resolved resonance Raman spectroscopies have been used to study the surface interactions of substituted bipyridyl complexes of ruthenium(l1) as sensitizers with the colloidal semiconductor Ti02. It has been shown that the adsorption of ruthenium(I1) tris( [2,2'-bipyridyl]-4,4'-dicarboxylate) (RB4H) onto a colloidal TiO, surface is through the solvation layer, whereas cis-diaquaruthenium( 11) bis( [ 2,2'-bipyridyl]-4,4'-dicarboxylate) (RBDA) adsorption is via the water ligands of the complex. The transient Raman spectrum of the metal-ligand charge-transfer triplet excited state of the ethyl ester of RB4H is reported. Analysis of the spectrum provides conclusive evidence for the excited electron being localized on one of the ligands. The photosensitization of Ti02 by RB4H and RBDA has also been studied by using time-resolved resonance Raman spectroscopy.

Introduction The sensitization of colloidal semiconductor photocatalysts using bipyridyl complexes of ruthenium( 11) has been widely studied due to their potential importance in solar energy conversion.2-* The ( I ) (a) On leave from Department of Chemistry, University of Waikato, Hamilton, New Zealand. (b) Laser Support Facility, Rutherford Appleton Laboratory, Chilton, Didcot, OX1 1 OQX,United Kingdom. (2) Rotzinger. F. P.; Munavalli, S.; Comte, P.; Hurst, J. K.; Gratzel, M.; Pern, F.: Frank, A. J. J. Am. Chem. Soc. 1987, 109, 6619. (3) Vlachopoulos. N.: Liska, P.: Augustynski, J.: Gratzel, M. J. Am. Chem.

SOC.1988, 110, 1216. (4) Dabestani, R.; Bard, A. J.; Campion, A.; Fox, M. A,; Mallouk, T. K.; Webben, S. E.; White, J . M. J . Phys. Chem. 1988, 92, 1872. ( 5 ) Furlong, D. N.; Wells, D.; Sasse, W. H. F. J . Phys. Chem. 1986, 90, 1107. (6) Desilvestro, J.; Gratzel, M.; Kavan, L.; Augustynski, J. J. Am. Chem. Sor. 1985. 107. 2988.

sensitization process involves (a) adsorption of the ruthenium complex onto the colloidal surface, (b) excitation of the adsorbed complex to a higher electronic state by exposure to light, and (c) electron transfer from the excited state to the conduction band of the semiconductor. The efficiency of this electron-transfer process has been reported to be between 25% and 100% for a monochromatic light source, depending on nature of the substituent groups attached to the bipyridyl ligands of the c o m p l e x e ~ . ~A~ ' ~ ~~

~

~

~

~

~

(7) Borgarello, E.; Kiwi, J.: Pelizzetti, E.; Visca. M.; Gratzel, M. Nature 1981, 289, 158.

(8) Anderson, S.; Constable, E. C.; Dare-Edwards, M. P.; G d e n o u g h , J . 8.; Hamnett, A.; Seddon, K. R.: Wright, R. D.Narure 1979, 280, 571. (9) Dare-Edwards, M. P.; G d e n o u g h , J. B.; Hamnett, A.; Seddon, K. R.; Wright, R. D. Faraday Discuss. Chem. SOC.1980, 70, 285. (IO) Liska, P.; Vlachopoulos, N.; Nazeeruddin. M. K.; Comte. P.: Gratzel. M. Personal communication, 1989.

0022-3654/90/2094-8880$02.50/0 0 1990 American Chemical Society

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